Re-introduce build-in type code for core types

binding_generator.py

@@ -19,6 +19,9 @@ def print_file_list(api_filepath, output_dir, headers=False, sources=False):
         if is_pod_type(builtin_class["name"]):
             continue
 
+        if is_included_type(builtin_class["name"]):
+            continue
+
         header_filename = include_gen_folder / "variant" / (camel_to_snake(builtin_class["name"]) + ".hpp")
         source_filename = source_gen_folder / "variant" / (camel_to_snake(builtin_class["name"]) + ".cpp")
         if headers:
@@ -112,6 +115,8 @@ def generate_builtin_bindings(api, output_dir, build_config):
     for builtin_api in api["builtin_classes"]:
         if is_pod_type(builtin_api["name"]):
             continue
+        if is_included_type(builtin_api["name"]):
+            continue
 
         size = builtin_sizes[builtin_api["name"]]
 
@@ -413,6 +418,19 @@ def generate_builtin_class_header(builtin_api, size, used_classes, fully_used_cl
         result.append("bool operator!=(const wchar_t *p_str) const;")
         result.append("bool operator!=(const char16_t *p_str) const;")
         result.append("bool operator!=(const char32_t *p_str) const;")
+        result.append(f'\tconst char32_t &operator[](int p_index) const;')
+        result.append(f'\tchar32_t &operator[](int p_index);')
+
+    if is_packed_array(class_name):
+        return_type = correct_type(builtin_api["indexing_return_type"])
+        if class_name == "PackedByteArray":
+            return_type = 'uint8_t'
+        elif class_name == "PackedInt32Array":
+            return_type = 'int32_t'
+        elif class_name == "PackedFloat32Array":
+            return_type = 'float'
+        result.append(f'\tconst ' + return_type + f' &operator[](int p_index) const;')
+        result.append(f'\t' + return_type + f' &operator[](int p_index);')
 
     result.append("};")
 
@@ -430,7 +448,7 @@ def generate_builtin_class_header(builtin_api, size, used_classes, fully_used_cl
         result.append("String operator+(const wchar_t *p_chr, const String &p_str);")
         result.append("String operator+(const char16_t *p_chr, const String &p_str);")
         result.append("String operator+(const char32_t *p_chr, const String &p_str);")
-
+    
     result.append("")
     result.append("} // namespace godot")
 
@@ -1497,6 +1515,42 @@ def is_pod_type(type_name):
         "uint64_t",
     ]
 
+def is_included_type(type_name):
+    """
+    Those are types for which we already have a class file implemented.
+    """
+    return type_name in [
+        "AABB",
+        "Basis",
+        "Color",
+        "Plane",
+        "Quaternion",
+        "Rect2",
+        "Rect2i",
+        "Transform2D",
+        "Transform3D",
+        "Vector2",
+        "Vector2i",
+        "Vector3",
+        "Vector3i",
+    ]
+
+def is_packed_array(type_name):
+    """
+    Those are types for which we add our extra packed array functions.
+    """
+    return type_name in [
+        "PackedByteArray",
+        "PackedColorArray",
+        "PackedFloat32Array",
+        "PackedFloat64Array",
+        "PackedInt32Array",
+        "PackedInt64Array",
+        "PackedStringArray",
+        "PackedVector2Array",
+        "PackedVector3Array",
+    ]
+
 
 def is_enum(type_name):
     return type_name.startswith("enum::")

godot-headers-temp/godot/gdnative_interface.h

@@ -387,6 +387,32 @@ typedef struct {
 	char32_t *(*string_operator_index)(GDNativeStringPtr p_self, GDNativeInt p_index);
 	const char32_t *(*string_operator_index_const)(const GDNativeStringPtr p_self, GDNativeInt p_index);
 
+	/* Packed array functions */
+
+	uint8_t *(*packed_byte_array_operator_index)(GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedByteArray
+	const uint8_t *(*packed_byte_array_operator_index_const)(const GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedByteArray
+
+	GDNativeTypePtr (*packed_color_array_operator_index)(GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedColorArray, returns Color ptr
+	GDNativeTypePtr (*packed_color_array_operator_index_const)(const GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedColorArray, returns Color ptr
+
+	float *(*packed_float32_array_operator_index)(GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedFloat32Array
+	const float *(*packed_float32_array_operator_index_const)(const GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedFloat32Array
+	double *(*packed_float64_array_operator_index)(GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedFloat64Array
+	const double *(*packed_float64_array_operator_index_const)(const GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedFloat64Array
+
+	int32_t *(*packed_int32_array_operator_index)(GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedInt32Array
+	const int32_t *(*packed_int32_array_operator_index_const)(const GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedInt32Array
+	int64_t *(*packed_int64_array_operator_index)(GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedInt32Array
+	const int64_t *(*packed_int64_array_operator_index_const)(const GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedInt32Array
+
+	GDNativeStringPtr (*packed_string_array_operator_index)(GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedStringArray
+	GDNativeStringPtr (*packed_string_array_operator_index_const)(const GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedStringArray
+
+	GDNativeTypePtr (*packed_vector2_array_operator_index)(GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedVector2Array, returns Vector2 ptr
+	GDNativeTypePtr (*packed_vector2_array_operator_index_const)(const GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedVector2Array, returns Vector2 ptr
+	GDNativeTypePtr (*packed_vector3_array_operator_index)(GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedVector3Array, returns Vector3 ptr
+	GDNativeTypePtr (*packed_vector3_array_operator_index_const)(const GDNativeTypePtr p_self, GDNativeInt p_index); // p_self should be a PackedVector3Array, returns Vector3 ptr
+
 	/* OBJECT */
 
 	void (*object_method_bind_call)(const GDNativeMethodBindPtr p_method_bind, GDNativeObjectPtr p_instance, const GDNativeVariantPtr *p_args, GDNativeInt p_arg_count, GDNativeVariantPtr r_ret, GDNativeCallError *r_error);

include/godot_cpp/core/defs.hpp

@@ -92,6 +92,23 @@
 #define unlikely(x) x
 #endif
 
+#ifdef REAL_T_IS_DOUBLE
+typedef double real_t;
+#else
+typedef float real_t;
+#endif
+
+// Generic swap template.
+#ifndef SWAP
+#define SWAP(m_x, m_y) __swap_tmpl((m_x), (m_y))
+template <class T>
+inline void __swap_tmpl(T &x, T &y) {
+	T aux = x;
+	x = y;
+	y = aux;
+}
+#endif // SWAP
+
 // Home-made index sequence trick, so it can be used everywhere without the costly include of std::tuple.
 // https://stackoverflow.com/questions/15014096/c-index-of-type-during-variadic-template-expansion
 template <size_t... Is>

include/godot_cpp/core/math.hpp

@@ -0,0 +1,424 @@
+#ifndef GODOT_MATH_H
+#define GODOT_MATH_H
+
+#include <godot_cpp/core/defs.hpp>
+
+#include <godot/gdnative_interface.h>
+
+#include <cmath>
+
+namespace godot {
+namespace Math {
+
+// This epsilon should match the one used by Godot for consistency.
+// Using `f` when `real_t` is float.
+#define CMP_EPSILON 0.00001f
+#define CMP_EPSILON2 (CMP_EPSILON * CMP_EPSILON)
+
+// This epsilon is for values related to a unit size (scalar or vector len).
+#ifdef PRECISE_MATH_CHECKS
+#define UNIT_EPSILON 0.00001
+#else
+// Tolerate some more floating point error normally.
+#define UNIT_EPSILON 0.001
+#endif
+
+#define Math_SQRT12 0.7071067811865475244008443621048490
+#define Math_SQRT2 1.4142135623730950488016887242
+#define Math_LN2 0.6931471805599453094172321215
+#define Math_PI 3.1415926535897932384626433833
+#define Math_TAU 6.2831853071795864769252867666
+#define Math_E 2.7182818284590452353602874714
+#define Math_INF INFINITY
+#define Math_NAN NAN
+
+// Functions reproduced as in Godot's source code `math_funcs.h`.
+// Some are overloads to automatically support changing real_t into either double or float in the way Godot does.
+
+inline double fmod(double p_x, double p_y) {
+	return ::fmod(p_x, p_y);
+}
+inline float fmod(float p_x, float p_y) {
+	return ::fmodf(p_x, p_y);
+}
+
+inline double fposmod(double p_x, double p_y) {
+	double value = Math::fmod(p_x, p_y);
+	if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) {
+		value += p_y;
+	}
+	value += 0.0;
+	return value;
+}
+inline float fposmod(float p_x, float p_y) {
+	float value = Math::fmod(p_x, p_y);
+	if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) {
+		value += p_y;
+	}
+	value += 0.0;
+	return value;
+}
+
+inline float fposmodp(float p_x, float p_y) {
+	float value = Math::fmod(p_x, p_y);
+	if (value < 0) {
+		value += p_y;
+	}
+	value += 0.0;
+	return value;
+}
+inline double fposmodp(double p_x, double p_y) {
+	double value = Math::fmod(p_x, p_y);
+	if (value < 0) {
+		value += p_y;
+	}
+	value += 0.0;
+	return value;
+}
+
+inline double floor(double p_x) {
+	return ::floor(p_x);
+}
+inline float floor(float p_x) {
+	return ::floorf(p_x);
+}
+
+inline double ceil(double p_x) {
+	return ::ceil(p_x);
+}
+inline float ceil(float p_x) {
+	return ::ceilf(p_x);
+}
+
+inline double exp(double p_x) {
+	return ::exp(p_x);
+}
+inline float exp(float p_x) {
+	return ::expf(p_x);
+}
+
+inline double sin(double p_x) {
+	return ::sin(p_x);
+}
+inline float sin(float p_x) {
+	return ::sinf(p_x);
+}
+
+inline double cos(double p_x) {
+	return ::cos(p_x);
+}
+inline float cos(float p_x) {
+	return ::cosf(p_x);
+}
+
+inline double tan(double p_x) {
+	return ::tan(p_x);
+}
+inline float tan(float p_x) {
+	return ::tanf(p_x);
+}
+
+inline double sinh(double p_x) {
+	return ::sinh(p_x);
+}
+inline float sinh(float p_x) {
+	return ::sinhf(p_x);
+}
+
+inline float sinc(float p_x) {
+	return p_x == 0 ? 1 : ::sin(p_x) / p_x;
+}
+inline double sinc(double p_x) {
+	return p_x == 0 ? 1 : ::sin(p_x) / p_x;
+}
+
+inline float sincn(float p_x) {
+	return sinc(Math_PI * p_x);
+}
+inline double sincn(double p_x) {
+	return sinc(Math_PI * p_x);
+}
+
+inline double cosh(double p_x) {
+	return ::cosh(p_x);
+}
+inline float cosh(float p_x) {
+	return ::coshf(p_x);
+}
+
+inline double tanh(double p_x) {
+	return ::tanh(p_x);
+}
+inline float tanh(float p_x) {
+	return ::tanhf(p_x);
+}
+
+inline double asin(double p_x) {
+	return ::asin(p_x);
+}
+inline float asin(float p_x) {
+	return ::asinf(p_x);
+}
+
+inline double acos(double p_x) {
+	return ::acos(p_x);
+}
+inline float acos(float p_x) {
+	return ::acosf(p_x);
+}
+
+inline double atan(double p_x) {
+	return ::atan(p_x);
+}
+inline float atan(float p_x) {
+	return ::atanf(p_x);
+}
+
+inline double atan2(double p_y, double p_x) {
+	return ::atan2(p_y, p_x);
+}
+inline float atan2(float p_y, float p_x) {
+	return ::atan2f(p_y, p_x);
+}
+
+inline double sqrt(double p_x) {
+	return ::sqrt(p_x);
+}
+inline float sqrt(float p_x) {
+	return ::sqrtf(p_x);
+}
+
+inline double pow(double p_x, double p_y) {
+	return ::pow(p_x, p_y);
+}
+inline float pow(float p_x, float p_y) {
+	return ::powf(p_x, p_y);
+}
+
+inline double log(double p_x) {
+	return ::log(p_x);
+}
+inline float log(float p_x) {
+	return ::logf(p_x);
+}
+
+inline float lerp(float minv, float maxv, float t) {
+	return minv + t * (maxv - minv);
+}
+inline double lerp(double minv, double maxv, double t) {
+	return minv + t * (maxv - minv);
+}
+
+inline double lerp_angle(double p_from, double p_to, double p_weight) {
+	double difference = fmod(p_to - p_from, Math_TAU);
+	double distance = fmod(2.0 * difference, Math_TAU) - difference;
+	return p_from + distance * p_weight;
+}
+inline float lerp_angle(float p_from, float p_to, float p_weight) {
+	float difference = fmod(p_to - p_from, (float)Math_TAU);
+	float distance = fmod(2.0f * difference, (float)Math_TAU) - difference;
+	return p_from + distance * p_weight;
+}
+
+template <typename T>
+inline T clamp(T x, T minv, T maxv) {
+	if (x < minv) {
+		return minv;
+	}
+	if (x > maxv) {
+		return maxv;
+	}
+	return x;
+}
+
+template <typename T>
+inline T min(T a, T b) {
+	return a < b ? a : b;
+}
+
+template <typename T>
+inline T max(T a, T b) {
+	return a > b ? a : b;
+}
+
+template <typename T>
+inline T sign(T x) {
+	return static_cast<T>(x < 0 ? -1 : 1);
+}
+
+template <typename T>
+inline T abs(T x) {
+	return std::abs(x);
+}
+
+inline double deg2rad(double p_y) {
+	return p_y * Math_PI / 180.0;
+}
+inline float deg2rad(float p_y) {
+	return p_y * static_cast<float>(Math_PI) / 180.f;
+}
+
+inline double rad2deg(double p_y) {
+	return p_y * 180.0 / Math_PI;
+}
+inline float rad2deg(float p_y) {
+	return p_y * 180.f / static_cast<float>(Math_PI);
+}
+
+inline double inverse_lerp(double p_from, double p_to, double p_value) {
+	return (p_value - p_from) / (p_to - p_from);
+}
+inline float inverse_lerp(float p_from, float p_to, float p_value) {
+	return (p_value - p_from) / (p_to - p_from);
+}
+
+inline double range_lerp(double p_value, double p_istart, double p_istop, double p_ostart, double p_ostop) {
+	return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value));
+}
+inline float range_lerp(float p_value, float p_istart, float p_istop, float p_ostart, float p_ostop) {
+	return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value));
+}
+
+inline bool is_equal_approx(real_t a, real_t b) {
+	// Check for exact equality first, required to handle "infinity" values.
+	if (a == b) {
+		return true;
+	}
+	// Then check for approximate equality.
+	real_t tolerance = CMP_EPSILON * std::abs(a);
+	if (tolerance < CMP_EPSILON) {
+		tolerance = CMP_EPSILON;
+	}
+	return std::abs(a - b) < tolerance;
+}
+
+inline bool is_equal_approx(real_t a, real_t b, real_t tolerance) {
+	// Check for exact equality first, required to handle "infinity" values.
+	if (a == b) {
+		return true;
+	}
+	// Then check for approximate equality.
+	return std::abs(a - b) < tolerance;
+}
+
+inline bool is_zero_approx(real_t s) {
+	return std::abs(s) < CMP_EPSILON;
+}
+
+inline double smoothstep(double p_from, double p_to, double p_weight) {
+	if (is_equal_approx(static_cast<real_t>(p_from), static_cast<real_t>(p_to))) {
+		return p_from;
+	}
+	double x = clamp((p_weight - p_from) / (p_to - p_from), 0.0, 1.0);
+	return x * x * (3.0 - 2.0 * x);
+}
+inline float smoothstep(float p_from, float p_to, float p_weight) {
+	if (is_equal_approx(p_from, p_to)) {
+		return p_from;
+	}
+	float x = clamp((p_weight - p_from) / (p_to - p_from), 0.0f, 1.0f);
+	return x * x * (3.0f - 2.0f * x);
+}
+
+inline double move_toward(double p_from, double p_to, double p_delta) {
+	return std::abs(p_to - p_from) <= p_delta ? p_to : p_from + sign(p_to - p_from) * p_delta;
+}
+
+inline float move_toward(float p_from, float p_to, float p_delta) {
+	return std::abs(p_to - p_from) <= p_delta ? p_to : p_from + sign(p_to - p_from) * p_delta;
+}
+
+inline double linear2db(double p_linear) {
+	return log(p_linear) * 8.6858896380650365530225783783321;
+}
+inline float linear2db(float p_linear) {
+	return log(p_linear) * 8.6858896380650365530225783783321f;
+}
+
+inline double db2linear(double p_db) {
+	return exp(p_db * 0.11512925464970228420089957273422);
+}
+inline float db2linear(float p_db) {
+	return exp(p_db * 0.11512925464970228420089957273422f);
+}
+
+inline double round(double p_val) {
+	return (p_val >= 0) ? floor(p_val + 0.5) : -floor(-p_val + 0.5);
+}
+inline float round(float p_val) {
+	return (p_val >= 0) ? floor(p_val + 0.5f) : -floor(-p_val + 0.5f);
+}
+
+inline int64_t wrapi(int64_t value, int64_t min, int64_t max) {
+	int64_t range = max - min;
+	return range == 0 ? min : min + ((((value - min) % range) + range) % range);
+}
+
+inline float wrapf(real_t value, real_t min, real_t max) {
+	const real_t range = max - min;
+	return is_zero_approx(range) ? min : value - (range * floor((value - min) / range));
+}
+
+inline float stepify(float p_value, float p_step) {
+	if (p_step != 0) {
+		p_value = floor(p_value / p_step + 0.5f) * p_step;
+	}
+	return p_value;
+}
+inline double stepify(double p_value, double p_step) {
+	if (p_step != 0) {
+		p_value = floor(p_value / p_step + 0.5) * p_step;
+	}
+	return p_value;
+}
+
+inline unsigned int next_power_of_2(unsigned int x) {
+
+	if (x == 0)
+		return 0;
+
+	--x;
+	x |= x >> 1;
+	x |= x >> 2;
+	x |= x >> 4;
+	x |= x >> 8;
+	x |= x >> 16;
+
+	return ++x;
+}
+
+// This function should be as fast as possible and rounding mode should not matter.
+inline int fast_ftoi(float a) {
+	static int b;
+
+#if (defined(_WIN32_WINNT) && _WIN32_WINNT >= 0x0603) || WINAPI_FAMILY == WINAPI_FAMILY_PHONE_APP // windows 8 phone?
+	b = (int)((a > 0.0) ? (a + 0.5) : (a - 0.5));
+
+#elif defined(_MSC_VER) && _MSC_VER < 1800
+	__asm fld a __asm fistp b
+	/*#elif defined( __GNUC__ ) && ( defined( __i386__ ) || defined( __x86_64__ ) )
+	// use AT&T inline assembly style, document that
+	// we use memory as output (=m) and input (m)
+	__asm__ __volatile__ (
+	"flds %1        \n\t"
+	"fistpl %0      \n\t"
+	: "=m" (b)
+	: "m" (a));*/
+
+#else
+	b = lrintf(a); //assuming everything but msvc 2012 or earlier has lrint
+#endif
+	return b;
+}
+
+inline double snapped(double p_value, double p_step) {
+	if (p_step != 0) {
+		p_value = Math::floor(p_value / p_step + 0.5) * p_step;
+	}
+	return p_value;
+}
+
+} // namespace Math
+} // namespace godot
+
+#endif // GODOT_MATH_H

include/godot_cpp/variant/aabb.hpp

@@ -0,0 +1,430 @@
+#ifndef GODOT_AABB_HPP
+#define GODOT_AABB_HPP
+
+#include <godot_cpp/core/error_macros.hpp>
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/plane.hpp>
+#include <godot_cpp/variant/vector3.hpp>
+
+/**
+ * AABB / AABB (Axis Aligned Bounding Box)
+ * This is implemented by a point (position) and the box size
+ */
+
+namespace godot {
+
+class AABB {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	Vector3 position;
+	Vector3 size;
+
+	real_t get_area() const; /// get area
+	inline bool has_no_area() const {
+		return (size.x <= 0 || size.y <= 0 || size.z <= 0);
+	}
+
+	inline bool has_no_surface() const {
+		return (size.x <= 0 && size.y <= 0 && size.z <= 0);
+	}
+
+	const Vector3 &get_position() const { return position; }
+	void set_position(const Vector3 &p_pos) { position = p_pos; }
+	const Vector3 &get_size() const { return size; }
+	void set_size(const Vector3 &p_size) { size = p_size; }
+
+	bool operator==(const AABB &p_rval) const;
+	bool operator!=(const AABB &p_rval) const;
+
+	bool is_equal_approx(const AABB &p_aabb) const;
+	inline bool intersects(const AABB &p_aabb) const; /// Both AABBs overlap
+	inline bool intersects_inclusive(const AABB &p_aabb) const; /// Both AABBs (or their faces) overlap
+	inline bool encloses(const AABB &p_aabb) const; /// p_aabb is completely inside this
+
+	AABB merge(const AABB &p_with) const;
+	void merge_with(const AABB &p_aabb); ///merge with another AABB
+	AABB intersection(const AABB &p_aabb) const; ///get box where two intersect, empty if no intersection occurs
+	bool intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector3 *r_clip = nullptr, Vector3 *r_normal = nullptr) const;
+	bool intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *r_clip = nullptr, Vector3 *r_normal = nullptr) const;
+	inline bool smits_intersect_ray(const Vector3 &p_from, const Vector3 &p_dir, real_t t0, real_t t1) const;
+
+	inline bool intersects_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count) const;
+	inline bool inside_convex_shape(const Plane *p_planes, int p_plane_count) const;
+	bool intersects_plane(const Plane &p_plane) const;
+
+	inline bool has_point(const Vector3 &p_point) const;
+	inline Vector3 get_support(const Vector3 &p_normal) const;
+
+	Vector3 get_longest_axis() const;
+	int get_longest_axis_index() const;
+	inline real_t get_longest_axis_size() const;
+
+	Vector3 get_shortest_axis() const;
+	int get_shortest_axis_index() const;
+	inline real_t get_shortest_axis_size() const;
+
+	AABB grow(real_t p_by) const;
+	inline void grow_by(real_t p_amount);
+
+	void get_edge(int p_edge, Vector3 &r_from, Vector3 &r_to) const;
+	inline Vector3 get_endpoint(int p_point) const;
+
+	AABB expand(const Vector3 &p_vector) const;
+	inline void project_range_in_plane(const Plane &p_plane, real_t &r_min, real_t &r_max) const;
+	inline void expand_to(const Vector3 &p_vector); /** expand to contain a point if necessary */
+
+	inline AABB abs() const {
+		return AABB(Vector3(position.x + Math::min(size.x, (real_t)0), position.y + Math::min(size.y, (real_t)0), position.z + Math::min(size.z, (real_t)0)), size.abs());
+	}
+
+	inline void quantize(real_t p_unit);
+	inline AABB quantized(real_t p_unit) const;
+
+	inline void set_end(const Vector3 &p_end) {
+		size = p_end - position;
+	}
+
+	inline Vector3 get_end() const {
+		return position + size;
+	}
+
+	operator String() const;
+
+	inline AABB() {}
+	inline AABB(const Vector3 &p_pos, const Vector3 &p_size) :
+			position(p_pos),
+			size(p_size) {
+	}
+};
+
+inline bool AABB::intersects(const AABB &p_aabb) const {
+	if (position.x >= (p_aabb.position.x + p_aabb.size.x)) {
+		return false;
+	}
+	if ((position.x + size.x) <= p_aabb.position.x) {
+		return false;
+	}
+	if (position.y >= (p_aabb.position.y + p_aabb.size.y)) {
+		return false;
+	}
+	if ((position.y + size.y) <= p_aabb.position.y) {
+		return false;
+	}
+	if (position.z >= (p_aabb.position.z + p_aabb.size.z)) {
+		return false;
+	}
+	if ((position.z + size.z) <= p_aabb.position.z) {
+		return false;
+	}
+
+	return true;
+}
+
+inline bool AABB::intersects_inclusive(const AABB &p_aabb) const {
+	if (position.x > (p_aabb.position.x + p_aabb.size.x)) {
+		return false;
+	}
+	if ((position.x + size.x) < p_aabb.position.x) {
+		return false;
+	}
+	if (position.y > (p_aabb.position.y + p_aabb.size.y)) {
+		return false;
+	}
+	if ((position.y + size.y) < p_aabb.position.y) {
+		return false;
+	}
+	if (position.z > (p_aabb.position.z + p_aabb.size.z)) {
+		return false;
+	}
+	if ((position.z + size.z) < p_aabb.position.z) {
+		return false;
+	}
+
+	return true;
+}
+
+inline bool AABB::encloses(const AABB &p_aabb) const {
+	Vector3 src_min = position;
+	Vector3 src_max = position + size;
+	Vector3 dst_min = p_aabb.position;
+	Vector3 dst_max = p_aabb.position + p_aabb.size;
+
+	return (
+			(src_min.x <= dst_min.x) &&
+			(src_max.x > dst_max.x) &&
+			(src_min.y <= dst_min.y) &&
+			(src_max.y > dst_max.y) &&
+			(src_min.z <= dst_min.z) &&
+			(src_max.z > dst_max.z));
+}
+
+Vector3 AABB::get_support(const Vector3 &p_normal) const {
+	Vector3 half_extents = size * 0.5;
+	Vector3 ofs = position + half_extents;
+
+	return Vector3(
+				   (p_normal.x > 0) ? half_extents.x : -half_extents.x,
+				   (p_normal.y > 0) ? half_extents.y : -half_extents.y,
+				   (p_normal.z > 0) ? half_extents.z : -half_extents.z) +
+		   ofs;
+}
+
+Vector3 AABB::get_endpoint(int p_point) const {
+	switch (p_point) {
+		case 0:
+			return Vector3(position.x, position.y, position.z);
+		case 1:
+			return Vector3(position.x, position.y, position.z + size.z);
+		case 2:
+			return Vector3(position.x, position.y + size.y, position.z);
+		case 3:
+			return Vector3(position.x, position.y + size.y, position.z + size.z);
+		case 4:
+			return Vector3(position.x + size.x, position.y, position.z);
+		case 5:
+			return Vector3(position.x + size.x, position.y, position.z + size.z);
+		case 6:
+			return Vector3(position.x + size.x, position.y + size.y, position.z);
+		case 7:
+			return Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+	}
+
+	ERR_FAIL_V(Vector3());
+}
+
+bool AABB::intersects_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count) const {
+	Vector3 half_extents = size * 0.5;
+	Vector3 ofs = position + half_extents;
+
+	for (int i = 0; i < p_plane_count; i++) {
+		const Plane &p = p_planes[i];
+		Vector3 point(
+				(p.normal.x > 0) ? -half_extents.x : half_extents.x,
+				(p.normal.y > 0) ? -half_extents.y : half_extents.y,
+				(p.normal.z > 0) ? -half_extents.z : half_extents.z);
+		point += ofs;
+		if (p.is_point_over(point)) {
+			return false;
+		}
+	}
+
+	// Make sure all points in the shape aren't fully separated from the AABB on
+	// each axis.
+	int bad_point_counts_positive[3] = { 0 };
+	int bad_point_counts_negative[3] = { 0 };
+
+	for (int k = 0; k < 3; k++) {
+		for (int i = 0; i < p_point_count; i++) {
+			if (p_points[i].coord[k] > ofs.coord[k] + half_extents.coord[k]) {
+				bad_point_counts_positive[k]++;
+			}
+			if (p_points[i].coord[k] < ofs.coord[k] - half_extents.coord[k]) {
+				bad_point_counts_negative[k]++;
+			}
+		}
+
+		if (bad_point_counts_negative[k] == p_point_count) {
+			return false;
+		}
+		if (bad_point_counts_positive[k] == p_point_count) {
+			return false;
+		}
+	}
+
+	return true;
+}
+
+bool AABB::inside_convex_shape(const Plane *p_planes, int p_plane_count) const {
+	Vector3 half_extents = size * 0.5;
+	Vector3 ofs = position + half_extents;
+
+	for (int i = 0; i < p_plane_count; i++) {
+		const Plane &p = p_planes[i];
+		Vector3 point(
+				(p.normal.x < 0) ? -half_extents.x : half_extents.x,
+				(p.normal.y < 0) ? -half_extents.y : half_extents.y,
+				(p.normal.z < 0) ? -half_extents.z : half_extents.z);
+		point += ofs;
+		if (p.is_point_over(point)) {
+			return false;
+		}
+	}
+
+	return true;
+}
+
+bool AABB::has_point(const Vector3 &p_point) const {
+	if (p_point.x < position.x) {
+		return false;
+	}
+	if (p_point.y < position.y) {
+		return false;
+	}
+	if (p_point.z < position.z) {
+		return false;
+	}
+	if (p_point.x > position.x + size.x) {
+		return false;
+	}
+	if (p_point.y > position.y + size.y) {
+		return false;
+	}
+	if (p_point.z > position.z + size.z) {
+		return false;
+	}
+
+	return true;
+}
+
+inline void AABB::expand_to(const Vector3 &p_vector) {
+	Vector3 begin = position;
+	Vector3 end = position + size;
+
+	if (p_vector.x < begin.x) {
+		begin.x = p_vector.x;
+	}
+	if (p_vector.y < begin.y) {
+		begin.y = p_vector.y;
+	}
+	if (p_vector.z < begin.z) {
+		begin.z = p_vector.z;
+	}
+
+	if (p_vector.x > end.x) {
+		end.x = p_vector.x;
+	}
+	if (p_vector.y > end.y) {
+		end.y = p_vector.y;
+	}
+	if (p_vector.z > end.z) {
+		end.z = p_vector.z;
+	}
+
+	position = begin;
+	size = end - begin;
+}
+
+void AABB::project_range_in_plane(const Plane &p_plane, real_t &r_min, real_t &r_max) const {
+	Vector3 half_extents(size.x * 0.5, size.y * 0.5, size.z * 0.5);
+	Vector3 center(position.x + half_extents.x, position.y + half_extents.y, position.z + half_extents.z);
+
+	real_t length = p_plane.normal.abs().dot(half_extents);
+	real_t distance = p_plane.distance_to(center);
+	r_min = distance - length;
+	r_max = distance + length;
+}
+
+inline real_t AABB::get_longest_axis_size() const {
+	real_t max_size = size.x;
+
+	if (size.y > max_size) {
+		max_size = size.y;
+	}
+
+	if (size.z > max_size) {
+		max_size = size.z;
+	}
+
+	return max_size;
+}
+
+inline real_t AABB::get_shortest_axis_size() const {
+	real_t max_size = size.x;
+
+	if (size.y < max_size) {
+		max_size = size.y;
+	}
+
+	if (size.z < max_size) {
+		max_size = size.z;
+	}
+
+	return max_size;
+}
+
+bool AABB::smits_intersect_ray(const Vector3 &p_from, const Vector3 &p_dir, real_t t0, real_t t1) const {
+	real_t divx = 1.0 / p_dir.x;
+	real_t divy = 1.0 / p_dir.y;
+	real_t divz = 1.0 / p_dir.z;
+
+	Vector3 upbound = position + size;
+	real_t tmin, tmax, tymin, tymax, tzmin, tzmax;
+	if (p_dir.x >= 0) {
+		tmin = (position.x - p_from.x) * divx;
+		tmax = (upbound.x - p_from.x) * divx;
+	} else {
+		tmin = (upbound.x - p_from.x) * divx;
+		tmax = (position.x - p_from.x) * divx;
+	}
+	if (p_dir.y >= 0) {
+		tymin = (position.y - p_from.y) * divy;
+		tymax = (upbound.y - p_from.y) * divy;
+	} else {
+		tymin = (upbound.y - p_from.y) * divy;
+		tymax = (position.y - p_from.y) * divy;
+	}
+	if ((tmin > tymax) || (tymin > tmax)) {
+		return false;
+	}
+	if (tymin > tmin) {
+		tmin = tymin;
+	}
+	if (tymax < tmax) {
+		tmax = tymax;
+	}
+	if (p_dir.z >= 0) {
+		tzmin = (position.z - p_from.z) * divz;
+		tzmax = (upbound.z - p_from.z) * divz;
+	} else {
+		tzmin = (upbound.z - p_from.z) * divz;
+		tzmax = (position.z - p_from.z) * divz;
+	}
+	if ((tmin > tzmax) || (tzmin > tmax)) {
+		return false;
+	}
+	if (tzmin > tmin) {
+		tmin = tzmin;
+	}
+	if (tzmax < tmax) {
+		tmax = tzmax;
+	}
+	return ((tmin < t1) && (tmax > t0));
+}
+
+void AABB::grow_by(real_t p_amount) {
+	position.x -= p_amount;
+	position.y -= p_amount;
+	position.z -= p_amount;
+	size.x += 2.0 * p_amount;
+	size.y += 2.0 * p_amount;
+	size.z += 2.0 * p_amount;
+}
+
+void AABB::quantize(real_t p_unit) {
+	size += position;
+
+	position.x -= Math::fposmodp(position.x, p_unit);
+	position.y -= Math::fposmodp(position.y, p_unit);
+	position.z -= Math::fposmodp(position.z, p_unit);
+
+	size.x -= Math::fposmodp(size.x, p_unit);
+	size.y -= Math::fposmodp(size.y, p_unit);
+	size.z -= Math::fposmodp(size.z, p_unit);
+
+	size.x += p_unit;
+	size.y += p_unit;
+	size.z += p_unit;
+
+	size -= position;
+}
+
+AABB AABB::quantized(real_t p_unit) const {
+	AABB ret = *this;
+	ret.quantize(p_unit);
+	return ret;
+}
+
+} // namespace godot
+
+#endif // GODOT_AABB_HPP

include/godot_cpp/variant/basis.hpp

@@ -0,0 +1,310 @@
+#ifndef GODOT_BASIS_HPP
+#define GODOT_BASIS_HPP
+
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/quaternion.hpp>
+#include <godot_cpp/variant/vector3.hpp>
+
+namespace godot {
+
+class Basis {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	Vector3 elements[3] = {
+		Vector3(1, 0, 0),
+		Vector3(0, 1, 0),
+		Vector3(0, 0, 1)
+	};
+
+	inline const Vector3 &operator[](int axis) const {
+		return elements[axis];
+	}
+	inline Vector3 &operator[](int axis) {
+		return elements[axis];
+	}
+
+	void invert();
+	void transpose();
+
+	Basis inverse() const;
+	Basis transposed() const;
+
+	inline real_t determinant() const;
+
+	void from_z(const Vector3 &p_z);
+
+	inline Vector3 get_axis(int p_axis) const {
+		// get actual basis axis (elements is transposed for performance)
+		return Vector3(elements[0][p_axis], elements[1][p_axis], elements[2][p_axis]);
+	}
+	inline void set_axis(int p_axis, const Vector3 &p_value) {
+		// get actual basis axis (elements is transposed for performance)
+		elements[0][p_axis] = p_value.x;
+		elements[1][p_axis] = p_value.y;
+		elements[2][p_axis] = p_value.z;
+	}
+
+	void rotate(const Vector3 &p_axis, real_t p_phi);
+	Basis rotated(const Vector3 &p_axis, real_t p_phi) const;
+
+	void rotate_local(const Vector3 &p_axis, real_t p_phi);
+	Basis rotated_local(const Vector3 &p_axis, real_t p_phi) const;
+
+	void rotate(const Vector3 &p_euler);
+	Basis rotated(const Vector3 &p_euler) const;
+
+	void rotate(const Quaternion &p_quat);
+	Basis rotated(const Quaternion &p_quat) const;
+
+	Vector3 get_rotation_euler() const;
+	void get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const;
+	void get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) const;
+	Quaternion get_rotation_quat() const;
+	Vector3 get_rotation() const { return get_rotation_euler(); };
+
+	Vector3 rotref_posscale_decomposition(Basis &rotref) const;
+
+	Vector3 get_euler_xyz() const;
+	void set_euler_xyz(const Vector3 &p_euler);
+
+	Vector3 get_euler_xzy() const;
+	void set_euler_xzy(const Vector3 &p_euler);
+
+	Vector3 get_euler_yzx() const;
+	void set_euler_yzx(const Vector3 &p_euler);
+
+	Vector3 get_euler_yxz() const;
+	void set_euler_yxz(const Vector3 &p_euler);
+
+	Vector3 get_euler_zxy() const;
+	void set_euler_zxy(const Vector3 &p_euler);
+
+	Vector3 get_euler_zyx() const;
+	void set_euler_zyx(const Vector3 &p_euler);
+
+	Quaternion get_quat() const;
+	void set_quat(const Quaternion &p_quat);
+
+	Vector3 get_euler() const { return get_euler_yxz(); }
+	void set_euler(const Vector3 &p_euler) { set_euler_yxz(p_euler); }
+
+	void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const;
+	void set_axis_angle(const Vector3 &p_axis, real_t p_phi);
+
+	void scale(const Vector3 &p_scale);
+	Basis scaled(const Vector3 &p_scale) const;
+
+	void scale_local(const Vector3 &p_scale);
+	Basis scaled_local(const Vector3 &p_scale) const;
+
+	void make_scale_uniform();
+	float get_uniform_scale() const;
+
+	Vector3 get_scale() const;
+	Vector3 get_scale_abs() const;
+	Vector3 get_scale_local() const;
+
+	void set_axis_angle_scale(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale);
+	void set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale);
+	void set_quat_scale(const Quaternion &p_quat, const Vector3 &p_scale);
+
+	// transposed dot products
+	inline real_t tdotx(const Vector3 &v) const {
+		return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2];
+	}
+	inline real_t tdoty(const Vector3 &v) const {
+		return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2];
+	}
+	inline real_t tdotz(const Vector3 &v) const {
+		return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2];
+	}
+
+	bool is_equal_approx(const Basis &p_basis) const;
+
+	bool operator==(const Basis &p_matrix) const;
+	bool operator!=(const Basis &p_matrix) const;
+
+	inline Vector3 xform(const Vector3 &p_vector) const;
+	inline Vector3 xform_inv(const Vector3 &p_vector) const;
+	inline void operator*=(const Basis &p_matrix);
+	inline Basis operator*(const Basis &p_matrix) const;
+	inline void operator+=(const Basis &p_matrix);
+	inline Basis operator+(const Basis &p_matrix) const;
+	inline void operator-=(const Basis &p_matrix);
+	inline Basis operator-(const Basis &p_matrix) const;
+	inline void operator*=(real_t p_val);
+	inline Basis operator*(real_t p_val) const;
+
+	int get_orthogonal_index() const;
+	void set_orthogonal_index(int p_index);
+
+	void set_diagonal(const Vector3 &p_diag);
+
+	bool is_orthogonal() const;
+	bool is_diagonal() const;
+	bool is_rotation() const;
+
+	Basis slerp(const Basis &p_to, const real_t &p_weight) const;
+	void rotate_sh(real_t *p_values);
+
+	operator String() const;
+
+	/* create / set */
+
+	inline void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
+		elements[0][0] = xx;
+		elements[0][1] = xy;
+		elements[0][2] = xz;
+		elements[1][0] = yx;
+		elements[1][1] = yy;
+		elements[1][2] = yz;
+		elements[2][0] = zx;
+		elements[2][1] = zy;
+		elements[2][2] = zz;
+	}
+	inline void set(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z) {
+		set_axis(0, p_x);
+		set_axis(1, p_y);
+		set_axis(2, p_z);
+	}
+	inline Vector3 get_column(int i) const {
+		return Vector3(elements[0][i], elements[1][i], elements[2][i]);
+	}
+
+	inline Vector3 get_row(int i) const {
+		return Vector3(elements[i][0], elements[i][1], elements[i][2]);
+	}
+	inline Vector3 get_main_diagonal() const {
+		return Vector3(elements[0][0], elements[1][1], elements[2][2]);
+	}
+
+	inline void set_row(int i, const Vector3 &p_row) {
+		elements[i][0] = p_row.x;
+		elements[i][1] = p_row.y;
+		elements[i][2] = p_row.z;
+	}
+
+	inline void set_zero() {
+		elements[0].zero();
+		elements[1].zero();
+		elements[2].zero();
+	}
+
+	inline Basis transpose_xform(const Basis &m) const {
+		return Basis(
+				elements[0].x * m[0].x + elements[1].x * m[1].x + elements[2].x * m[2].x,
+				elements[0].x * m[0].y + elements[1].x * m[1].y + elements[2].x * m[2].y,
+				elements[0].x * m[0].z + elements[1].x * m[1].z + elements[2].x * m[2].z,
+				elements[0].y * m[0].x + elements[1].y * m[1].x + elements[2].y * m[2].x,
+				elements[0].y * m[0].y + elements[1].y * m[1].y + elements[2].y * m[2].y,
+				elements[0].y * m[0].z + elements[1].y * m[1].z + elements[2].y * m[2].z,
+				elements[0].z * m[0].x + elements[1].z * m[1].x + elements[2].z * m[2].x,
+				elements[0].z * m[0].y + elements[1].z * m[1].y + elements[2].z * m[2].y,
+				elements[0].z * m[0].z + elements[1].z * m[1].z + elements[2].z * m[2].z);
+	}
+	Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
+		set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
+	}
+
+	void orthonormalize();
+	Basis orthonormalized() const;
+
+#ifdef MATH_CHECKS
+	bool is_symmetric() const;
+#endif
+	Basis diagonalize();
+
+	operator Quaternion() const { return get_quat(); }
+
+	Basis(const Quaternion &p_quat) { set_quat(p_quat); };
+	Basis(const Quaternion &p_quat, const Vector3 &p_scale) { set_quat_scale(p_quat, p_scale); }
+
+	Basis(const Vector3 &p_euler) { set_euler(p_euler); }
+	Basis(const Vector3 &p_euler, const Vector3 &p_scale) { set_euler_scale(p_euler, p_scale); }
+
+	Basis(const Vector3 &p_axis, real_t p_phi) { set_axis_angle(p_axis, p_phi); }
+	Basis(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale) { set_axis_angle_scale(p_axis, p_phi, p_scale); }
+
+	inline Basis(const Vector3 &row0, const Vector3 &row1, const Vector3 &row2) {
+		elements[0] = row0;
+		elements[1] = row1;
+		elements[2] = row2;
+	}
+
+	inline Basis() {}
+};
+
+inline void Basis::operator*=(const Basis &p_matrix) {
+	set(
+			p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
+			p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
+			p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));
+}
+
+inline Basis Basis::operator*(const Basis &p_matrix) const {
+	return Basis(
+			p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
+			p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
+			p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));
+}
+
+inline void Basis::operator+=(const Basis &p_matrix) {
+	elements[0] += p_matrix.elements[0];
+	elements[1] += p_matrix.elements[1];
+	elements[2] += p_matrix.elements[2];
+}
+
+inline Basis Basis::operator+(const Basis &p_matrix) const {
+	Basis ret(*this);
+	ret += p_matrix;
+	return ret;
+}
+
+inline void Basis::operator-=(const Basis &p_matrix) {
+	elements[0] -= p_matrix.elements[0];
+	elements[1] -= p_matrix.elements[1];
+	elements[2] -= p_matrix.elements[2];
+}
+
+inline Basis Basis::operator-(const Basis &p_matrix) const {
+	Basis ret(*this);
+	ret -= p_matrix;
+	return ret;
+}
+
+inline void Basis::operator*=(real_t p_val) {
+	elements[0] *= p_val;
+	elements[1] *= p_val;
+	elements[2] *= p_val;
+}
+
+inline Basis Basis::operator*(real_t p_val) const {
+	Basis ret(*this);
+	ret *= p_val;
+	return ret;
+}
+
+Vector3 Basis::xform(const Vector3 &p_vector) const {
+	return Vector3(
+			elements[0].dot(p_vector),
+			elements[1].dot(p_vector),
+			elements[2].dot(p_vector));
+}
+
+Vector3 Basis::xform_inv(const Vector3 &p_vector) const {
+	return Vector3(
+			(elements[0][0] * p_vector.x) + (elements[1][0] * p_vector.y) + (elements[2][0] * p_vector.z),
+			(elements[0][1] * p_vector.x) + (elements[1][1] * p_vector.y) + (elements[2][1] * p_vector.z),
+			(elements[0][2] * p_vector.x) + (elements[1][2] * p_vector.y) + (elements[2][2] * p_vector.z));
+}
+
+real_t Basis::determinant() const {
+	return elements[0][0] * (elements[1][1] * elements[2][2] - elements[2][1] * elements[1][2]) -
+		   elements[1][0] * (elements[0][1] * elements[2][2] - elements[2][1] * elements[0][2]) +
+		   elements[2][0] * (elements[0][1] * elements[1][2] - elements[1][1] * elements[0][2]);
+}
+
+} // namespace godot
+
+#endif // GODOT_BASIS_HPP

include/godot_cpp/variant/color.hpp

@@ -0,0 +1,257 @@
+#ifndef GODOT_COLOR_HPP
+#define GODOT_COLOR_HPP
+
+#include <godot_cpp/core/math.hpp>
+
+namespace godot {
+
+class String;
+
+class Color {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	union {
+		struct {
+			float r;
+			float g;
+			float b;
+			float a;
+		};
+		float components[4] = { 0, 0, 0, 1.0 };
+	};
+
+	uint32_t to_rgba32() const;
+	uint32_t to_argb32() const;
+	uint32_t to_abgr32() const;
+	uint64_t to_rgba64() const;
+	uint64_t to_argb64() const;
+	uint64_t to_abgr64() const;
+	float get_h() const;
+	float get_s() const;
+	float get_v() const;
+	void set_hsv(float p_h, float p_s, float p_v, float p_alpha = 1.0);
+
+	inline float &operator[](int p_idx) {
+		return components[p_idx];
+	}
+	inline const float &operator[](int p_idx) const {
+		return components[p_idx];
+	}
+
+	bool operator==(const Color &p_color) const {
+		return (r == p_color.r && g == p_color.g && b == p_color.b && a == p_color.a);
+	}
+	bool operator!=(const Color &p_color) const {
+		return (r != p_color.r || g != p_color.g || b != p_color.b || a != p_color.a);
+	}
+
+	Color operator+(const Color &p_color) const;
+	void operator+=(const Color &p_color);
+
+	Color operator-() const;
+	Color operator-(const Color &p_color) const;
+	void operator-=(const Color &p_color);
+
+	Color operator*(const Color &p_color) const;
+	Color operator*(float p_scalar) const;
+	void operator*=(const Color &p_color);
+	void operator*=(float p_scalar);
+
+	Color operator/(const Color &p_color) const;
+	Color operator/(float p_scalar) const;
+	void operator/=(const Color &p_color);
+	void operator/=(float p_scalar);
+
+	bool is_equal_approx(const Color &p_color) const;
+
+	void invert();
+	Color inverted() const;
+
+	inline Color lerp(const Color &p_to, float p_weight) const {
+		Color res = *this;
+
+		res.r += (p_weight * (p_to.r - r));
+		res.g += (p_weight * (p_to.g - g));
+		res.b += (p_weight * (p_to.b - b));
+		res.a += (p_weight * (p_to.a - a));
+
+		return res;
+	}
+
+	inline Color darkened(float p_amount) const {
+		Color res = *this;
+		res.r = res.r * (1.0f - p_amount);
+		res.g = res.g * (1.0f - p_amount);
+		res.b = res.b * (1.0f - p_amount);
+		return res;
+	}
+
+	inline Color lightened(float p_amount) const {
+		Color res = *this;
+		res.r = res.r + (1.0f - res.r) * p_amount;
+		res.g = res.g + (1.0f - res.g) * p_amount;
+		res.b = res.b + (1.0f - res.b) * p_amount;
+		return res;
+	}
+
+	inline uint32_t to_rgbe9995() const {
+		const float pow2to9 = 512.0f;
+		const float B = 15.0f;
+		const float N = 9.0f;
+
+		float sharedexp = 65408.000f; // Result of: ((pow2to9 - 1.0f) / pow2to9) * powf(2.0f, 31.0f - 15.0f)
+
+		float cRed = Math::max(0.0f, Math::min(sharedexp, r));
+		float cGreen = Math::max(0.0f, Math::min(sharedexp, g));
+		float cBlue = Math::max(0.0f, Math::min(sharedexp, b));
+
+		float cMax = Math::max(cRed, Math::max(cGreen, cBlue));
+
+		float expp = Math::max(-B - 1.0f, Math::floor(Math::log(cMax) / (float)Math_LN2)) + 1.0f + B;
+
+		float sMax = (float)floor((cMax / Math::pow(2.0f, expp - B - N)) + 0.5f);
+
+		float exps = expp + 1.0f;
+
+		if (0.0 <= sMax && sMax < pow2to9) {
+			exps = expp;
+		}
+
+		float sRed = Math::floor((cRed / pow(2.0f, exps - B - N)) + 0.5f);
+		float sGreen = Math::floor((cGreen / pow(2.0f, exps - B - N)) + 0.5f);
+		float sBlue = Math::floor((cBlue / pow(2.0f, exps - B - N)) + 0.5f);
+
+		return (uint32_t(Math::fast_ftoi(sRed)) & 0x1FF) | ((uint32_t(Math::fast_ftoi(sGreen)) & 0x1FF) << 9) | ((uint32_t(Math::fast_ftoi(sBlue)) & 0x1FF) << 18) | ((uint32_t(Math::fast_ftoi(exps)) & 0x1F) << 27);
+	}
+
+	inline Color blend(const Color &p_over) const {
+		Color res;
+		float sa = 1.0 - p_over.a;
+		res.a = a * sa + p_over.a;
+		if (res.a == 0) {
+			return Color(0, 0, 0, 0);
+		} else {
+			res.r = (r * a * sa + p_over.r * p_over.a) / res.a;
+			res.g = (g * a * sa + p_over.g * p_over.a) / res.a;
+			res.b = (b * a * sa + p_over.b * p_over.a) / res.a;
+		}
+		return res;
+	}
+
+	inline Color to_linear() const {
+		return Color(
+				r < 0.04045 ? r * (1.0 / 12.92) : Math::pow((r + 0.055) * (1.0 / (1 + 0.055)), 2.4),
+				g < 0.04045 ? g * (1.0 / 12.92) : Math::pow((g + 0.055) * (1.0 / (1 + 0.055)), 2.4),
+				b < 0.04045 ? b * (1.0 / 12.92) : Math::pow((b + 0.055) * (1.0 / (1 + 0.055)), 2.4),
+				a);
+	}
+	inline Color to_srgb() const {
+		return Color(
+				r < 0.0031308 ? 12.92 * r : (1.0 + 0.055) * Math::pow(r, 1.0f / 2.4f) - 0.055,
+				g < 0.0031308 ? 12.92 * g : (1.0 + 0.055) * Math::pow(g, 1.0f / 2.4f) - 0.055,
+				b < 0.0031308 ? 12.92 * b : (1.0 + 0.055) * Math::pow(b, 1.0f / 2.4f) - 0.055, a);
+	}
+
+	static Color hex(uint32_t p_hex);
+	static Color hex64(uint64_t p_hex);
+	static Color html(const String &p_rgba);
+	static bool html_is_valid(const String &p_color);
+	static Color named(const String &p_name);
+	static Color named(const String &p_name, const Color &p_default);
+	static int find_named_color(const String &p_name);
+	static int get_named_color_count();
+	static String get_named_color_name(int p_idx);
+	static Color get_named_color(int p_idx);
+	static Color from_string(const String &p_string, const Color &p_default);
+	String to_html(bool p_alpha = true) const;
+	static Color from_hsv(float p_h, float p_s, float p_v, float p_a);
+	static Color from_rgbe9995(uint32_t p_rgbe);
+
+	inline bool operator<(const Color &p_color) const; //used in set keys
+	operator String() const;
+
+	// For the binder.
+	inline void set_r8(int32_t r8) { r = (Math::clamp(r8, 0, 255) / 255.0); }
+	inline int32_t get_r8() const { return int32_t(Math::clamp(r * 255.0, 0.0, 255.0)); }
+	inline void set_g8(int32_t g8) { g = (Math::clamp(g8, 0, 255) / 255.0); }
+	inline int32_t get_g8() const { return int32_t(Math::clamp(g * 255.0, 0.0, 255.0)); }
+	inline void set_b8(int32_t b8) { b = (Math::clamp(b8, 0, 255) / 255.0); }
+	inline int32_t get_b8() const { return int32_t(Math::clamp(b * 255.0, 0.0, 255.0)); }
+	inline void set_a8(int32_t a8) { a = (Math::clamp(a8, 0, 255) / 255.0); }
+	inline int32_t get_a8() const { return int32_t(Math::clamp(a * 255.0, 0.0, 255.0)); }
+
+	inline void set_h(float p_h) { set_hsv(p_h, get_s(), get_v()); }
+	inline void set_s(float p_s) { set_hsv(get_h(), p_s, get_v()); }
+	inline void set_v(float p_v) { set_hsv(get_h(), get_s(), p_v); }
+
+	inline Color() {}
+
+	/**
+	 * RGBA construct parameters.
+	 * Alpha is not optional as otherwise we can't bind the RGB version for scripting.
+	 */
+	inline Color(float p_r, float p_g, float p_b, float p_a) {
+		r = p_r;
+		g = p_g;
+		b = p_b;
+		a = p_a;
+	}
+
+	/**
+	 * RGB construct parameters.
+	 */
+	inline Color(float p_r, float p_g, float p_b) {
+		r = p_r;
+		g = p_g;
+		b = p_b;
+		a = 1.0;
+	}
+
+	/**
+	 * Construct a Color from another Color, but with the specified alpha value.
+	 */
+	inline Color(const Color &p_c, float p_a) {
+		r = p_c.r;
+		g = p_c.g;
+		b = p_c.b;
+		a = p_a;
+	}
+
+	Color(const String &p_code) {
+		if (html_is_valid(p_code)) {
+			*this = html(p_code);
+		} else {
+			*this = named(p_code);
+		}
+	}
+
+	Color(const String &p_code, float p_a) {
+		*this = Color(p_code);
+		a = p_a;
+	}
+};
+
+bool Color::operator<(const Color &p_color) const {
+	if (r == p_color.r) {
+		if (g == p_color.g) {
+			if (b == p_color.b) {
+				return (a < p_color.a);
+			} else {
+				return (b < p_color.b);
+			}
+		} else {
+			return g < p_color.g;
+		}
+	} else {
+		return r < p_color.r;
+	}
+}
+
+inline Color operator*(float p_scalar, const Color &p_color) {
+	return p_color * p_scalar;
+}
+
+} // namespace godot
+
+#endif // GODOT_COLOR_HPP

include/godot_cpp/variant/color_names.inc.hpp

@@ -0,0 +1,158 @@
+namespace godot {
+
+struct NamedColor {
+	const char *name;
+	Color color;
+};
+
+static NamedColor named_colors[] = {
+	{ "aliceblue", Color(0.94, 0.97, 1.00) },
+	{ "antiquewhite", Color(0.98, 0.92, 0.84) },
+	{ "aqua", Color(0.00, 1.00, 1.00) },
+	{ "aquamarine", Color(0.50, 1.00, 0.83) },
+	{ "azure", Color(0.94, 1.00, 1.00) },
+	{ "beige", Color(0.96, 0.96, 0.86) },
+	{ "bisque", Color(1.00, 0.89, 0.77) },
+	{ "black", Color(0.00, 0.00, 0.00) },
+	{ "blanchedalmond", Color(1.00, 0.92, 0.80) },
+	{ "blue", Color(0.00, 0.00, 1.00) },
+	{ "blueviolet", Color(0.54, 0.17, 0.89) },
+	{ "brown", Color(0.65, 0.16, 0.16) },
+	{ "burlywood", Color(0.87, 0.72, 0.53) },
+	{ "cadetblue", Color(0.37, 0.62, 0.63) },
+	{ "chartreuse", Color(0.50, 1.00, 0.00) },
+	{ "chocolate", Color(0.82, 0.41, 0.12) },
+	{ "coral", Color(1.00, 0.50, 0.31) },
+	{ "cornflower", Color(0.39, 0.58, 0.93) },
+	{ "cornsilk", Color(1.00, 0.97, 0.86) },
+	{ "crimson", Color(0.86, 0.08, 0.24) },
+	{ "cyan", Color(0.00, 1.00, 1.00) },
+	{ "darkblue", Color(0.00, 0.00, 0.55) },
+	{ "darkcyan", Color(0.00, 0.55, 0.55) },
+	{ "darkgoldenrod", Color(0.72, 0.53, 0.04) },
+	{ "darkgray", Color(0.66, 0.66, 0.66) },
+	{ "darkgreen", Color(0.00, 0.39, 0.00) },
+	{ "darkkhaki", Color(0.74, 0.72, 0.42) },
+	{ "darkmagenta", Color(0.55, 0.00, 0.55) },
+	{ "darkolivegreen", Color(0.33, 0.42, 0.18) },
+	{ "darkorange", Color(1.00, 0.55, 0.00) },
+	{ "darkorchid", Color(0.60, 0.20, 0.80) },
+	{ "darkred", Color(0.55, 0.00, 0.00) },
+	{ "darksalmon", Color(0.91, 0.59, 0.48) },
+	{ "darkseagreen", Color(0.56, 0.74, 0.56) },
+	{ "darkslateblue", Color(0.28, 0.24, 0.55) },
+	{ "darkslategray", Color(0.18, 0.31, 0.31) },
+	{ "darkturquoise", Color(0.00, 0.81, 0.82) },
+	{ "darkviolet", Color(0.58, 0.00, 0.83) },
+	{ "deeppink", Color(1.00, 0.08, 0.58) },
+	{ "deepskyblue", Color(0.00, 0.75, 1.00) },
+	{ "dimgray", Color(0.41, 0.41, 0.41) },
+	{ "dodgerblue", Color(0.12, 0.56, 1.00) },
+	{ "firebrick", Color(0.70, 0.13, 0.13) },
+	{ "floralwhite", Color(1.00, 0.98, 0.94) },
+	{ "forestgreen", Color(0.13, 0.55, 0.13) },
+	{ "fuchsia", Color(1.00, 0.00, 1.00) },
+	{ "gainsboro", Color(0.86, 0.86, 0.86) },
+	{ "ghostwhite", Color(0.97, 0.97, 1.00) },
+	{ "gold", Color(1.00, 0.84, 0.00) },
+	{ "goldenrod", Color(0.85, 0.65, 0.13) },
+	{ "gray", Color(0.75, 0.75, 0.75) },
+	{ "green", Color(0.00, 1.00, 0.00) },
+	{ "greenyellow", Color(0.68, 1.00, 0.18) },
+	{ "honeydew", Color(0.94, 1.00, 0.94) },
+	{ "hotpink", Color(1.00, 0.41, 0.71) },
+	{ "indianred", Color(0.80, 0.36, 0.36) },
+	{ "indigo", Color(0.29, 0.00, 0.51) },
+	{ "ivory", Color(1.00, 1.00, 0.94) },
+	{ "khaki", Color(0.94, 0.90, 0.55) },
+	{ "lavender", Color(0.90, 0.90, 0.98) },
+	{ "lavenderblush", Color(1.00, 0.94, 0.96) },
+	{ "lawngreen", Color(0.49, 0.99, 0.00) },
+	{ "lemonchiffon", Color(1.00, 0.98, 0.80) },
+	{ "lightblue", Color(0.68, 0.85, 0.90) },
+	{ "lightcoral", Color(0.94, 0.50, 0.50) },
+	{ "lightcyan", Color(0.88, 1.00, 1.00) },
+	{ "lightgoldenrod", Color(0.98, 0.98, 0.82) },
+	{ "lightgray", Color(0.83, 0.83, 0.83) },
+	{ "lightgreen", Color(0.56, 0.93, 0.56) },
+	{ "lightpink", Color(1.00, 0.71, 0.76) },
+	{ "lightsalmon", Color(1.00, 0.63, 0.48) },
+	{ "lightseagreen", Color(0.13, 0.70, 0.67) },
+	{ "lightskyblue", Color(0.53, 0.81, 0.98) },
+	{ "lightslategray", Color(0.47, 0.53, 0.60) },
+	{ "lightsteelblue", Color(0.69, 0.77, 0.87) },
+	{ "lightyellow", Color(1.00, 1.00, 0.88) },
+	{ "lime", Color(0.00, 1.00, 0.00) },
+	{ "limegreen", Color(0.20, 0.80, 0.20) },
+	{ "linen", Color(0.98, 0.94, 0.90) },
+	{ "magenta", Color(1.00, 0.00, 1.00) },
+	{ "maroon", Color(0.69, 0.19, 0.38) },
+	{ "mediumaquamarine", Color(0.40, 0.80, 0.67) },
+	{ "mediumblue", Color(0.00, 0.00, 0.80) },
+	{ "mediumorchid", Color(0.73, 0.33, 0.83) },
+	{ "mediumpurple", Color(0.58, 0.44, 0.86) },
+	{ "mediumseagreen", Color(0.24, 0.70, 0.44) },
+	{ "mediumslateblue", Color(0.48, 0.41, 0.93) },
+	{ "mediumspringgreen", Color(0.00, 0.98, 0.60) },
+	{ "mediumturquoise", Color(0.28, 0.82, 0.80) },
+	{ "mediumvioletred", Color(0.78, 0.08, 0.52) },
+	{ "midnightblue", Color(0.10, 0.10, 0.44) },
+	{ "mintcream", Color(0.96, 1.00, 0.98) },
+	{ "mistyrose", Color(1.00, 0.89, 0.88) },
+	{ "moccasin", Color(1.00, 0.89, 0.71) },
+	{ "navajowhite", Color(1.00, 0.87, 0.68) },
+	{ "navyblue", Color(0.00, 0.00, 0.50) },
+	{ "oldlace", Color(0.99, 0.96, 0.90) },
+	{ "olive", Color(0.50, 0.50, 0.00) },
+	{ "olivedrab", Color(0.42, 0.56, 0.14) },
+	{ "orange", Color(1.00, 0.65, 0.00) },
+	{ "orangered", Color(1.00, 0.27, 0.00) },
+	{ "orchid", Color(0.85, 0.44, 0.84) },
+	{ "palegoldenrod", Color(0.93, 0.91, 0.67) },
+	{ "palegreen", Color(0.60, 0.98, 0.60) },
+	{ "paleturquoise", Color(0.69, 0.93, 0.93) },
+	{ "palevioletred", Color(0.86, 0.44, 0.58) },
+	{ "papayawhip", Color(1.00, 0.94, 0.84) },
+	{ "peachpuff", Color(1.00, 0.85, 0.73) },
+	{ "peru", Color(0.80, 0.52, 0.25) },
+	{ "pink", Color(1.00, 0.75, 0.80) },
+	{ "plum", Color(0.87, 0.63, 0.87) },
+	{ "powderblue", Color(0.69, 0.88, 0.90) },
+	{ "purple", Color(0.63, 0.13, 0.94) },
+	{ "rebeccapurple", Color(0.40, 0.20, 0.60) },
+	{ "red", Color(1.00, 0.00, 0.00) },
+	{ "rosybrown", Color(0.74, 0.56, 0.56) },
+	{ "royalblue", Color(0.25, 0.41, 0.88) },
+	{ "saddlebrown", Color(0.55, 0.27, 0.07) },
+	{ "salmon", Color(0.98, 0.50, 0.45) },
+	{ "sandybrown", Color(0.96, 0.64, 0.38) },
+	{ "seagreen", Color(0.18, 0.55, 0.34) },
+	{ "seashell", Color(1.00, 0.96, 0.93) },
+	{ "sienna", Color(0.63, 0.32, 0.18) },
+	{ "silver", Color(0.75, 0.75, 0.75) },
+	{ "skyblue", Color(0.53, 0.81, 0.92) },
+	{ "slateblue", Color(0.42, 0.35, 0.80) },
+	{ "slategray", Color(0.44, 0.50, 0.56) },
+	{ "snow", Color(1.00, 0.98, 0.98) },
+	{ "springgreen", Color(0.00, 1.00, 0.50) },
+	{ "steelblue", Color(0.27, 0.51, 0.71) },
+	{ "tan", Color(0.82, 0.71, 0.55) },
+	{ "teal", Color(0.00, 0.50, 0.50) },
+	{ "thistle", Color(0.85, 0.75, 0.85) },
+	{ "tomato", Color(1.00, 0.39, 0.28) },
+	{ "transparent", Color(1.00, 1.00, 1.00, 0.00) },
+	{ "turquoise", Color(0.25, 0.88, 0.82) },
+	{ "violet", Color(0.93, 0.51, 0.93) },
+	{ "webgray", Color(0.50, 0.50, 0.50) },
+	{ "webgreen", Color(0.00, 0.50, 0.00) },
+	{ "webmaroon", Color(0.50, 0.00, 0.00) },
+	{ "webpurple", Color(0.50, 0.00, 0.50) },
+	{ "wheat", Color(0.96, 0.87, 0.70) },
+	{ "white", Color(1.00, 1.00, 1.00) },
+	{ "whitesmoke", Color(0.96, 0.96, 0.96) },
+	{ "yellow", Color(1.00, 1.00, 0.00) },
+	{ "yellowgreen", Color(0.60, 0.80, 0.20) },
+	{ nullptr, Color() },
+};
+
+} // namespace godot

include/godot_cpp/variant/plane.hpp

@@ -0,0 +1,106 @@
+#ifndef GODOT_PLANE_HPP
+#define GODOT_PLANE_HPP
+
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/vector3.hpp>
+#include <godot_cpp/classes/global_constants.hpp>
+
+namespace godot {
+
+class Plane {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	Vector3 normal;
+	real_t d = 0;
+
+	void set_normal(const Vector3 &p_normal);
+	inline Vector3 get_normal() const { return normal; }; ///Point is coplanar, CMP_EPSILON for precision
+
+	void normalize();
+	Plane normalized() const;
+
+	/* Plane-Point operations */
+
+	inline Vector3 center() const { return normal * d; }
+	Vector3 get_any_perpendicular_normal() const;
+
+	inline bool is_point_over(const Vector3 &p_point) const; ///< Point is over plane
+	inline real_t distance_to(const Vector3 &p_point) const;
+	inline bool has_point(const Vector3 &p_point, real_t _epsilon = CMP_EPSILON) const;
+
+	/* intersections */
+
+	bool intersect_3(const Plane &p_plane1, const Plane &p_plane2, Vector3 *r_result = nullptr) const;
+	bool intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection) const;
+	bool intersects_segment(const Vector3 &p_begin, const Vector3 &p_end, Vector3 *p_intersection) const;
+
+	inline Vector3 project(const Vector3 &p_point) const {
+		return p_point - normal * distance_to(p_point);
+	}
+
+	/* misc */
+
+	Plane operator-() const { return Plane(-normal, -d); }
+	bool is_equal_approx(const Plane &p_plane) const;
+	bool is_equal_approx_any_side(const Plane &p_plane) const;
+
+	inline bool operator==(const Plane &p_plane) const;
+	inline bool operator!=(const Plane &p_plane) const;
+	operator String() const;
+
+	inline Plane() {}
+	inline Plane(real_t p_a, real_t p_b, real_t p_c, real_t p_d) :
+			normal(p_a, p_b, p_c),
+			d(p_d) {}
+
+	inline Plane(const Vector3 &p_normal, real_t p_d);
+	inline Plane(const Vector3 &p_point, const Vector3 &p_normal);
+	inline Plane(const Vector3 &p_point1, const Vector3 &p_point2, const Vector3 &p_point3, ClockDirection p_dir = CLOCKWISE);
+};
+
+bool Plane::is_point_over(const Vector3 &p_point) const {
+	return (normal.dot(p_point) > d);
+}
+
+real_t Plane::distance_to(const Vector3 &p_point) const {
+	return (normal.dot(p_point) - d);
+}
+
+bool Plane::has_point(const Vector3 &p_point, real_t _epsilon) const {
+	real_t dist = normal.dot(p_point) - d;
+	dist = Math::abs(dist);
+	return (dist <= _epsilon);
+}
+
+Plane::Plane(const Vector3 &p_normal, real_t p_d) :
+		normal(p_normal),
+		d(p_d) {
+}
+
+Plane::Plane(const Vector3 &p_point, const Vector3 &p_normal) :
+		normal(p_normal),
+		d(p_normal.dot(p_point)) {
+}
+
+Plane::Plane(const Vector3 &p_point1, const Vector3 &p_point2, const Vector3 &p_point3, ClockDirection p_dir) {
+	if (p_dir == CLOCKWISE) {
+		normal = (p_point1 - p_point3).cross(p_point1 - p_point2);
+	} else {
+		normal = (p_point1 - p_point2).cross(p_point1 - p_point3);
+	}
+
+	normal.normalize();
+	d = normal.dot(p_point1);
+}
+
+bool Plane::operator==(const Plane &p_plane) const {
+	return normal == p_plane.normal && d == p_plane.d;
+}
+
+bool Plane::operator!=(const Plane &p_plane) const {
+	return normal != p_plane.normal || d != p_plane.d;
+}
+} // namespace godot
+
+#endif // GODOT_PLANE_HPP

include/godot_cpp/variant/quaternion.hpp

@@ -0,0 +1,212 @@
+#ifndef GODOT_QUAT_HPP
+#define GODOT_QUAT_HPP
+
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/vector3.hpp>
+
+namespace godot {
+
+class Quaternion {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	union {
+		struct {
+			real_t x;
+			real_t y;
+			real_t z;
+			real_t w;
+		};
+		real_t components[4] = { 0, 0, 0, 1.0 };
+	};
+
+	inline real_t &operator[](int idx) {
+		return components[idx];
+	}
+	inline const real_t &operator[](int idx) const {
+		return components[idx];
+	}
+	inline real_t length_squared() const;
+	bool is_equal_approx(const Quaternion &p_quat) const;
+	real_t length() const;
+	void normalize();
+	Quaternion normalized() const;
+	bool is_normalized() const;
+	Quaternion inverse() const;
+	inline real_t dot(const Quaternion &p_q) const;
+
+	Vector3 get_euler_xyz() const;
+	Vector3 get_euler_yxz() const;
+	Vector3 get_euler() const { return get_euler_yxz(); };
+
+	Quaternion slerp(const Quaternion &p_to, const real_t &p_weight) const;
+	Quaternion slerpni(const Quaternion &p_to, const real_t &p_weight) const;
+	Quaternion cubic_slerp(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const;
+
+	inline void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
+		r_angle = 2 * Math::acos(w);
+		real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
+		r_axis.x = x * r;
+		r_axis.y = y * r;
+		r_axis.z = z * r;
+	}
+
+	void operator*=(const Quaternion &p_q);
+	Quaternion operator*(const Quaternion &p_q) const;
+
+	Quaternion operator*(const Vector3 &v) const {
+		return Quaternion(w * v.x + y * v.z - z * v.y,
+				w * v.y + z * v.x - x * v.z,
+				w * v.z + x * v.y - y * v.x,
+				-x * v.x - y * v.y - z * v.z);
+	}
+
+	inline Vector3 xform(const Vector3 &v) const {
+#ifdef MATH_CHECKS
+		ERR_FAIL_COND_V(!is_normalized(), v);
+#endif
+		Vector3 u(x, y, z);
+		Vector3 uv = u.cross(v);
+		return v + ((uv * w) + u.cross(uv)) * ((real_t)2);
+	}
+
+	inline Vector3 xform_inv(const Vector3 &v) const {
+		return inverse().xform(v);
+	}
+
+	inline void operator+=(const Quaternion &p_q);
+	inline void operator-=(const Quaternion &p_q);
+	inline void operator*=(const real_t &s);
+	inline void operator/=(const real_t &s);
+	inline Quaternion operator+(const Quaternion &q2) const;
+	inline Quaternion operator-(const Quaternion &q2) const;
+	inline Quaternion operator-() const;
+	inline Quaternion operator*(const real_t &s) const;
+	inline Quaternion operator/(const real_t &s) const;
+
+	inline bool operator==(const Quaternion &p_quat) const;
+	inline bool operator!=(const Quaternion &p_quat) const;
+
+	operator String() const;
+
+	inline Quaternion() {}
+
+	inline Quaternion(real_t p_x, real_t p_y, real_t p_z, real_t p_w) :
+			x(p_x),
+			y(p_y),
+			z(p_z),
+			w(p_w) {
+	}
+
+	Quaternion(const Vector3 &p_axis, real_t p_angle);
+
+	Quaternion(const Vector3 &p_euler);
+
+	Quaternion(const Quaternion &p_q) :
+			x(p_q.x),
+			y(p_q.y),
+			z(p_q.z),
+			w(p_q.w) {
+	}
+
+	Quaternion &operator=(const Quaternion &p_q) {
+		x = p_q.x;
+		y = p_q.y;
+		z = p_q.z;
+		w = p_q.w;
+		return *this;
+	}
+
+	Quaternion(const Vector3 &v0, const Vector3 &v1) // shortest arc
+	{
+		Vector3 c = v0.cross(v1);
+		real_t d = v0.dot(v1);
+
+		if (d < -1.0 + CMP_EPSILON) {
+			x = 0;
+			y = 1;
+			z = 0;
+			w = 0;
+		} else {
+			real_t s = Math::sqrt((1.0 + d) * 2.0);
+			real_t rs = 1.0 / s;
+
+			x = c.x * rs;
+			y = c.y * rs;
+			z = c.z * rs;
+			w = s * 0.5;
+		}
+	}
+};
+
+real_t Quaternion::dot(const Quaternion &p_q) const {
+	return x * p_q.x + y * p_q.y + z * p_q.z + w * p_q.w;
+}
+
+real_t Quaternion::length_squared() const {
+	return dot(*this);
+}
+
+void Quaternion::operator+=(const Quaternion &p_q) {
+	x += p_q.x;
+	y += p_q.y;
+	z += p_q.z;
+	w += p_q.w;
+}
+
+void Quaternion::operator-=(const Quaternion &p_q) {
+	x -= p_q.x;
+	y -= p_q.y;
+	z -= p_q.z;
+	w -= p_q.w;
+}
+
+void Quaternion::operator*=(const real_t &s) {
+	x *= s;
+	y *= s;
+	z *= s;
+	w *= s;
+}
+
+void Quaternion::operator/=(const real_t &s) {
+	*this *= 1.0 / s;
+}
+
+Quaternion Quaternion::operator+(const Quaternion &q2) const {
+	const Quaternion &q1 = *this;
+	return Quaternion(q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w);
+}
+
+Quaternion Quaternion::operator-(const Quaternion &q2) const {
+	const Quaternion &q1 = *this;
+	return Quaternion(q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w);
+}
+
+Quaternion Quaternion::operator-() const {
+	const Quaternion &q2 = *this;
+	return Quaternion(-q2.x, -q2.y, -q2.z, -q2.w);
+}
+
+Quaternion Quaternion::operator*(const real_t &s) const {
+	return Quaternion(x * s, y * s, z * s, w * s);
+}
+
+Quaternion Quaternion::operator/(const real_t &s) const {
+	return *this * (1.0 / s);
+}
+
+bool Quaternion::operator==(const Quaternion &p_quat) const {
+	return x == p_quat.x && y == p_quat.y && z == p_quat.z && w == p_quat.w;
+}
+
+bool Quaternion::operator!=(const Quaternion &p_quat) const {
+	return x != p_quat.x || y != p_quat.y || z != p_quat.z || w != p_quat.w;
+}
+
+inline Quaternion operator*(const real_t &p_real, const Quaternion &p_quat) {
+	return p_quat * p_real;
+}
+
+} // namespace godot
+
+#endif // GODOT_QUAT_HPP

include/godot_cpp/variant/rect2.hpp

@@ -0,0 +1,312 @@
+
+#ifndef GODOT_RECT2_HPP
+#define GODOT_RECT2_HPP
+
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/vector2.hpp>
+#include <godot_cpp/classes/global_constants.hpp>
+
+namespace godot {
+
+struct Transform2D;
+
+class Rect2 {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	Point2 position;
+	Size2 size;
+
+	const Vector2 &get_position() const { return position; }
+	void set_position(const Vector2 &p_pos) { position = p_pos; }
+	const Vector2 &get_size() const { return size; }
+	void set_size(const Vector2 &p_size) { size = p_size; }
+
+	real_t get_area() const { return size.width * size.height; }
+
+	inline bool intersects(const Rect2 &p_rect, const bool p_include_borders = false) const {
+		if (p_include_borders) {
+			if (position.x > (p_rect.position.x + p_rect.size.width)) {
+				return false;
+			}
+			if ((position.x + size.width) < p_rect.position.x) {
+				return false;
+			}
+			if (position.y > (p_rect.position.y + p_rect.size.height)) {
+				return false;
+			}
+			if ((position.y + size.height) < p_rect.position.y) {
+				return false;
+			}
+		} else {
+			if (position.x >= (p_rect.position.x + p_rect.size.width)) {
+				return false;
+			}
+			if ((position.x + size.width) <= p_rect.position.x) {
+				return false;
+			}
+			if (position.y >= (p_rect.position.y + p_rect.size.height)) {
+				return false;
+			}
+			if ((position.y + size.height) <= p_rect.position.y) {
+				return false;
+			}
+		}
+
+		return true;
+	}
+
+	inline real_t distance_to(const Vector2 &p_point) const {
+		real_t dist = 0.0;
+		bool inside = true;
+
+		if (p_point.x < position.x) {
+			real_t d = position.x - p_point.x;
+			dist = d;
+			inside = false;
+		}
+		if (p_point.y < position.y) {
+			real_t d = position.y - p_point.y;
+			dist = inside ? d : Math::min(dist, d);
+			inside = false;
+		}
+		if (p_point.x >= (position.x + size.x)) {
+			real_t d = p_point.x - (position.x + size.x);
+			dist = inside ? d : Math::min(dist, d);
+			inside = false;
+		}
+		if (p_point.y >= (position.y + size.y)) {
+			real_t d = p_point.y - (position.y + size.y);
+			dist = inside ? d : Math::min(dist, d);
+			inside = false;
+		}
+
+		if (inside) {
+			return 0;
+		} else {
+			return dist;
+		}
+	}
+
+	bool intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const;
+
+	bool intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos = nullptr, Point2 *r_normal = nullptr) const;
+
+	inline bool encloses(const Rect2 &p_rect) const {
+		return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
+			   ((p_rect.position.x + p_rect.size.x) <= (position.x + size.x)) &&
+			   ((p_rect.position.y + p_rect.size.y) <= (position.y + size.y));
+	}
+
+	inline bool has_no_area() const {
+		return (size.x <= 0 || size.y <= 0);
+	}
+
+	// Returns the instersection between two Rect2s or an empty Rect2 if there is no intersection
+	inline Rect2 intersection(const Rect2 &p_rect) const {
+		Rect2 new_rect = p_rect;
+
+		if (!intersects(new_rect)) {
+			return Rect2();
+		}
+
+		new_rect.position.x = Math::max(p_rect.position.x, position.x);
+		new_rect.position.y = Math::max(p_rect.position.y, position.y);
+
+		Point2 p_rect_end = p_rect.position + p_rect.size;
+		Point2 end = position + size;
+
+		new_rect.size.x = Math::min(p_rect_end.x, end.x) - new_rect.position.x;
+		new_rect.size.y = Math::min(p_rect_end.y, end.y) - new_rect.position.y;
+
+		return new_rect;
+	}
+
+	inline Rect2 merge(const Rect2 &p_rect) const { ///< return a merged rect
+
+		Rect2 new_rect;
+
+		new_rect.position.x = Math::min(p_rect.position.x, position.x);
+		new_rect.position.y = Math::min(p_rect.position.y, position.y);
+
+		new_rect.size.x = Math::max(p_rect.position.x + p_rect.size.x, position.x + size.x);
+		new_rect.size.y = Math::max(p_rect.position.y + p_rect.size.y, position.y + size.y);
+
+		new_rect.size = new_rect.size - new_rect.position; //make relative again
+
+		return new_rect;
+	}
+	inline bool has_point(const Point2 &p_point) const {
+		if (p_point.x < position.x) {
+			return false;
+		}
+		if (p_point.y < position.y) {
+			return false;
+		}
+
+		if (p_point.x >= (position.x + size.x)) {
+			return false;
+		}
+		if (p_point.y >= (position.y + size.y)) {
+			return false;
+		}
+
+		return true;
+	}
+	bool is_equal_approx(const Rect2 &p_rect) const;
+
+	bool operator==(const Rect2 &p_rect) const { return position == p_rect.position && size == p_rect.size; }
+	bool operator!=(const Rect2 &p_rect) const { return position != p_rect.position || size != p_rect.size; }
+
+	inline Rect2 grow(real_t p_amount) const {
+		Rect2 g = *this;
+		g.position.x -= p_amount;
+		g.position.y -= p_amount;
+		g.size.width += p_amount * 2;
+		g.size.height += p_amount * 2;
+		return g;
+	}
+
+	inline Rect2 grow_side(Side p_side, real_t p_amount) const {
+		Rect2 g = *this;
+		g = g.grow_individual((SIDE_LEFT == p_side) ? p_amount : 0,
+				(SIDE_TOP == p_side) ? p_amount : 0,
+				(SIDE_RIGHT == p_side) ? p_amount : 0,
+				(SIDE_BOTTOM == p_side) ? p_amount : 0);
+		return g;
+	}
+
+	inline Rect2 grow_side_bind(uint32_t p_side, real_t p_amount) const {
+		return grow_side(Side(p_side), p_amount);
+	}
+
+	inline Rect2 grow_individual(real_t p_left, real_t p_top, real_t p_right, real_t p_bottom) const {
+		Rect2 g = *this;
+		g.position.x -= p_left;
+		g.position.y -= p_top;
+		g.size.width += p_left + p_right;
+		g.size.height += p_top + p_bottom;
+
+		return g;
+	}
+
+	inline Rect2 expand(const Vector2 &p_vector) const {
+		Rect2 r = *this;
+		r.expand_to(p_vector);
+		return r;
+	}
+
+	inline void expand_to(const Vector2 &p_vector) { //in place function for speed
+
+		Vector2 begin = position;
+		Vector2 end = position + size;
+
+		if (p_vector.x < begin.x) {
+			begin.x = p_vector.x;
+		}
+		if (p_vector.y < begin.y) {
+			begin.y = p_vector.y;
+		}
+
+		if (p_vector.x > end.x) {
+			end.x = p_vector.x;
+		}
+		if (p_vector.y > end.y) {
+			end.y = p_vector.y;
+		}
+
+		position = begin;
+		size = end - begin;
+	}
+
+	inline Rect2 abs() const {
+		return Rect2(Point2(position.x + Math::min(size.x, (real_t)0), position.y + Math::min(size.y, (real_t)0)), size.abs());
+	}
+
+	Vector2 get_support(const Vector2 &p_normal) const {
+		Vector2 half_extents = size * 0.5;
+		Vector2 ofs = position + half_extents;
+		return Vector2(
+					   (p_normal.x > 0) ? -half_extents.x : half_extents.x,
+					   (p_normal.y > 0) ? -half_extents.y : half_extents.y) +
+			   ofs;
+	}
+
+	inline bool intersects_filled_polygon(const Vector2 *p_points, int p_point_count) const {
+		Vector2 center = position + size * 0.5;
+		int side_plus = 0;
+		int side_minus = 0;
+		Vector2 end = position + size;
+
+		int i_f = p_point_count - 1;
+		for (int i = 0; i < p_point_count; i++) {
+			const Vector2 &a = p_points[i_f];
+			const Vector2 &b = p_points[i];
+			i_f = i;
+
+			Vector2 r = (b - a);
+			float l = r.length();
+			if (l == 0.0) {
+				continue;
+			}
+
+			//check inside
+			Vector2 tg = r.orthogonal();
+			float s = tg.dot(center) - tg.dot(a);
+			if (s < 0.0) {
+				side_plus++;
+			} else {
+				side_minus++;
+			}
+
+			//check ray box
+			r /= l;
+			Vector2 ir(1.0 / r.x, 1.0 / r.y);
+
+			// lb is the corner of AABB with minimal coordinates - left bottom, rt is maximal corner
+			// r.org is origin of ray
+			Vector2 t13 = (position - a) * ir;
+			Vector2 t24 = (end - a) * ir;
+
+			float tmin = Math::max(Math::min(t13.x, t24.x), Math::min(t13.y, t24.y));
+			float tmax = Math::min(Math::max(t13.x, t24.x), Math::max(t13.y, t24.y));
+
+			// if tmax < 0, ray (line) is intersecting AABB, but the whole AABB is behind us
+			if (tmax < 0 || tmin > tmax || tmin >= l) {
+				continue;
+			}
+
+			return true;
+		}
+
+		if (side_plus * side_minus == 0) {
+			return true; //all inside
+		} else {
+			return false;
+		}
+	}
+
+	inline void set_end(const Vector2 &p_end) {
+		size = p_end - position;
+	}
+
+	inline Vector2 get_end() const {
+		return position + size;
+	}
+
+	operator String() const;
+
+	Rect2() {}
+	Rect2(real_t p_x, real_t p_y, real_t p_width, real_t p_height) :
+			position(Point2(p_x, p_y)),
+			size(Size2(p_width, p_height)) {
+	}
+	Rect2(const Point2 &p_pos, const Size2 &p_size) :
+			position(p_pos),
+			size(p_size) {
+	}
+};
+
+} // namespace godot
+
+#endif // GODOT_RECT2_HPP

include/godot_cpp/variant/rect2i.hpp

@@ -0,0 +1,198 @@
+#ifndef GODOT_RECT2I_HPP
+#define GODOT_RECT2I_HPP
+
+#include <godot_cpp/variant/rect2.hpp>
+#include <godot_cpp/variant/vector2i.hpp>
+
+namespace godot {
+
+class Rect2i {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	Point2i position;
+	Size2i size;
+
+	const Point2i &get_position() const { return position; }
+	void set_position(const Point2i &p_position) { position = p_position; }
+	const Size2i &get_size() const { return size; }
+	void set_size(const Size2i &p_size) { size = p_size; }
+
+	int get_area() const { return size.width * size.height; }
+
+	inline bool intersects(const Rect2i &p_rect) const {
+		if (position.x > (p_rect.position.x + p_rect.size.width)) {
+			return false;
+		}
+		if ((position.x + size.width) < p_rect.position.x) {
+			return false;
+		}
+		if (position.y > (p_rect.position.y + p_rect.size.height)) {
+			return false;
+		}
+		if ((position.y + size.height) < p_rect.position.y) {
+			return false;
+		}
+
+		return true;
+	}
+
+	inline bool encloses(const Rect2i &p_rect) const {
+		return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
+			   ((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) &&
+			   ((p_rect.position.y + p_rect.size.y) < (position.y + size.y));
+	}
+
+	inline bool has_no_area() const {
+		return (size.x <= 0 || size.y <= 0);
+	}
+
+	// Returns the instersection between two Rect2is or an empty Rect2i if there is no intersection
+	inline Rect2i intersection(const Rect2i &p_rect) const {
+		Rect2i new_rect = p_rect;
+
+		if (!intersects(new_rect)) {
+			return Rect2i();
+		}
+
+		new_rect.position.x = Math::max(p_rect.position.x, position.x);
+		new_rect.position.y = Math::max(p_rect.position.y, position.y);
+
+		Point2i p_rect_end = p_rect.position + p_rect.size;
+		Point2i end = position + size;
+
+		new_rect.size.x = (int)(Math::min(p_rect_end.x, end.x) - new_rect.position.x);
+		new_rect.size.y = (int)(Math::min(p_rect_end.y, end.y) - new_rect.position.y);
+
+		return new_rect;
+	}
+
+	inline Rect2i merge(const Rect2i &p_rect) const { ///< return a merged rect
+
+		Rect2i new_rect;
+
+		new_rect.position.x = Math::min(p_rect.position.x, position.x);
+		new_rect.position.y = Math::min(p_rect.position.y, position.y);
+
+		new_rect.size.x = Math::max(p_rect.position.x + p_rect.size.x, position.x + size.x);
+		new_rect.size.y = Math::max(p_rect.position.y + p_rect.size.y, position.y + size.y);
+
+		new_rect.size = new_rect.size - new_rect.position; //make relative again
+
+		return new_rect;
+	}
+	bool has_point(const Point2i &p_point) const {
+		if (p_point.x < position.x) {
+			return false;
+		}
+		if (p_point.y < position.y) {
+			return false;
+		}
+
+		if (p_point.x >= (position.x + size.x)) {
+			return false;
+		}
+		if (p_point.y >= (position.y + size.y)) {
+			return false;
+		}
+
+		return true;
+	}
+
+	bool operator==(const Rect2i &p_rect) const { return position == p_rect.position && size == p_rect.size; }
+	bool operator!=(const Rect2i &p_rect) const { return position != p_rect.position || size != p_rect.size; }
+
+	Rect2i grow(int p_amount) const {
+		Rect2i g = *this;
+		g.position.x -= p_amount;
+		g.position.y -= p_amount;
+		g.size.width += p_amount * 2;
+		g.size.height += p_amount * 2;
+		return g;
+	}
+
+	inline Rect2i grow_side(Side p_side, int p_amount) const {
+		Rect2i g = *this;
+		g = g.grow_individual((SIDE_LEFT == p_side) ? p_amount : 0,
+				(SIDE_TOP == p_side) ? p_amount : 0,
+				(SIDE_RIGHT == p_side) ? p_amount : 0,
+				(SIDE_BOTTOM == p_side) ? p_amount : 0);
+		return g;
+	}
+
+	inline Rect2i grow_side_bind(uint32_t p_side, int p_amount) const {
+		return grow_side(Side(p_side), p_amount);
+	}
+
+	inline Rect2i grow_individual(int p_left, int p_top, int p_right, int p_bottom) const {
+		Rect2i g = *this;
+		g.position.x -= p_left;
+		g.position.y -= p_top;
+		g.size.width += p_left + p_right;
+		g.size.height += p_top + p_bottom;
+
+		return g;
+	}
+
+	inline Rect2i expand(const Vector2i &p_vector) const {
+		Rect2i r = *this;
+		r.expand_to(p_vector);
+		return r;
+	}
+
+	inline void expand_to(const Point2i &p_vector) {
+		Point2i begin = position;
+		Point2i end = position + size;
+
+		if (p_vector.x < begin.x) {
+			begin.x = p_vector.x;
+		}
+		if (p_vector.y < begin.y) {
+			begin.y = p_vector.y;
+		}
+
+		if (p_vector.x > end.x) {
+			end.x = p_vector.x;
+		}
+		if (p_vector.y > end.y) {
+			end.y = p_vector.y;
+		}
+
+		position = begin;
+		size = end - begin;
+	}
+
+	inline Rect2i abs() const {
+		return Rect2i(Point2i(position.x + Math::min(size.x, 0), position.y + Math::min(size.y, 0)), size.abs());
+	}
+
+	inline void set_end(const Vector2i &p_end) {
+		size = p_end - position;
+	}
+
+	inline Vector2i get_end() const {
+		return position + size;
+	}
+
+	operator String() const { return String(position) + ", " + String(size); }
+
+	operator Rect2() const { return Rect2(position, size); }
+
+	Rect2i() {}
+	Rect2i(const Rect2 &p_r2) :
+			position(p_r2.position),
+			size(p_r2.size) {
+	}
+	Rect2i(int p_x, int p_y, int p_width, int p_height) :
+			position(Point2i(p_x, p_y)),
+			size(Size2i(p_width, p_height)) {
+	}
+	Rect2i(const Point2i &p_pos, const Size2i &p_size) :
+			position(p_pos),
+			size(p_size) {
+	}
+};
+
+} // namespace godot
+
+#endif // GODOT_RECT2I_HPP

include/godot_cpp/variant/transform2d.hpp

@@ -0,0 +1,216 @@
+#ifndef GODOT_TRANSFORM2D_HPP
+#define GODOT_TRANSFORM2D_HPP
+
+#include <godot_cpp/core/error_macros.hpp>
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/packed_vector2_array.hpp>
+#include <godot_cpp/variant/rect2.hpp>
+#include <godot_cpp/variant/vector2.hpp>
+
+namespace godot {
+
+class Transform2D {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	// Warning #1: basis of Transform2D is stored differently from Basis. In terms of elements array, the basis matrix looks like "on paper":
+	// M = (elements[0][0] elements[1][0])
+	//     (elements[0][1] elements[1][1])
+	// This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as elements[i].
+	// Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to elements[1][0] here.
+	// This requires additional care when working with explicit indices.
+	// See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading.
+
+	// Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down,
+	// and angle is measure from +X to +Y in a clockwise-fashion.
+
+	Vector2 elements[3];
+
+	inline real_t tdotx(const Vector2 &v) const { return elements[0][0] * v.x + elements[1][0] * v.y; }
+	inline real_t tdoty(const Vector2 &v) const { return elements[0][1] * v.x + elements[1][1] * v.y; }
+
+	const Vector2 &operator[](int p_idx) const { return elements[p_idx]; }
+	Vector2 &operator[](int p_idx) { return elements[p_idx]; }
+
+	inline Vector2 get_axis(int p_axis) const {
+		ERR_FAIL_INDEX_V(p_axis, 3, Vector2());
+		return elements[p_axis];
+	}
+	inline void set_axis(int p_axis, const Vector2 &p_vec) {
+		ERR_FAIL_INDEX(p_axis, 3);
+		elements[p_axis] = p_vec;
+	}
+
+	void invert();
+	Transform2D inverse() const;
+
+	void affine_invert();
+	Transform2D affine_inverse() const;
+
+	void set_rotation(real_t p_rot);
+	real_t get_rotation() const;
+	real_t get_skew() const;
+	void set_skew(float p_angle);
+	inline void set_rotation_and_scale(real_t p_rot, const Size2 &p_scale);
+	inline void set_rotation_scale_and_skew(real_t p_rot, const Size2 &p_scale, float p_skew);
+	void rotate(real_t p_phi);
+
+	void scale(const Size2 &p_scale);
+	void scale_basis(const Size2 &p_scale);
+	void translate(real_t p_tx, real_t p_ty);
+	void translate(const Vector2 &p_translation);
+
+	real_t basis_determinant() const;
+
+	Size2 get_scale() const;
+	void set_scale(const Size2 &p_scale);
+
+	inline const Vector2 &get_origin() const { return elements[2]; }
+	inline void set_origin(const Vector2 &p_origin) { elements[2] = p_origin; }
+
+	Transform2D scaled(const Size2 &p_scale) const;
+	Transform2D basis_scaled(const Size2 &p_scale) const;
+	Transform2D translated(const Vector2 &p_offset) const;
+	Transform2D rotated(real_t p_phi) const;
+
+	Transform2D untranslated() const;
+
+	void orthonormalize();
+	Transform2D orthonormalized() const;
+	bool is_equal_approx(const Transform2D &p_transform) const;
+
+	bool operator==(const Transform2D &p_transform) const;
+	bool operator!=(const Transform2D &p_transform) const;
+
+	void operator*=(const Transform2D &p_transform);
+	Transform2D operator*(const Transform2D &p_transform) const;
+
+	Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const;
+
+	inline Vector2 basis_xform(const Vector2 &p_vec) const;
+	inline Vector2 basis_xform_inv(const Vector2 &p_vec) const;
+	inline Vector2 xform(const Vector2 &p_vec) const;
+	inline Vector2 xform_inv(const Vector2 &p_vec) const;
+	inline Rect2 xform(const Rect2 &p_rect) const;
+	inline Rect2 xform_inv(const Rect2 &p_rect) const;
+	inline PackedVector2Array xform(const PackedVector2Array &p_array) const;
+	inline PackedVector2Array xform_inv(const PackedVector2Array &p_array) const;
+
+	operator String() const;
+
+	Transform2D(real_t xx, real_t xy, real_t yx, real_t yy, real_t ox, real_t oy) {
+		elements[0][0] = xx;
+		elements[0][1] = xy;
+		elements[1][0] = yx;
+		elements[1][1] = yy;
+		elements[2][0] = ox;
+		elements[2][1] = oy;
+	}
+
+	Transform2D(const Vector2 &p_x, const Vector2 &p_y, const Vector2 &p_origin) {
+		elements[0] = p_x;
+		elements[1] = p_y;
+		elements[2] = p_origin;
+	}
+
+	Transform2D(real_t p_rot, const Vector2 &p_pos);
+	Transform2D() {
+		elements[0][0] = 1.0;
+		elements[1][1] = 1.0;
+	}
+};
+
+Vector2 Transform2D::basis_xform(const Vector2 &p_vec) const {
+	return Vector2(
+			tdotx(p_vec),
+			tdoty(p_vec));
+}
+
+Vector2 Transform2D::basis_xform_inv(const Vector2 &p_vec) const {
+	return Vector2(
+			elements[0].dot(p_vec),
+			elements[1].dot(p_vec));
+}
+
+Vector2 Transform2D::xform(const Vector2 &p_vec) const {
+	return Vector2(
+				   tdotx(p_vec),
+				   tdoty(p_vec)) +
+		   elements[2];
+}
+
+Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const {
+	Vector2 v = p_vec - elements[2];
+
+	return Vector2(
+			elements[0].dot(v),
+			elements[1].dot(v));
+}
+
+Rect2 Transform2D::xform(const Rect2 &p_rect) const {
+	Vector2 x = elements[0] * p_rect.size.x;
+	Vector2 y = elements[1] * p_rect.size.y;
+	Vector2 pos = xform(p_rect.position);
+
+	Rect2 new_rect;
+	new_rect.position = pos;
+	new_rect.expand_to(pos + x);
+	new_rect.expand_to(pos + y);
+	new_rect.expand_to(pos + x + y);
+	return new_rect;
+}
+
+void Transform2D::set_rotation_and_scale(real_t p_rot, const Size2 &p_scale) {
+	elements[0][0] = Math::cos(p_rot) * p_scale.x;
+	elements[1][1] = Math::cos(p_rot) * p_scale.y;
+	elements[1][0] = -Math::sin(p_rot) * p_scale.y;
+	elements[0][1] = Math::sin(p_rot) * p_scale.x;
+}
+
+void Transform2D::set_rotation_scale_and_skew(real_t p_rot, const Size2 &p_scale, float p_skew) {
+	elements[0][0] = Math::cos(p_rot) * p_scale.x;
+	elements[1][1] = Math::cos(p_rot + p_skew) * p_scale.y;
+	elements[1][0] = -Math::sin(p_rot + p_skew) * p_scale.y;
+	elements[0][1] = Math::sin(p_rot) * p_scale.x;
+}
+
+Rect2 Transform2D::xform_inv(const Rect2 &p_rect) const {
+	Vector2 ends[4] = {
+		xform_inv(p_rect.position),
+		xform_inv(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
+		xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
+		xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y))
+	};
+
+	Rect2 new_rect;
+	new_rect.position = ends[0];
+	new_rect.expand_to(ends[1]);
+	new_rect.expand_to(ends[2]);
+	new_rect.expand_to(ends[3]);
+
+	return new_rect;
+}
+
+PackedVector2Array Transform2D::xform(const PackedVector2Array &p_array) const {
+	PackedVector2Array array;
+	array.resize(p_array.size());
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		array[i] = xform(p_array[i]);
+	}
+	return array;
+}
+
+PackedVector2Array Transform2D::xform_inv(const PackedVector2Array &p_array) const {
+	PackedVector2Array array;
+	array.resize(p_array.size());
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		array[i] = xform_inv(p_array[i]);
+	}
+	return array;
+}
+
+} // namespace godot
+
+#endif // GODOT_TRANSFORM2D_HPP

include/godot_cpp/variant/transform3d.hpp

@@ -0,0 +1,204 @@
+#ifndef GODOT_TRANSFORM3D_HPP
+#define GODOT_TRANSFORM3D_HPP
+
+#include <godot_cpp/variant/aabb.hpp>
+#include <godot_cpp/variant/basis.hpp>
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/packed_vector3_array.hpp>
+#include <godot_cpp/variant/plane.hpp>
+
+namespace godot {
+
+class Transform3D {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	Basis basis;
+	Vector3 origin;
+
+	void invert();
+	Transform3D inverse() const;
+
+	void affine_invert();
+	Transform3D affine_inverse() const;
+
+	Transform3D rotated(const Vector3 &p_axis, real_t p_phi) const;
+
+	void rotate(const Vector3 &p_axis, real_t p_phi);
+	void rotate_basis(const Vector3 &p_axis, real_t p_phi);
+
+	void set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0));
+	Transform3D looking_at(const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0)) const;
+
+	void scale(const Vector3 &p_scale);
+	Transform3D scaled(const Vector3 &p_scale) const;
+	void scale_basis(const Vector3 &p_scale);
+	void translate(real_t p_tx, real_t p_ty, real_t p_tz);
+	void translate(const Vector3 &p_translation);
+	Transform3D translated(const Vector3 &p_translation) const;
+
+	const Basis &get_basis() const { return basis; }
+	void set_basis(const Basis &p_basis) { basis = p_basis; }
+
+	const Vector3 &get_origin() const { return origin; }
+	void set_origin(const Vector3 &p_origin) { origin = p_origin; }
+
+	void orthonormalize();
+	Transform3D orthonormalized() const;
+	bool is_equal_approx(const Transform3D &p_transform) const;
+
+	bool operator==(const Transform3D &p_transform) const;
+	bool operator!=(const Transform3D &p_transform) const;
+
+	inline Vector3 xform(const Vector3 &p_vector) const;
+	inline Vector3 xform_inv(const Vector3 &p_vector) const;
+
+	inline Plane xform(const Plane &p_plane) const;
+	inline Plane xform_inv(const Plane &p_plane) const;
+
+	inline AABB xform(const AABB &p_aabb) const;
+	inline AABB xform_inv(const AABB &p_aabb) const;
+
+	inline PackedVector3Array xform(const PackedVector3Array &p_array) const;
+	inline PackedVector3Array xform_inv(const PackedVector3Array &p_array) const;
+
+	void operator*=(const Transform3D &p_transform);
+	Transform3D operator*(const Transform3D &p_transform) const;
+
+	Transform3D interpolate_with(const Transform3D &p_transform, real_t p_c) const;
+
+	inline Transform3D inverse_xform(const Transform3D &t) const {
+		Vector3 v = t.origin - origin;
+		return Transform3D(basis.transpose_xform(t.basis),
+				basis.xform(v));
+	}
+
+	void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t tx, real_t ty, real_t tz) {
+		basis.set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
+		origin.x = tx;
+		origin.y = ty;
+		origin.z = tz;
+	}
+
+	operator String() const;
+
+	Transform3D() {}
+	Transform3D(const Basis &p_basis, const Vector3 &p_origin = Vector3());
+	Transform3D(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z, const Vector3 &p_origin);
+	Transform3D(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t ox, real_t oy, real_t oz);
+};
+
+inline Vector3 Transform3D::xform(const Vector3 &p_vector) const {
+	return Vector3(
+			basis[0].dot(p_vector) + origin.x,
+			basis[1].dot(p_vector) + origin.y,
+			basis[2].dot(p_vector) + origin.z);
+}
+
+inline Vector3 Transform3D::xform_inv(const Vector3 &p_vector) const {
+	Vector3 v = p_vector - origin;
+
+	return Vector3(
+			(basis.elements[0][0] * v.x) + (basis.elements[1][0] * v.y) + (basis.elements[2][0] * v.z),
+			(basis.elements[0][1] * v.x) + (basis.elements[1][1] * v.y) + (basis.elements[2][1] * v.z),
+			(basis.elements[0][2] * v.x) + (basis.elements[1][2] * v.y) + (basis.elements[2][2] * v.z));
+}
+
+inline Plane Transform3D::xform(const Plane &p_plane) const {
+	Vector3 point = p_plane.normal * p_plane.d;
+	Vector3 point_dir = point + p_plane.normal;
+	point = xform(point);
+	point_dir = xform(point_dir);
+
+	Vector3 normal = point_dir - point;
+	normal.normalize();
+	real_t d = normal.dot(point);
+
+	return Plane(normal, d);
+}
+
+inline Plane Transform3D::xform_inv(const Plane &p_plane) const {
+	Vector3 point = p_plane.normal * p_plane.d;
+	Vector3 point_dir = point + p_plane.normal;
+	point = xform_inv(point);
+	point_dir = xform_inv(point_dir);
+
+	Vector3 normal = point_dir - point;
+	normal.normalize();
+	real_t d = normal.dot(point);
+
+	return Plane(normal, d);
+}
+
+inline AABB Transform3D::xform(const AABB &p_aabb) const {
+	/* http://dev.theomader.com/transform-bounding-boxes/ */
+	Vector3 min = p_aabb.position;
+	Vector3 max = p_aabb.position + p_aabb.size;
+	Vector3 tmin, tmax;
+	for (int i = 0; i < 3; i++) {
+		tmin[i] = tmax[i] = origin[i];
+		for (int j = 0; j < 3; j++) {
+			real_t e = basis[i][j] * min[j];
+			real_t f = basis[i][j] * max[j];
+			if (e < f) {
+				tmin[i] += e;
+				tmax[i] += f;
+			} else {
+				tmin[i] += f;
+				tmax[i] += e;
+			}
+		}
+	}
+	AABB r_aabb;
+	r_aabb.position = tmin;
+	r_aabb.size = tmax - tmin;
+	return r_aabb;
+}
+
+inline AABB Transform3D::xform_inv(const AABB &p_aabb) const {
+	/* define vertices */
+	Vector3 vertices[8] = {
+		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z),
+		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z),
+		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z),
+		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z),
+		Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z),
+		Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z),
+		Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z),
+		Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z)
+	};
+
+	AABB ret;
+
+	ret.position = xform_inv(vertices[0]);
+
+	for (int i = 1; i < 8; i++) {
+		ret.expand_to(xform_inv(vertices[i]));
+	}
+
+	return ret;
+}
+
+PackedVector3Array Transform3D::xform(const PackedVector3Array &p_array) const {
+	PackedVector3Array array;
+	array.resize(p_array.size());
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		array[i] = xform(p_array[i]);
+	}
+	return array;
+}
+
+PackedVector3Array Transform3D::xform_inv(const PackedVector3Array &p_array) const {
+	PackedVector3Array array;
+	array.resize(p_array.size());
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		array[i] = xform_inv(p_array[i]);
+	}
+	return array;
+}
+
+} // namespace godot
+
+#endif // GODOT_TRANSFORM_HPP

include/godot_cpp/variant/vector2.hpp

@@ -0,0 +1,236 @@
+#ifndef GODOT_VECTOR2_HPP
+#define GODOT_VECTOR2_HPP
+
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+class Vector2i;
+
+class Vector2 {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	enum Axis {
+		AXIS_X,
+		AXIS_Y,
+	};
+
+	union {
+		real_t x = 0;
+		real_t width;
+	};
+	union {
+		real_t y = 0;
+		real_t height;
+	};
+
+	inline real_t &operator[](int p_idx) {
+		return p_idx ? y : x;
+	}
+	inline const real_t &operator[](int p_idx) const {
+		return p_idx ? y : x;
+	}
+
+	void normalize();
+	Vector2 normalized() const;
+	bool is_normalized() const;
+
+	real_t length() const;
+	real_t length_squared() const;
+
+	Vector2 min(const Vector2 &p_vector2) const {
+		return Vector2(Math::min(x, p_vector2.x), Math::min(y, p_vector2.y));
+	}
+
+	Vector2 max(const Vector2 &p_vector2) const {
+		return Vector2(Math::max(x, p_vector2.x), Math::max(y, p_vector2.y));
+	}
+
+	real_t distance_to(const Vector2 &p_vector2) const;
+	real_t distance_squared_to(const Vector2 &p_vector2) const;
+	real_t angle_to(const Vector2 &p_vector2) const;
+	real_t angle_to_point(const Vector2 &p_vector2) const;
+	inline Vector2 direction_to(const Vector2 &p_to) const;
+
+	real_t dot(const Vector2 &p_other) const;
+	real_t cross(const Vector2 &p_other) const;
+	Vector2 posmod(const real_t p_mod) const;
+	Vector2 posmodv(const Vector2 &p_modv) const;
+	Vector2 project(const Vector2 &p_to) const;
+
+	Vector2 plane_project(real_t p_d, const Vector2 &p_vec) const;
+
+	Vector2 clamped(real_t p_len) const;
+
+	inline Vector2 lerp(const Vector2 &p_to, real_t p_weight) const;
+	inline Vector2 slerp(const Vector2 &p_to, real_t p_weight) const;
+	Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_weight) const;
+	Vector2 move_toward(const Vector2 &p_to, const real_t p_delta) const;
+
+	Vector2 slide(const Vector2 &p_normal) const;
+	Vector2 bounce(const Vector2 &p_normal) const;
+	Vector2 reflect(const Vector2 &p_normal) const;
+
+	bool is_equal_approx(const Vector2 &p_v) const;
+
+	Vector2 operator+(const Vector2 &p_v) const;
+	void operator+=(const Vector2 &p_v);
+	Vector2 operator-(const Vector2 &p_v) const;
+	void operator-=(const Vector2 &p_v);
+	Vector2 operator*(const Vector2 &p_v1) const;
+
+	Vector2 operator*(const real_t &rvalue) const;
+	void operator*=(const real_t &rvalue);
+	void operator*=(const Vector2 &rvalue) { *this = *this * rvalue; }
+
+	Vector2 operator/(const Vector2 &p_v1) const;
+
+	Vector2 operator/(const real_t &rvalue) const;
+
+	void operator/=(const real_t &rvalue);
+	void operator/=(const Vector2 &rvalue) { *this = *this / rvalue; }
+
+	Vector2 operator-() const;
+
+	bool operator==(const Vector2 &p_vec2) const;
+	bool operator!=(const Vector2 &p_vec2) const;
+
+	bool operator<(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y < p_vec2.y) : (x < p_vec2.x); }
+	bool operator>(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y > p_vec2.y) : (x > p_vec2.x); }
+	bool operator<=(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y <= p_vec2.y) : (x < p_vec2.x); }
+	bool operator>=(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y >= p_vec2.y) : (x > p_vec2.x); }
+
+	real_t angle() const;
+
+	inline Vector2 abs() const {
+		return Vector2(Math::abs(x), Math::abs(y));
+	}
+
+	Vector2 rotated(real_t p_by) const;
+	Vector2 orthogonal() const {
+		return Vector2(y, -x);
+	}
+
+	Vector2 sign() const;
+	Vector2 floor() const;
+	Vector2 ceil() const;
+	Vector2 round() const;
+	Vector2 snapped(const Vector2 &p_by) const;
+	real_t aspect() const { return width / height; }
+
+	operator String() const;
+
+	inline Vector2() {}
+	inline Vector2(real_t p_x, real_t p_y) {
+		x = p_x;
+		y = p_y;
+	}
+};
+
+inline Vector2 Vector2::plane_project(real_t p_d, const Vector2 &p_vec) const {
+	return p_vec - *this * (dot(p_vec) - p_d);
+}
+
+inline Vector2 operator*(float p_scalar, const Vector2 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+inline Vector2 operator*(double p_scalar, const Vector2 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+inline Vector2 operator*(int32_t p_scalar, const Vector2 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+inline Vector2 operator*(int64_t p_scalar, const Vector2 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+inline Vector2 Vector2::operator+(const Vector2 &p_v) const {
+	return Vector2(x + p_v.x, y + p_v.y);
+}
+
+inline void Vector2::operator+=(const Vector2 &p_v) {
+	x += p_v.x;
+	y += p_v.y;
+}
+
+inline Vector2 Vector2::operator-(const Vector2 &p_v) const {
+	return Vector2(x - p_v.x, y - p_v.y);
+}
+
+inline void Vector2::operator-=(const Vector2 &p_v) {
+	x -= p_v.x;
+	y -= p_v.y;
+}
+
+inline Vector2 Vector2::operator*(const Vector2 &p_v1) const {
+	return Vector2(x * p_v1.x, y * p_v1.y);
+}
+
+inline Vector2 Vector2::operator*(const real_t &rvalue) const {
+	return Vector2(x * rvalue, y * rvalue);
+}
+
+inline void Vector2::operator*=(const real_t &rvalue) {
+	x *= rvalue;
+	y *= rvalue;
+}
+
+inline Vector2 Vector2::operator/(const Vector2 &p_v1) const {
+	return Vector2(x / p_v1.x, y / p_v1.y);
+}
+
+inline Vector2 Vector2::operator/(const real_t &rvalue) const {
+	return Vector2(x / rvalue, y / rvalue);
+}
+
+inline void Vector2::operator/=(const real_t &rvalue) {
+	x /= rvalue;
+	y /= rvalue;
+}
+
+inline Vector2 Vector2::operator-() const {
+	return Vector2(-x, -y);
+}
+
+inline bool Vector2::operator==(const Vector2 &p_vec2) const {
+	return x == p_vec2.x && y == p_vec2.y;
+}
+
+inline bool Vector2::operator!=(const Vector2 &p_vec2) const {
+	return x != p_vec2.x || y != p_vec2.y;
+}
+
+Vector2 Vector2::lerp(const Vector2 &p_to, real_t p_weight) const {
+	Vector2 res = *this;
+
+	res.x += (p_weight * (p_to.x - x));
+	res.y += (p_weight * (p_to.y - y));
+
+	return res;
+}
+
+Vector2 Vector2::slerp(const Vector2 &p_to, real_t p_weight) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!is_normalized(), Vector2());
+#endif
+	real_t theta = angle_to(p_to);
+	return rotated(theta * p_weight);
+}
+
+Vector2 Vector2::direction_to(const Vector2 &p_to) const {
+	Vector2 ret(p_to.x - x, p_to.y - y);
+	ret.normalize();
+	return ret;
+}
+
+typedef Vector2 Size2;
+typedef Vector2 Point2;
+
+} // namespace godot
+
+#endif // GODOT_VECTOR2_HPP

include/godot_cpp/variant/vector2i.hpp

@@ -0,0 +1,102 @@
+#ifndef GODOT_VECTOR2I_HPP
+#define GODOT_VECTOR2I_HPP
+
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/string.hpp>
+#include <godot_cpp/variant/vector2.hpp>
+
+namespace godot {
+
+class Vector2i {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	enum Axis {
+		AXIS_X,
+		AXIS_Y,
+	};
+
+	union {
+		int32_t x = 0;
+		int32_t width;
+	};
+	union {
+		int32_t y = 0;
+		int32_t height;
+	};
+
+	inline int32_t &operator[](int p_idx) {
+		return p_idx ? y : x;
+	}
+	inline const int32_t &operator[](int p_idx) const {
+		return p_idx ? y : x;
+	}
+
+	Vector2i operator+(const Vector2i &p_v) const;
+	void operator+=(const Vector2i &p_v);
+	Vector2i operator-(const Vector2i &p_v) const;
+	void operator-=(const Vector2i &p_v);
+	Vector2i operator*(const Vector2i &p_v1) const;
+
+	Vector2i operator*(const int32_t &rvalue) const;
+	void operator*=(const int32_t &rvalue);
+
+	Vector2i operator/(const Vector2i &p_v1) const;
+	Vector2i operator/(const int32_t &rvalue) const;
+	void operator/=(const int32_t &rvalue);
+
+	Vector2i operator%(const Vector2i &p_v1) const;
+	Vector2i operator%(const int32_t &rvalue) const;
+	void operator%=(const int32_t &rvalue);
+
+	Vector2i operator-() const;
+	bool operator<(const Vector2i &p_vec2) const { return (x == p_vec2.x) ? (y < p_vec2.y) : (x < p_vec2.x); }
+	bool operator>(const Vector2i &p_vec2) const { return (x == p_vec2.x) ? (y > p_vec2.y) : (x > p_vec2.x); }
+
+	bool operator<=(const Vector2i &p_vec2) const { return x == p_vec2.x ? (y <= p_vec2.y) : (x < p_vec2.x); }
+	bool operator>=(const Vector2i &p_vec2) const { return x == p_vec2.x ? (y >= p_vec2.y) : (x > p_vec2.x); }
+
+	bool operator==(const Vector2i &p_vec2) const;
+	bool operator!=(const Vector2i &p_vec2) const;
+
+	real_t aspect() const { return width / (real_t)height; }
+	Vector2i sign() const { return Vector2i(Math::sign(x), Math::sign(y)); }
+	Vector2i abs() const { return Vector2i(Math::abs(x), Math::abs(y)); }
+
+	operator String() const;
+
+	operator Vector2() const { return Vector2(x, y); }
+
+	inline Vector2i() {}
+	inline Vector2i(const Vector2 &p_vec2) {
+		x = (int32_t)p_vec2.x;
+		y = (int32_t)p_vec2.y;
+	}
+	inline Vector2i(int32_t p_x, int32_t p_y) {
+		x = p_x;
+		y = p_y;
+	}
+};
+
+inline Vector2i operator*(const int32_t &p_scalar, const Vector2i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+inline Vector2i operator*(const int64_t &p_scalar, const Vector2i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+inline Vector2i operator*(const float &p_scalar, const Vector2i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+inline Vector2i operator*(const double &p_scalar, const Vector2i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+typedef Vector2i Size2i;
+typedef Vector2i Point2i;
+
+} // namespace godot
+
+#endif // GODOT_VECTOR2I_HPP

include/godot_cpp/variant/vector3.hpp

@@ -0,0 +1,408 @@
+#ifndef GODOT_VECTOR3_HPP
+#define GODOT_VECTOR3_HPP
+
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+class Basis;
+class Vector3i;
+
+class Vector3 {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	enum Axis {
+		AXIS_X,
+		AXIS_Y,
+		AXIS_Z,
+	};
+
+	union {
+		struct {
+			real_t x;
+			real_t y;
+			real_t z;
+		};
+
+		real_t coord[3] = { 0 };
+	};
+
+	inline const real_t &operator[](int p_axis) const {
+		return coord[p_axis];
+	}
+
+	inline real_t &operator[](int p_axis) {
+		return coord[p_axis];
+	}
+
+	void set_axis(int p_axis, real_t p_value);
+	real_t get_axis(int p_axis) const;
+
+	int min_axis() const;
+	int max_axis() const;
+
+	inline real_t length() const;
+	inline real_t length_squared() const;
+
+	inline void normalize();
+	inline Vector3 normalized() const;
+	inline bool is_normalized() const;
+	inline Vector3 inverse() const;
+
+	inline void zero();
+
+	void snap(Vector3 p_val);
+	Vector3 snapped(Vector3 p_val) const;
+
+	void rotate(const Vector3 &p_axis, real_t p_phi);
+	Vector3 rotated(const Vector3 &p_axis, real_t p_phi) const;
+
+	/* Static Methods between 2 vector3s */
+
+	inline Vector3 lerp(const Vector3 &p_to, real_t p_weight) const;
+	inline Vector3 slerp(const Vector3 &p_to, real_t p_weight) const;
+	Vector3 cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight) const;
+	Vector3 move_toward(const Vector3 &p_to, const real_t p_delta) const;
+
+	inline Vector3 cross(const Vector3 &p_b) const;
+	inline real_t dot(const Vector3 &p_b) const;
+	Basis outer(const Vector3 &p_b) const;
+	Basis to_diagonal_matrix() const;
+
+	inline Vector3 abs() const;
+	inline Vector3 floor() const;
+	inline Vector3 sign() const;
+	inline Vector3 ceil() const;
+	inline Vector3 round() const;
+
+	inline real_t distance_to(const Vector3 &p_to) const;
+	inline real_t distance_squared_to(const Vector3 &p_to) const;
+
+	inline Vector3 posmod(const real_t p_mod) const;
+	inline Vector3 posmodv(const Vector3 &p_modv) const;
+	inline Vector3 project(const Vector3 &p_to) const;
+
+	inline real_t angle_to(const Vector3 &p_to) const;
+	inline Vector3 direction_to(const Vector3 &p_to) const;
+
+	inline Vector3 slide(const Vector3 &p_normal) const;
+	inline Vector3 bounce(const Vector3 &p_normal) const;
+	inline Vector3 reflect(const Vector3 &p_normal) const;
+
+	bool is_equal_approx(const Vector3 &p_v) const;
+
+	/* Operators */
+
+	inline Vector3 &operator+=(const Vector3 &p_v);
+	inline Vector3 operator+(const Vector3 &p_v) const;
+	inline Vector3 &operator-=(const Vector3 &p_v);
+	inline Vector3 operator-(const Vector3 &p_v) const;
+	inline Vector3 &operator*=(const Vector3 &p_v);
+	inline Vector3 operator*(const Vector3 &p_v) const;
+	inline Vector3 &operator/=(const Vector3 &p_v);
+	inline Vector3 operator/(const Vector3 &p_v) const;
+
+	inline Vector3 &operator*=(real_t p_scalar);
+	inline Vector3 operator*(real_t p_scalar) const;
+	inline Vector3 &operator/=(real_t p_scalar);
+	inline Vector3 operator/(real_t p_scalar) const;
+
+	inline Vector3 operator-() const;
+
+	inline bool operator==(const Vector3 &p_v) const;
+	inline bool operator!=(const Vector3 &p_v) const;
+	inline bool operator<(const Vector3 &p_v) const;
+	inline bool operator<=(const Vector3 &p_v) const;
+	inline bool operator>(const Vector3 &p_v) const;
+	inline bool operator>=(const Vector3 &p_v) const;
+
+	operator String() const;
+	operator Vector3i() const;
+
+	inline Vector3() {}
+	inline Vector3(real_t p_x, real_t p_y, real_t p_z) {
+		x = p_x;
+		y = p_y;
+		z = p_z;
+	}
+	Vector3(const Vector3i &p_ivec);
+};
+
+Vector3 Vector3::cross(const Vector3 &p_b) const {
+	Vector3 ret(
+			(y * p_b.z) - (z * p_b.y),
+			(z * p_b.x) - (x * p_b.z),
+			(x * p_b.y) - (y * p_b.x));
+
+	return ret;
+}
+
+real_t Vector3::dot(const Vector3 &p_b) const {
+	return x * p_b.x + y * p_b.y + z * p_b.z;
+}
+
+Vector3 Vector3::abs() const {
+	return Vector3(Math::abs(x), Math::abs(y), Math::abs(z));
+}
+
+Vector3 Vector3::sign() const {
+	return Vector3(Math::sign(x), Math::sign(y), Math::sign(z));
+}
+
+Vector3 Vector3::floor() const {
+	return Vector3(Math::floor(x), Math::floor(y), Math::floor(z));
+}
+
+Vector3 Vector3::ceil() const {
+	return Vector3(Math::ceil(x), Math::ceil(y), Math::ceil(z));
+}
+
+Vector3 Vector3::round() const {
+	return Vector3(Math::round(x), Math::round(y), Math::round(z));
+}
+
+Vector3 Vector3::lerp(const Vector3 &p_to, real_t p_weight) const {
+	return Vector3(
+			x + (p_weight * (p_to.x - x)),
+			y + (p_weight * (p_to.y - y)),
+			z + (p_weight * (p_to.z - z)));
+}
+
+Vector3 Vector3::slerp(const Vector3 &p_to, real_t p_weight) const {
+	real_t theta = angle_to(p_to);
+	return rotated(cross(p_to).normalized(), theta * p_weight);
+}
+
+real_t Vector3::distance_to(const Vector3 &p_to) const {
+	return (p_to - *this).length();
+}
+
+real_t Vector3::distance_squared_to(const Vector3 &p_to) const {
+	return (p_to - *this).length_squared();
+}
+
+Vector3 Vector3::posmod(const real_t p_mod) const {
+	return Vector3(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod), Math::fposmod(z, p_mod));
+}
+
+Vector3 Vector3::posmodv(const Vector3 &p_modv) const {
+	return Vector3(Math::fposmod(x, p_modv.x), Math::fposmod(y, p_modv.y), Math::fposmod(z, p_modv.z));
+}
+
+Vector3 Vector3::project(const Vector3 &p_to) const {
+	return p_to * (dot(p_to) / p_to.length_squared());
+}
+
+real_t Vector3::angle_to(const Vector3 &p_to) const {
+	return Math::atan2(cross(p_to).length(), dot(p_to));
+}
+
+Vector3 Vector3::direction_to(const Vector3 &p_to) const {
+	Vector3 ret(p_to.x - x, p_to.y - y, p_to.z - z);
+	ret.normalize();
+	return ret;
+}
+
+/* Operators */
+
+Vector3 &Vector3::operator+=(const Vector3 &p_v) {
+	x += p_v.x;
+	y += p_v.y;
+	z += p_v.z;
+	return *this;
+}
+
+Vector3 Vector3::operator+(const Vector3 &p_v) const {
+	return Vector3(x + p_v.x, y + p_v.y, z + p_v.z);
+}
+
+Vector3 &Vector3::operator-=(const Vector3 &p_v) {
+	x -= p_v.x;
+	y -= p_v.y;
+	z -= p_v.z;
+	return *this;
+}
+
+Vector3 Vector3::operator-(const Vector3 &p_v) const {
+	return Vector3(x - p_v.x, y - p_v.y, z - p_v.z);
+}
+
+Vector3 &Vector3::operator*=(const Vector3 &p_v) {
+	x *= p_v.x;
+	y *= p_v.y;
+	z *= p_v.z;
+	return *this;
+}
+
+Vector3 Vector3::operator*(const Vector3 &p_v) const {
+	return Vector3(x * p_v.x, y * p_v.y, z * p_v.z);
+}
+
+Vector3 &Vector3::operator/=(const Vector3 &p_v) {
+	x /= p_v.x;
+	y /= p_v.y;
+	z /= p_v.z;
+	return *this;
+}
+
+Vector3 Vector3::operator/(const Vector3 &p_v) const {
+	return Vector3(x / p_v.x, y / p_v.y, z / p_v.z);
+}
+
+Vector3 &Vector3::operator*=(real_t p_scalar) {
+	x *= p_scalar;
+	y *= p_scalar;
+	z *= p_scalar;
+	return *this;
+}
+
+inline Vector3 operator*(real_t p_scalar, const Vector3 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+Vector3 Vector3::operator*(real_t p_scalar) const {
+	return Vector3(x * p_scalar, y * p_scalar, z * p_scalar);
+}
+
+Vector3 &Vector3::operator/=(real_t p_scalar) {
+	x /= p_scalar;
+	y /= p_scalar;
+	z /= p_scalar;
+	return *this;
+}
+
+Vector3 Vector3::operator/(real_t p_scalar) const {
+	return Vector3(x / p_scalar, y / p_scalar, z / p_scalar);
+}
+
+Vector3 Vector3::operator-() const {
+	return Vector3(-x, -y, -z);
+}
+
+bool Vector3::operator==(const Vector3 &p_v) const {
+	return x == p_v.x && y == p_v.y && z == p_v.z;
+}
+
+bool Vector3::operator!=(const Vector3 &p_v) const {
+	return x != p_v.x || y != p_v.y || z != p_v.z;
+}
+
+bool Vector3::operator<(const Vector3 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z < p_v.z;
+		}
+		return y < p_v.y;
+	}
+	return x < p_v.x;
+}
+
+bool Vector3::operator>(const Vector3 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z > p_v.z;
+		}
+		return y > p_v.y;
+	}
+	return x > p_v.x;
+}
+
+bool Vector3::operator<=(const Vector3 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z <= p_v.z;
+		}
+		return y < p_v.y;
+	}
+	return x < p_v.x;
+}
+
+bool Vector3::operator>=(const Vector3 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z >= p_v.z;
+		}
+		return y > p_v.y;
+	}
+	return x > p_v.x;
+}
+
+inline Vector3 vec3_cross(const Vector3 &p_a, const Vector3 &p_b) {
+	return p_a.cross(p_b);
+}
+
+inline real_t vec3_dot(const Vector3 &p_a, const Vector3 &p_b) {
+	return p_a.dot(p_b);
+}
+
+real_t Vector3::length() const {
+	real_t x2 = x * x;
+	real_t y2 = y * y;
+	real_t z2 = z * z;
+
+	return Math::sqrt(x2 + y2 + z2);
+}
+
+real_t Vector3::length_squared() const {
+	real_t x2 = x * x;
+	real_t y2 = y * y;
+	real_t z2 = z * z;
+
+	return x2 + y2 + z2;
+}
+
+void Vector3::normalize() {
+	real_t lengthsq = length_squared();
+	if (lengthsq == 0) {
+		x = y = z = 0;
+	} else {
+		real_t length = Math::sqrt(lengthsq);
+		x /= length;
+		y /= length;
+		z /= length;
+	}
+}
+
+Vector3 Vector3::normalized() const {
+	Vector3 v = *this;
+	v.normalize();
+	return v;
+}
+
+bool Vector3::is_normalized() const {
+	// use length_squared() instead of length() to avoid sqrt(), makes it more stringent.
+	return Math::is_equal_approx(length_squared(), 1.0, UNIT_EPSILON);
+}
+
+Vector3 Vector3::inverse() const {
+	return Vector3(1.0 / x, 1.0 / y, 1.0 / z);
+}
+
+void Vector3::zero() {
+	x = y = z = 0;
+}
+
+// slide returns the component of the vector along the given plane, specified by its normal vector.
+Vector3 Vector3::slide(const Vector3 &p_normal) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!p_normal.is_normalized(), Vector3());
+#endif
+	return *this - p_normal * this->dot(p_normal);
+}
+
+Vector3 Vector3::bounce(const Vector3 &p_normal) const {
+	return -reflect(p_normal);
+}
+
+Vector3 Vector3::reflect(const Vector3 &p_normal) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!p_normal.is_normalized(), Vector3());
+#endif
+	return 2.0 * p_normal * this->dot(p_normal) - *this;
+}
+
+} // namespace godot
+
+#endif // GODOT_VECTOR3_HPP

include/godot_cpp/variant/vector3i.hpp

@@ -0,0 +1,255 @@
+#ifndef GODOT_VECTOR3I_HPP
+#define GODOT_VECTOR3I_HPP
+
+#include <godot_cpp/core/math.hpp>
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+class Vector3i {
+public:
+	_FORCE_INLINE_ GDNativeTypePtr ptr() const { return (void *)this; }
+
+	enum Axis {
+		AXIS_X,
+		AXIS_Y,
+		AXIS_Z,
+	};
+
+	union {
+		struct {
+			int32_t x;
+			int32_t y;
+			int32_t z;
+		};
+
+		int32_t coord[3] = { 0 };
+	};
+
+	inline const int32_t &operator[](int p_axis) const {
+		return coord[p_axis];
+	}
+
+	inline int32_t &operator[](int p_axis) {
+		return coord[p_axis];
+	}
+
+	void set_axis(int p_axis, int32_t p_value);
+	int32_t get_axis(int p_axis) const;
+
+	int min_axis() const;
+	int max_axis() const;
+
+	inline void zero();
+
+	inline Vector3i abs() const;
+	inline Vector3i sign() const;
+
+	/* Operators */
+
+	inline Vector3i &operator+=(const Vector3i &p_v);
+	inline Vector3i operator+(const Vector3i &p_v) const;
+	inline Vector3i &operator-=(const Vector3i &p_v);
+	inline Vector3i operator-(const Vector3i &p_v) const;
+	inline Vector3i &operator*=(const Vector3i &p_v);
+	inline Vector3i operator*(const Vector3i &p_v) const;
+	inline Vector3i &operator/=(const Vector3i &p_v);
+	inline Vector3i operator/(const Vector3i &p_v) const;
+	inline Vector3i &operator%=(const Vector3i &p_v);
+	inline Vector3i operator%(const Vector3i &p_v) const;
+
+	inline Vector3i &operator*=(int32_t p_scalar);
+	inline Vector3i operator*(int32_t p_scalar) const;
+	inline Vector3i &operator/=(int32_t p_scalar);
+	inline Vector3i operator/(int32_t p_scalar) const;
+	inline Vector3i &operator%=(int32_t p_scalar);
+	inline Vector3i operator%(int32_t p_scalar) const;
+
+	inline Vector3i operator-() const;
+
+	inline bool operator==(const Vector3i &p_v) const;
+	inline bool operator!=(const Vector3i &p_v) const;
+	inline bool operator<(const Vector3i &p_v) const;
+	inline bool operator<=(const Vector3i &p_v) const;
+	inline bool operator>(const Vector3i &p_v) const;
+	inline bool operator>=(const Vector3i &p_v) const;
+
+	operator String() const;
+
+	inline Vector3i() {}
+	inline Vector3i(int32_t p_x, int32_t p_y, int32_t p_z) {
+		x = p_x;
+		y = p_y;
+		z = p_z;
+	}
+};
+
+Vector3i Vector3i::abs() const {
+	return Vector3i(Math::abs(x), Math::abs(y), Math::abs(z));
+}
+
+Vector3i Vector3i::sign() const {
+	return Vector3i(Math::sign(x), Math::sign(y), Math::sign(z));
+}
+
+/* Operators */
+
+Vector3i &Vector3i::operator+=(const Vector3i &p_v) {
+	x += p_v.x;
+	y += p_v.y;
+	z += p_v.z;
+	return *this;
+}
+
+Vector3i Vector3i::operator+(const Vector3i &p_v) const {
+	return Vector3i(x + p_v.x, y + p_v.y, z + p_v.z);
+}
+
+Vector3i &Vector3i::operator-=(const Vector3i &p_v) {
+	x -= p_v.x;
+	y -= p_v.y;
+	z -= p_v.z;
+	return *this;
+}
+
+Vector3i Vector3i::operator-(const Vector3i &p_v) const {
+	return Vector3i(x - p_v.x, y - p_v.y, z - p_v.z);
+}
+
+Vector3i &Vector3i::operator*=(const Vector3i &p_v) {
+	x *= p_v.x;
+	y *= p_v.y;
+	z *= p_v.z;
+	return *this;
+}
+
+Vector3i Vector3i::operator*(const Vector3i &p_v) const {
+	return Vector3i(x * p_v.x, y * p_v.y, z * p_v.z);
+}
+
+Vector3i &Vector3i::operator/=(const Vector3i &p_v) {
+	x /= p_v.x;
+	y /= p_v.y;
+	z /= p_v.z;
+	return *this;
+}
+
+Vector3i Vector3i::operator/(const Vector3i &p_v) const {
+	return Vector3i(x / p_v.x, y / p_v.y, z / p_v.z);
+}
+
+Vector3i &Vector3i::operator%=(const Vector3i &p_v) {
+	x %= p_v.x;
+	y %= p_v.y;
+	z %= p_v.z;
+	return *this;
+}
+
+Vector3i Vector3i::operator%(const Vector3i &p_v) const {
+	return Vector3i(x % p_v.x, y % p_v.y, z % p_v.z);
+}
+
+Vector3i &Vector3i::operator*=(int32_t p_scalar) {
+	x *= p_scalar;
+	y *= p_scalar;
+	z *= p_scalar;
+	return *this;
+}
+
+inline Vector3i operator*(int32_t p_scalar, const Vector3i &p_vec) {
+	return p_vec * p_scalar;
+}
+
+Vector3i Vector3i::operator*(int32_t p_scalar) const {
+	return Vector3i(x * p_scalar, y * p_scalar, z * p_scalar);
+}
+
+Vector3i &Vector3i::operator/=(int32_t p_scalar) {
+	x /= p_scalar;
+	y /= p_scalar;
+	z /= p_scalar;
+	return *this;
+}
+
+Vector3i Vector3i::operator/(int32_t p_scalar) const {
+	return Vector3i(x / p_scalar, y / p_scalar, z / p_scalar);
+}
+
+Vector3i &Vector3i::operator%=(int32_t p_scalar) {
+	x %= p_scalar;
+	y %= p_scalar;
+	z %= p_scalar;
+	return *this;
+}
+
+Vector3i Vector3i::operator%(int32_t p_scalar) const {
+	return Vector3i(x % p_scalar, y % p_scalar, z % p_scalar);
+}
+
+Vector3i Vector3i::operator-() const {
+	return Vector3i(-x, -y, -z);
+}
+
+bool Vector3i::operator==(const Vector3i &p_v) const {
+	return (x == p_v.x && y == p_v.y && z == p_v.z);
+}
+
+bool Vector3i::operator!=(const Vector3i &p_v) const {
+	return (x != p_v.x || y != p_v.y || z != p_v.z);
+}
+
+bool Vector3i::operator<(const Vector3i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z < p_v.z;
+		} else {
+			return y < p_v.y;
+		}
+	} else {
+		return x < p_v.x;
+	}
+}
+
+bool Vector3i::operator>(const Vector3i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z > p_v.z;
+		} else {
+			return y > p_v.y;
+		}
+	} else {
+		return x > p_v.x;
+	}
+}
+
+bool Vector3i::operator<=(const Vector3i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z <= p_v.z;
+		} else {
+			return y < p_v.y;
+		}
+	} else {
+		return x < p_v.x;
+	}
+}
+
+bool Vector3i::operator>=(const Vector3i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z >= p_v.z;
+		} else {
+			return y > p_v.y;
+		}
+	} else {
+		return x > p_v.x;
+	}
+}
+
+void Vector3i::zero() {
+	x = y = z = 0;
+}
+
+} // namespace godot
+
+#endif // GODOT_VECTOR3I_HPP

src/variant/aabb.cpp

@@ -0,0 +1,355 @@
+#include <godot_cpp/variant/aabb.hpp>
+
+#include <godot_cpp/core/defs.hpp>
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+real_t AABB::get_area() const {
+	return size.x * size.y * size.z;
+}
+
+bool AABB::operator==(const AABB &p_rval) const {
+	return ((position == p_rval.position) && (size == p_rval.size));
+}
+
+bool AABB::operator!=(const AABB &p_rval) const {
+	return ((position != p_rval.position) || (size != p_rval.size));
+}
+
+void AABB::merge_with(const AABB &p_aabb) {
+	Vector3 beg_1, beg_2;
+	Vector3 end_1, end_2;
+	Vector3 min, max;
+
+	beg_1 = position;
+	beg_2 = p_aabb.position;
+	end_1 = Vector3(size.x, size.y, size.z) + beg_1;
+	end_2 = Vector3(p_aabb.size.x, p_aabb.size.y, p_aabb.size.z) + beg_2;
+
+	min.x = (beg_1.x < beg_2.x) ? beg_1.x : beg_2.x;
+	min.y = (beg_1.y < beg_2.y) ? beg_1.y : beg_2.y;
+	min.z = (beg_1.z < beg_2.z) ? beg_1.z : beg_2.z;
+
+	max.x = (end_1.x > end_2.x) ? end_1.x : end_2.x;
+	max.y = (end_1.y > end_2.y) ? end_1.y : end_2.y;
+	max.z = (end_1.z > end_2.z) ? end_1.z : end_2.z;
+
+	position = min;
+	size = max - min;
+}
+
+bool AABB::is_equal_approx(const AABB &p_aabb) const {
+	return position.is_equal_approx(p_aabb.position) && size.is_equal_approx(p_aabb.size);
+}
+
+AABB AABB::intersection(const AABB &p_aabb) const {
+	Vector3 src_min = position;
+	Vector3 src_max = position + size;
+	Vector3 dst_min = p_aabb.position;
+	Vector3 dst_max = p_aabb.position + p_aabb.size;
+
+	Vector3 min, max;
+
+	if (src_min.x > dst_max.x || src_max.x < dst_min.x) {
+		return AABB();
+	} else {
+		min.x = (src_min.x > dst_min.x) ? src_min.x : dst_min.x;
+		max.x = (src_max.x < dst_max.x) ? src_max.x : dst_max.x;
+	}
+
+	if (src_min.y > dst_max.y || src_max.y < dst_min.y) {
+		return AABB();
+	} else {
+		min.y = (src_min.y > dst_min.y) ? src_min.y : dst_min.y;
+		max.y = (src_max.y < dst_max.y) ? src_max.y : dst_max.y;
+	}
+
+	if (src_min.z > dst_max.z || src_max.z < dst_min.z) {
+		return AABB();
+	} else {
+		min.z = (src_min.z > dst_min.z) ? src_min.z : dst_min.z;
+		max.z = (src_max.z < dst_max.z) ? src_max.z : dst_max.z;
+	}
+
+	return AABB(min, max - min);
+}
+
+bool AABB::intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *r_clip, Vector3 *r_normal) const {
+	Vector3 c1, c2;
+	Vector3 end = position + size;
+	real_t near = -1e20;
+	real_t far = 1e20;
+	int axis = 0;
+
+	for (int i = 0; i < 3; i++) {
+		if (p_dir[i] == 0) {
+			if ((p_from[i] < position[i]) || (p_from[i] > end[i])) {
+				return false;
+			}
+		} else { // ray not parallel to planes in this direction
+			c1[i] = (position[i] - p_from[i]) / p_dir[i];
+			c2[i] = (end[i] - p_from[i]) / p_dir[i];
+
+			if (c1[i] > c2[i]) {
+				SWAP(c1, c2);
+			}
+			if (c1[i] > near) {
+				near = c1[i];
+				axis = i;
+			}
+			if (c2[i] < far) {
+				far = c2[i];
+			}
+			if ((near > far) || (far < 0)) {
+				return false;
+			}
+		}
+	}
+
+	if (r_clip) {
+		*r_clip = c1;
+	}
+	if (r_normal) {
+		*r_normal = Vector3();
+		(*r_normal)[axis] = p_dir[axis] ? -1 : 1;
+	}
+
+	return true;
+}
+
+bool AABB::intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector3 *r_clip, Vector3 *r_normal) const {
+	real_t min = 0, max = 1;
+	int axis = 0;
+	real_t sign = 0;
+
+	for (int i = 0; i < 3; i++) {
+		real_t seg_from = p_from[i];
+		real_t seg_to = p_to[i];
+		real_t box_begin = position[i];
+		real_t box_end = box_begin + size[i];
+		real_t cmin, cmax;
+		real_t csign;
+
+		if (seg_from < seg_to) {
+			if (seg_from > box_end || seg_to < box_begin) {
+				return false;
+			}
+			real_t length = seg_to - seg_from;
+			cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
+			cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;
+			csign = -1.0;
+
+		} else {
+			if (seg_to > box_end || seg_from < box_begin) {
+				return false;
+			}
+			real_t length = seg_to - seg_from;
+			cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
+			cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
+			csign = 1.0;
+		}
+
+		if (cmin > min) {
+			min = cmin;
+			axis = i;
+			sign = csign;
+		}
+		if (cmax < max) {
+			max = cmax;
+		}
+		if (max < min) {
+			return false;
+		}
+	}
+
+	Vector3 rel = p_to - p_from;
+
+	if (r_normal) {
+		Vector3 normal;
+		normal[axis] = sign;
+		*r_normal = normal;
+	}
+
+	if (r_clip) {
+		*r_clip = p_from + rel * min;
+	}
+
+	return true;
+}
+
+bool AABB::intersects_plane(const Plane &p_plane) const {
+	Vector3 points[8] = {
+		Vector3(position.x, position.y, position.z),
+		Vector3(position.x, position.y, position.z + size.z),
+		Vector3(position.x, position.y + size.y, position.z),
+		Vector3(position.x, position.y + size.y, position.z + size.z),
+		Vector3(position.x + size.x, position.y, position.z),
+		Vector3(position.x + size.x, position.y, position.z + size.z),
+		Vector3(position.x + size.x, position.y + size.y, position.z),
+		Vector3(position.x + size.x, position.y + size.y, position.z + size.z),
+	};
+
+	bool over = false;
+	bool under = false;
+
+	for (int i = 0; i < 8; i++) {
+		if (p_plane.distance_to(points[i]) > 0) {
+			over = true;
+		} else {
+			under = true;
+		}
+	}
+
+	return under && over;
+}
+
+Vector3 AABB::get_longest_axis() const {
+	Vector3 axis(1, 0, 0);
+	real_t max_size = size.x;
+
+	if (size.y > max_size) {
+		axis = Vector3(0, 1, 0);
+		max_size = size.y;
+	}
+
+	if (size.z > max_size) {
+		axis = Vector3(0, 0, 1);
+	}
+
+	return axis;
+}
+
+int AABB::get_longest_axis_index() const {
+	int axis = 0;
+	real_t max_size = size.x;
+
+	if (size.y > max_size) {
+		axis = 1;
+		max_size = size.y;
+	}
+
+	if (size.z > max_size) {
+		axis = 2;
+	}
+
+	return axis;
+}
+
+Vector3 AABB::get_shortest_axis() const {
+	Vector3 axis(1, 0, 0);
+	real_t max_size = size.x;
+
+	if (size.y < max_size) {
+		axis = Vector3(0, 1, 0);
+		max_size = size.y;
+	}
+
+	if (size.z < max_size) {
+		axis = Vector3(0, 0, 1);
+	}
+
+	return axis;
+}
+
+int AABB::get_shortest_axis_index() const {
+	int axis = 0;
+	real_t max_size = size.x;
+
+	if (size.y < max_size) {
+		axis = 1;
+		max_size = size.y;
+	}
+
+	if (size.z < max_size) {
+		axis = 2;
+	}
+
+	return axis;
+}
+
+AABB AABB::merge(const AABB &p_with) const {
+	AABB aabb = *this;
+	aabb.merge_with(p_with);
+	return aabb;
+}
+
+AABB AABB::expand(const Vector3 &p_vector) const {
+	AABB aabb = *this;
+	aabb.expand_to(p_vector);
+	return aabb;
+}
+
+AABB AABB::grow(real_t p_by) const {
+	AABB aabb = *this;
+	aabb.grow_by(p_by);
+	return aabb;
+}
+
+void AABB::get_edge(int p_edge, Vector3 &r_from, Vector3 &r_to) const {
+	ERR_FAIL_INDEX(p_edge, 12);
+	switch (p_edge) {
+		case 0: {
+			r_from = Vector3(position.x + size.x, position.y, position.z);
+			r_to = Vector3(position.x, position.y, position.z);
+		} break;
+		case 1: {
+			r_from = Vector3(position.x + size.x, position.y, position.z + size.z);
+			r_to = Vector3(position.x + size.x, position.y, position.z);
+		} break;
+		case 2: {
+			r_from = Vector3(position.x, position.y, position.z + size.z);
+			r_to = Vector3(position.x + size.x, position.y, position.z + size.z);
+
+		} break;
+		case 3: {
+			r_from = Vector3(position.x, position.y, position.z);
+			r_to = Vector3(position.x, position.y, position.z + size.z);
+
+		} break;
+		case 4: {
+			r_from = Vector3(position.x, position.y + size.y, position.z);
+			r_to = Vector3(position.x + size.x, position.y + size.y, position.z);
+		} break;
+		case 5: {
+			r_from = Vector3(position.x + size.x, position.y + size.y, position.z);
+			r_to = Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+		} break;
+		case 6: {
+			r_from = Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+			r_to = Vector3(position.x, position.y + size.y, position.z + size.z);
+
+		} break;
+		case 7: {
+			r_from = Vector3(position.x, position.y + size.y, position.z + size.z);
+			r_to = Vector3(position.x, position.y + size.y, position.z);
+
+		} break;
+		case 8: {
+			r_from = Vector3(position.x, position.y, position.z + size.z);
+			r_to = Vector3(position.x, position.y + size.y, position.z + size.z);
+
+		} break;
+		case 9: {
+			r_from = Vector3(position.x, position.y, position.z);
+			r_to = Vector3(position.x, position.y + size.y, position.z);
+
+		} break;
+		case 10: {
+			r_from = Vector3(position.x + size.x, position.y, position.z);
+			r_to = Vector3(position.x + size.x, position.y + size.y, position.z);
+
+		} break;
+		case 11: {
+			r_from = Vector3(position.x + size.x, position.y, position.z + size.z);
+			r_to = Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+
+		} break;
+	}
+}
+
+AABB::operator String() const {
+	return position.operator String() + " - " + size.operator String();
+}
+
+} // namespace godot

src/variant/basis.cpp

@@ -0,0 +1,1113 @@
+#include <godot_cpp/core/error_macros.hpp>
+#include <godot_cpp/variant/basis.hpp>
+#include <godot_cpp/variant/string.hpp>
+
+#define cofac(row1, col1, row2, col2) \
+	(elements[row1][col1] * elements[row2][col2] - elements[row1][col2] * elements[row2][col1])
+
+namespace godot {
+
+void Basis::from_z(const Vector3 &p_z) {
+	if (Math::abs(p_z.z) > Math_SQRT12) {
+		// choose p in y-z plane
+		real_t a = p_z[1] * p_z[1] + p_z[2] * p_z[2];
+		real_t k = 1.0 / Math::sqrt(a);
+		elements[0] = Vector3(0, -p_z[2] * k, p_z[1] * k);
+		elements[1] = Vector3(a * k, -p_z[0] * elements[0][2], p_z[0] * elements[0][1]);
+	} else {
+		// choose p in x-y plane
+		real_t a = p_z.x * p_z.x + p_z.y * p_z.y;
+		real_t k = 1.0 / Math::sqrt(a);
+		elements[0] = Vector3(-p_z.y * k, p_z.x * k, 0);
+		elements[1] = Vector3(-p_z.z * elements[0].y, p_z.z * elements[0].x, a * k);
+	}
+	elements[2] = p_z;
+}
+
+void Basis::invert() {
+	real_t co[3] = {
+		cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1)
+	};
+	real_t det = elements[0][0] * co[0] +
+				 elements[0][1] * co[1] +
+				 elements[0][2] * co[2];
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND(det == 0);
+#endif
+	real_t s = 1.0 / det;
+
+	set(co[0] * s, cofac(0, 2, 2, 1) * s, cofac(0, 1, 1, 2) * s,
+			co[1] * s, cofac(0, 0, 2, 2) * s, cofac(0, 2, 1, 0) * s,
+			co[2] * s, cofac(0, 1, 2, 0) * s, cofac(0, 0, 1, 1) * s);
+}
+
+void Basis::orthonormalize() {
+	// Gram-Schmidt Process
+
+	Vector3 x = get_axis(0);
+	Vector3 y = get_axis(1);
+	Vector3 z = get_axis(2);
+
+	x.normalize();
+	y = (y - x * (x.dot(y)));
+	y.normalize();
+	z = (z - x * (x.dot(z)) - y * (y.dot(z)));
+	z.normalize();
+
+	set_axis(0, x);
+	set_axis(1, y);
+	set_axis(2, z);
+}
+
+Basis Basis::orthonormalized() const {
+	Basis c = *this;
+	c.orthonormalize();
+	return c;
+}
+
+bool Basis::is_orthogonal() const {
+	Basis identity;
+	Basis m = (*this) * transposed();
+
+	return m.is_equal_approx(identity);
+}
+
+bool Basis::is_diagonal() const {
+	return (
+			Math::is_zero_approx(elements[0][1]) && Math::is_zero_approx(elements[0][2]) &&
+			Math::is_zero_approx(elements[1][0]) && Math::is_zero_approx(elements[1][2]) &&
+			Math::is_zero_approx(elements[2][0]) && Math::is_zero_approx(elements[2][1]));
+}
+
+bool Basis::is_rotation() const {
+	return Math::is_equal_approx(determinant(), 1, UNIT_EPSILON) && is_orthogonal();
+}
+
+#ifdef MATH_CHECKS
+// This method is only used once, in diagonalize. If it's desired elsewhere, feel free to remove the #ifdef.
+bool Basis::is_symmetric() const {
+	if (!Math::is_equal_approx(elements[0][1], elements[1][0])) {
+		return false;
+	}
+	if (!Math::is_equal_approx(elements[0][2], elements[2][0])) {
+		return false;
+	}
+	if (!Math::is_equal_approx(elements[1][2], elements[2][1])) {
+		return false;
+	}
+
+	return true;
+}
+#endif
+
+Basis Basis::diagonalize() {
+//NOTE: only implemented for symmetric matrices
+//with the Jacobi iterative method method
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!is_symmetric(), Basis());
+#endif
+	const int ite_max = 1024;
+
+	real_t off_matrix_norm_2 = elements[0][1] * elements[0][1] + elements[0][2] * elements[0][2] + elements[1][2] * elements[1][2];
+
+	int ite = 0;
+	Basis acc_rot;
+	while (off_matrix_norm_2 > CMP_EPSILON2 && ite++ < ite_max) {
+		real_t el01_2 = elements[0][1] * elements[0][1];
+		real_t el02_2 = elements[0][2] * elements[0][2];
+		real_t el12_2 = elements[1][2] * elements[1][2];
+		// Find the pivot element
+		int i, j;
+		if (el01_2 > el02_2) {
+			if (el12_2 > el01_2) {
+				i = 1;
+				j = 2;
+			} else {
+				i = 0;
+				j = 1;
+			}
+		} else {
+			if (el12_2 > el02_2) {
+				i = 1;
+				j = 2;
+			} else {
+				i = 0;
+				j = 2;
+			}
+		}
+
+		// Compute the rotation angle
+		real_t angle;
+		if (Math::is_equal_approx(elements[j][j], elements[i][i])) {
+			angle = Math_PI / 4;
+		} else {
+			angle = 0.5 * Math::atan(2 * elements[i][j] / (elements[j][j] - elements[i][i]));
+		}
+
+		// Compute the rotation matrix
+		Basis rot;
+		rot.elements[i][i] = rot.elements[j][j] = Math::cos(angle);
+		rot.elements[i][j] = -(rot.elements[j][i] = Math::sin(angle));
+
+		// Update the off matrix norm
+		off_matrix_norm_2 -= elements[i][j] * elements[i][j];
+
+		// Apply the rotation
+		*this = rot * *this * rot.transposed();
+		acc_rot = rot * acc_rot;
+	}
+
+	return acc_rot;
+}
+
+Basis Basis::inverse() const {
+	Basis inv = *this;
+	inv.invert();
+	return inv;
+}
+
+void Basis::transpose() {
+	SWAP(elements[0][1], elements[1][0]);
+	SWAP(elements[0][2], elements[2][0]);
+	SWAP(elements[1][2], elements[2][1]);
+}
+
+Basis Basis::transposed() const {
+	Basis tr = *this;
+	tr.transpose();
+	return tr;
+}
+
+// Multiplies the matrix from left by the scaling matrix: M -> S.M
+// See the comment for Basis::rotated for further explanation.
+void Basis::scale(const Vector3 &p_scale) {
+	elements[0][0] *= p_scale.x;
+	elements[0][1] *= p_scale.x;
+	elements[0][2] *= p_scale.x;
+	elements[1][0] *= p_scale.y;
+	elements[1][1] *= p_scale.y;
+	elements[1][2] *= p_scale.y;
+	elements[2][0] *= p_scale.z;
+	elements[2][1] *= p_scale.z;
+	elements[2][2] *= p_scale.z;
+}
+
+Basis Basis::scaled(const Vector3 &p_scale) const {
+	Basis m = *this;
+	m.scale(p_scale);
+	return m;
+}
+
+void Basis::scale_local(const Vector3 &p_scale) {
+	// performs a scaling in object-local coordinate system:
+	// M -> (M.S.Minv).M = M.S.
+	*this = scaled_local(p_scale);
+}
+
+float Basis::get_uniform_scale() const {
+	return (elements[0].length() + elements[1].length() + elements[2].length()) / 3.0;
+}
+
+void Basis::make_scale_uniform() {
+	float l = (elements[0].length() + elements[1].length() + elements[2].length()) / 3.0;
+	for (int i = 0; i < 3; i++) {
+		elements[i].normalize();
+		elements[i] *= l;
+	}
+}
+
+Basis Basis::scaled_local(const Vector3 &p_scale) const {
+	Basis b;
+	b.set_diagonal(p_scale);
+
+	return (*this) * b;
+}
+
+Vector3 Basis::get_scale_abs() const {
+	return Vector3(
+			Vector3(elements[0][0], elements[1][0], elements[2][0]).length(),
+			Vector3(elements[0][1], elements[1][1], elements[2][1]).length(),
+			Vector3(elements[0][2], elements[1][2], elements[2][2]).length());
+}
+
+Vector3 Basis::get_scale_local() const {
+	real_t det_sign = Math::sign(determinant());
+	return det_sign * Vector3(elements[0].length(), elements[1].length(), elements[2].length());
+}
+
+// get_scale works with get_rotation, use get_scale_abs if you need to enforce positive signature.
+Vector3 Basis::get_scale() const {
+	// FIXME: We are assuming M = R.S (R is rotation and S is scaling), and use polar decomposition to extract R and S.
+	// A polar decomposition is M = O.P, where O is an orthogonal matrix (meaning rotation and reflection) and
+	// P is a positive semi-definite matrix (meaning it contains absolute values of scaling along its diagonal).
+	//
+	// Despite being different from what we want to achieve, we can nevertheless make use of polar decomposition
+	// here as follows. We can split O into a rotation and a reflection as O = R.Q, and obtain M = R.S where
+	// we defined S = Q.P. Now, R is a proper rotation matrix and S is a (signed) scaling matrix,
+	// which can involve negative scalings. However, there is a catch: unlike the polar decomposition of M = O.P,
+	// the decomposition of O into a rotation and reflection matrix as O = R.Q is not unique.
+	// Therefore, we are going to do this decomposition by sticking to a particular convention.
+	// This may lead to confusion for some users though.
+	//
+	// The convention we use here is to absorb the sign flip into the scaling matrix.
+	// The same convention is also used in other similar functions such as get_rotation_axis_angle, get_rotation, ...
+	//
+	// A proper way to get rid of this issue would be to store the scaling values (or at least their signs)
+	// as a part of Basis. However, if we go that path, we need to disable direct (write) access to the
+	// matrix elements.
+	//
+	// The rotation part of this decomposition is returned by get_rotation* functions.
+	real_t det_sign = Math::sign(determinant());
+	return det_sign * Vector3(
+							  Vector3(elements[0][0], elements[1][0], elements[2][0]).length(),
+							  Vector3(elements[0][1], elements[1][1], elements[2][1]).length(),
+							  Vector3(elements[0][2], elements[1][2], elements[2][2]).length());
+}
+
+// Decomposes a Basis into a rotation-reflection matrix (an element of the group O(3)) and a positive scaling matrix as B = O.S.
+// Returns the rotation-reflection matrix via reference argument, and scaling information is returned as a Vector3.
+// This (internal) function is too specific and named too ugly to expose to users, and probably there's no need to do so.
+Vector3 Basis::rotref_posscale_decomposition(Basis &rotref) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(determinant() == 0, Vector3());
+
+	Basis m = transposed() * (*this);
+	ERR_FAIL_COND_V(!m.is_diagonal(), Vector3());
+#endif
+	Vector3 scale = get_scale();
+	Basis inv_scale = Basis().scaled(scale.inverse()); // this will also absorb the sign of scale
+	rotref = (*this) * inv_scale;
+
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!rotref.is_orthogonal(), Vector3());
+#endif
+	return scale.abs();
+}
+
+// Multiplies the matrix from left by the rotation matrix: M -> R.M
+// Note that this does *not* rotate the matrix itself.
+//
+// The main use of Basis is as Transform3D.basis, which is used a the transformation matrix
+// of 3D object. Rotate here refers to rotation of the object (which is R * (*this)),
+// not the matrix itself (which is R * (*this) * R.transposed()).
+Basis Basis::rotated(const Vector3 &p_axis, real_t p_phi) const {
+	return Basis(p_axis, p_phi) * (*this);
+}
+
+void Basis::rotate(const Vector3 &p_axis, real_t p_phi) {
+	*this = rotated(p_axis, p_phi);
+}
+
+void Basis::rotate_local(const Vector3 &p_axis, real_t p_phi) {
+	// performs a rotation in object-local coordinate system:
+	// M -> (M.R.Minv).M = M.R.
+	*this = rotated_local(p_axis, p_phi);
+}
+
+Basis Basis::rotated_local(const Vector3 &p_axis, real_t p_phi) const {
+	return (*this) * Basis(p_axis, p_phi);
+}
+
+Basis Basis::rotated(const Vector3 &p_euler) const {
+	return Basis(p_euler) * (*this);
+}
+
+void Basis::rotate(const Vector3 &p_euler) {
+	*this = rotated(p_euler);
+}
+
+Basis Basis::rotated(const Quaternion &p_quat) const {
+	return Basis(p_quat) * (*this);
+}
+
+void Basis::rotate(const Quaternion &p_quat) {
+	*this = rotated(p_quat);
+}
+
+Vector3 Basis::get_rotation_euler() const {
+	// Assumes that the matrix can be decomposed into a proper rotation and scaling matrix as M = R.S,
+	// and returns the Euler angles corresponding to the rotation part, complementing get_scale().
+	// See the comment in get_scale() for further information.
+	Basis m = orthonormalized();
+	real_t det = m.determinant();
+	if (det < 0) {
+		// Ensure that the determinant is 1, such that result is a proper rotation matrix which can be represented by Euler angles.
+		m.scale(Vector3(-1, -1, -1));
+	}
+
+	return m.get_euler();
+}
+
+Quaternion Basis::get_rotation_quat() const {
+	// Assumes that the matrix can be decomposed into a proper rotation and scaling matrix as M = R.S,
+	// and returns the Euler angles corresponding to the rotation part, complementing get_scale().
+	// See the comment in get_scale() for further information.
+	Basis m = orthonormalized();
+	real_t det = m.determinant();
+	if (det < 0) {
+		// Ensure that the determinant is 1, such that result is a proper rotation matrix which can be represented by Euler angles.
+		m.scale(Vector3(-1, -1, -1));
+	}
+
+	return m.get_quat();
+}
+
+void Basis::get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const {
+	// Assumes that the matrix can be decomposed into a proper rotation and scaling matrix as M = R.S,
+	// and returns the Euler angles corresponding to the rotation part, complementing get_scale().
+	// See the comment in get_scale() for further information.
+	Basis m = orthonormalized();
+	real_t det = m.determinant();
+	if (det < 0) {
+		// Ensure that the determinant is 1, such that result is a proper rotation matrix which can be represented by Euler angles.
+		m.scale(Vector3(-1, -1, -1));
+	}
+
+	m.get_axis_angle(p_axis, p_angle);
+}
+
+void Basis::get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) const {
+	// Assumes that the matrix can be decomposed into a proper rotation and scaling matrix as M = R.S,
+	// and returns the Euler angles corresponding to the rotation part, complementing get_scale().
+	// See the comment in get_scale() for further information.
+	Basis m = transposed();
+	m.orthonormalize();
+	real_t det = m.determinant();
+	if (det < 0) {
+		// Ensure that the determinant is 1, such that result is a proper rotation matrix which can be represented by Euler angles.
+		m.scale(Vector3(-1, -1, -1));
+	}
+
+	m.get_axis_angle(p_axis, p_angle);
+	p_angle = -p_angle;
+}
+
+// get_euler_xyz returns a vector containing the Euler angles in the format
+// (a1,a2,a3), where a3 is the angle of the first rotation, and a1 is the last
+// (following the convention they are commonly defined in the literature).
+//
+// The current implementation uses XYZ convention (Z is the first rotation),
+// so euler.z is the angle of the (first) rotation around Z axis and so on,
+//
+// And thus, assuming the matrix is a rotation matrix, this function returns
+// the angles in the decomposition R = X(a1).Y(a2).Z(a3) where Z(a) rotates
+// around the z-axis by a and so on.
+Vector3 Basis::get_euler_xyz() const {
+	// Euler angles in XYZ convention.
+	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+	//
+	// rot =  cy*cz          -cy*sz           sy
+	//        cz*sx*sy+cx*sz  cx*cz-sx*sy*sz -cy*sx
+	//       -cx*cz*sy+sx*sz  cz*sx+cx*sy*sz  cx*cy
+
+	Vector3 euler;
+	real_t sy = elements[0][2];
+	if (sy < (1.0 - CMP_EPSILON)) {
+		if (sy > -(1.0 - CMP_EPSILON)) {
+			// is this a pure Y rotation?
+			if (elements[1][0] == 0.0 && elements[0][1] == 0.0 && elements[1][2] == 0 && elements[2][1] == 0 && elements[1][1] == 1) {
+				// return the simplest form (human friendlier in editor and scripts)
+				euler.x = 0;
+				euler.y = atan2(elements[0][2], elements[0][0]);
+				euler.z = 0;
+			} else {
+				euler.x = Math::atan2(-elements[1][2], elements[2][2]);
+				euler.y = Math::asin(sy);
+				euler.z = Math::atan2(-elements[0][1], elements[0][0]);
+			}
+		} else {
+			euler.x = Math::atan2(elements[2][1], elements[1][1]);
+			euler.y = -Math_PI / 2.0;
+			euler.z = 0.0;
+		}
+	} else {
+		euler.x = Math::atan2(elements[2][1], elements[1][1]);
+		euler.y = Math_PI / 2.0;
+		euler.z = 0.0;
+	}
+	return euler;
+}
+
+// set_euler_xyz expects a vector containing the Euler angles in the format
+// (ax,ay,az), where ax is the angle of rotation around x axis,
+// and similar for other axes.
+// The current implementation uses XYZ convention (Z is the first rotation).
+void Basis::set_euler_xyz(const Vector3 &p_euler) {
+	real_t c, s;
+
+	c = Math::cos(p_euler.x);
+	s = Math::sin(p_euler.x);
+	Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c);
+
+	c = Math::cos(p_euler.y);
+	s = Math::sin(p_euler.y);
+	Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c);
+
+	c = Math::cos(p_euler.z);
+	s = Math::sin(p_euler.z);
+	Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0);
+
+	//optimizer will optimize away all this anyway
+	*this = xmat * (ymat * zmat);
+}
+
+Vector3 Basis::get_euler_xzy() const {
+	// Euler angles in XZY convention.
+	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+	//
+	// rot =  cz*cy             -sz             cz*sy
+	//        sx*sy+cx*cy*sz    cx*cz           cx*sz*sy-cy*sx
+	//        cy*sx*sz          cz*sx           cx*cy+sx*sz*sy
+
+	Vector3 euler;
+	real_t sz = elements[0][1];
+	if (sz < (1.0 - CMP_EPSILON)) {
+		if (sz > -(1.0 - CMP_EPSILON)) {
+			euler.x = Math::atan2(elements[2][1], elements[1][1]);
+			euler.y = Math::atan2(elements[0][2], elements[0][0]);
+			euler.z = Math::asin(-sz);
+		} else {
+			// It's -1
+			euler.x = -Math::atan2(elements[1][2], elements[2][2]);
+			euler.y = 0.0;
+			euler.z = Math_PI / 2.0;
+		}
+	} else {
+		// It's 1
+		euler.x = -Math::atan2(elements[1][2], elements[2][2]);
+		euler.y = 0.0;
+		euler.z = -Math_PI / 2.0;
+	}
+	return euler;
+}
+
+void Basis::set_euler_xzy(const Vector3 &p_euler) {
+	real_t c, s;
+
+	c = Math::cos(p_euler.x);
+	s = Math::sin(p_euler.x);
+	Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c);
+
+	c = Math::cos(p_euler.y);
+	s = Math::sin(p_euler.y);
+	Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c);
+
+	c = Math::cos(p_euler.z);
+	s = Math::sin(p_euler.z);
+	Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0);
+
+	*this = xmat * zmat * ymat;
+}
+
+Vector3 Basis::get_euler_yzx() const {
+	// Euler angles in YZX convention.
+	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+	//
+	// rot =  cy*cz             sy*sx-cy*cx*sz     cx*sy+cy*sz*sx
+	//        sz                cz*cx              -cz*sx
+	//        -cz*sy            cy*sx+cx*sy*sz     cy*cx-sy*sz*sx
+
+	Vector3 euler;
+	real_t sz = elements[1][0];
+	if (sz < (1.0 - CMP_EPSILON)) {
+		if (sz > -(1.0 - CMP_EPSILON)) {
+			euler.x = Math::atan2(-elements[1][2], elements[1][1]);
+			euler.y = Math::atan2(-elements[2][0], elements[0][0]);
+			euler.z = Math::asin(sz);
+		} else {
+			// It's -1
+			euler.x = Math::atan2(elements[2][1], elements[2][2]);
+			euler.y = 0.0;
+			euler.z = -Math_PI / 2.0;
+		}
+	} else {
+		// It's 1
+		euler.x = Math::atan2(elements[2][1], elements[2][2]);
+		euler.y = 0.0;
+		euler.z = Math_PI / 2.0;
+	}
+	return euler;
+}
+
+void Basis::set_euler_yzx(const Vector3 &p_euler) {
+	real_t c, s;
+
+	c = Math::cos(p_euler.x);
+	s = Math::sin(p_euler.x);
+	Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c);
+
+	c = Math::cos(p_euler.y);
+	s = Math::sin(p_euler.y);
+	Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c);
+
+	c = Math::cos(p_euler.z);
+	s = Math::sin(p_euler.z);
+	Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0);
+
+	*this = ymat * zmat * xmat;
+}
+
+// get_euler_yxz returns a vector containing the Euler angles in the YXZ convention,
+// as in first-Z, then-X, last-Y. The angles for X, Y, and Z rotations are returned
+// as the x, y, and z components of a Vector3 respectively.
+Vector3 Basis::get_euler_yxz() const {
+	// Euler angles in YXZ convention.
+	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+	//
+	// rot =  cy*cz+sy*sx*sz    cz*sy*sx-cy*sz        cx*sy
+	//        cx*sz             cx*cz                 -sx
+	//        cy*sx*sz-cz*sy    cy*cz*sx+sy*sz        cy*cx
+
+	Vector3 euler;
+
+	real_t m12 = elements[1][2];
+
+	if (m12 < (1 - CMP_EPSILON)) {
+		if (m12 > -(1 - CMP_EPSILON)) {
+			// is this a pure X rotation?
+			if (elements[1][0] == 0 && elements[0][1] == 0 && elements[0][2] == 0 && elements[2][0] == 0 && elements[0][0] == 1) {
+				// return the simplest form (human friendlier in editor and scripts)
+				euler.x = atan2(-m12, elements[1][1]);
+				euler.y = 0;
+				euler.z = 0;
+			} else {
+				euler.x = asin(-m12);
+				euler.y = atan2(elements[0][2], elements[2][2]);
+				euler.z = atan2(elements[1][0], elements[1][1]);
+			}
+		} else { // m12 == -1
+			euler.x = Math_PI * 0.5;
+			euler.y = atan2(elements[0][1], elements[0][0]);
+			euler.z = 0;
+		}
+	} else { // m12 == 1
+		euler.x = -Math_PI * 0.5;
+		euler.y = -atan2(elements[0][1], elements[0][0]);
+		euler.z = 0;
+	}
+
+	return euler;
+}
+
+// set_euler_yxz expects a vector containing the Euler angles in the format
+// (ax,ay,az), where ax is the angle of rotation around x axis,
+// and similar for other axes.
+// The current implementation uses YXZ convention (Z is the first rotation).
+void Basis::set_euler_yxz(const Vector3 &p_euler) {
+	real_t c, s;
+
+	c = Math::cos(p_euler.x);
+	s = Math::sin(p_euler.x);
+	Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c);
+
+	c = Math::cos(p_euler.y);
+	s = Math::sin(p_euler.y);
+	Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c);
+
+	c = Math::cos(p_euler.z);
+	s = Math::sin(p_euler.z);
+	Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0);
+
+	//optimizer will optimize away all this anyway
+	*this = ymat * xmat * zmat;
+}
+
+Vector3 Basis::get_euler_zxy() const {
+	// Euler angles in ZXY convention.
+	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+	//
+	// rot =  cz*cy-sz*sx*sy    -cx*sz                cz*sy+cy*sz*sx
+	//        cy*sz+cz*sx*sy    cz*cx                 sz*sy-cz*cy*sx
+	//        -cx*sy            sx                    cx*cy
+	Vector3 euler;
+	real_t sx = elements[2][1];
+	if (sx < (1.0 - CMP_EPSILON)) {
+		if (sx > -(1.0 - CMP_EPSILON)) {
+			euler.x = Math::asin(sx);
+			euler.y = Math::atan2(-elements[2][0], elements[2][2]);
+			euler.z = Math::atan2(-elements[0][1], elements[1][1]);
+		} else {
+			// It's -1
+			euler.x = -Math_PI / 2.0;
+			euler.y = Math::atan2(elements[0][2], elements[0][0]);
+			euler.z = 0;
+		}
+	} else {
+		// It's 1
+		euler.x = Math_PI / 2.0;
+		euler.y = Math::atan2(elements[0][2], elements[0][0]);
+		euler.z = 0;
+	}
+	return euler;
+}
+
+void Basis::set_euler_zxy(const Vector3 &p_euler) {
+	real_t c, s;
+
+	c = Math::cos(p_euler.x);
+	s = Math::sin(p_euler.x);
+	Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c);
+
+	c = Math::cos(p_euler.y);
+	s = Math::sin(p_euler.y);
+	Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c);
+
+	c = Math::cos(p_euler.z);
+	s = Math::sin(p_euler.z);
+	Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0);
+
+	*this = zmat * xmat * ymat;
+}
+
+Vector3 Basis::get_euler_zyx() const {
+	// Euler angles in ZYX convention.
+	// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+	//
+	// rot =  cz*cy             cz*sy*sx-cx*sz        sz*sx+cz*cx*cy
+	//        cy*sz             cz*cx+sz*sy*sx        cx*sz*sy-cz*sx
+	//        -sy               cy*sx                 cy*cx
+	Vector3 euler;
+	real_t sy = elements[2][0];
+	if (sy < (1.0 - CMP_EPSILON)) {
+		if (sy > -(1.0 - CMP_EPSILON)) {
+			euler.x = Math::atan2(elements[2][1], elements[2][2]);
+			euler.y = Math::asin(-sy);
+			euler.z = Math::atan2(elements[1][0], elements[0][0]);
+		} else {
+			// It's -1
+			euler.x = 0;
+			euler.y = Math_PI / 2.0;
+			euler.z = -Math::atan2(elements[0][1], elements[1][1]);
+		}
+	} else {
+		// It's 1
+		euler.x = 0;
+		euler.y = -Math_PI / 2.0;
+		euler.z = -Math::atan2(elements[0][1], elements[1][1]);
+	}
+	return euler;
+}
+
+void Basis::set_euler_zyx(const Vector3 &p_euler) {
+	real_t c, s;
+
+	c = Math::cos(p_euler.x);
+	s = Math::sin(p_euler.x);
+	Basis xmat(1.0, 0.0, 0.0, 0.0, c, -s, 0.0, s, c);
+
+	c = Math::cos(p_euler.y);
+	s = Math::sin(p_euler.y);
+	Basis ymat(c, 0.0, s, 0.0, 1.0, 0.0, -s, 0.0, c);
+
+	c = Math::cos(p_euler.z);
+	s = Math::sin(p_euler.z);
+	Basis zmat(c, -s, 0.0, s, c, 0.0, 0.0, 0.0, 1.0);
+
+	*this = zmat * ymat * xmat;
+}
+
+bool Basis::is_equal_approx(const Basis &p_basis) const {
+	return elements[0].is_equal_approx(p_basis.elements[0]) && elements[1].is_equal_approx(p_basis.elements[1]) && elements[2].is_equal_approx(p_basis.elements[2]);
+}
+
+bool Basis::operator==(const Basis &p_matrix) const {
+	for (int i = 0; i < 3; i++) {
+		for (int j = 0; j < 3; j++) {
+			if (elements[i][j] != p_matrix.elements[i][j]) {
+				return false;
+			}
+		}
+	}
+
+	return true;
+}
+
+bool Basis::operator!=(const Basis &p_matrix) const {
+	return (!(*this == p_matrix));
+}
+
+Basis::operator String() const {
+	String mtx;
+	for (int i = 0; i < 3; i++) {
+		for (int j = 0; j < 3; j++) {
+			if (i != 0 || j != 0) {
+				mtx = mtx + ", ";
+			}
+
+			mtx = mtx + String::num(elements[j][i]); //matrix is stored transposed for performance, so print it transposed
+		}
+	}
+
+	return mtx;
+}
+
+Quaternion Basis::get_quat() const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!is_rotation(), Quaternion());
+#endif
+	/* Allow getting a quaternion from an unnormalized transform */
+	Basis m = *this;
+	real_t trace = m.elements[0][0] + m.elements[1][1] + m.elements[2][2];
+	real_t temp[4];
+
+	if (trace > 0.0) {
+		real_t s = Math::sqrt(trace + 1.0);
+		temp[3] = (s * 0.5);
+		s = 0.5 / s;
+
+		temp[0] = ((m.elements[2][1] - m.elements[1][2]) * s);
+		temp[1] = ((m.elements[0][2] - m.elements[2][0]) * s);
+		temp[2] = ((m.elements[1][0] - m.elements[0][1]) * s);
+	} else {
+		int i = m.elements[0][0] < m.elements[1][1] ?
+						  (m.elements[1][1] < m.elements[2][2] ? 2 : 1) :
+						  (m.elements[0][0] < m.elements[2][2] ? 2 : 0);
+		int j = (i + 1) % 3;
+		int k = (i + 2) % 3;
+
+		real_t s = Math::sqrt(m.elements[i][i] - m.elements[j][j] - m.elements[k][k] + 1.0);
+		temp[i] = s * 0.5;
+		s = 0.5 / s;
+
+		temp[3] = (m.elements[k][j] - m.elements[j][k]) * s;
+		temp[j] = (m.elements[j][i] + m.elements[i][j]) * s;
+		temp[k] = (m.elements[k][i] + m.elements[i][k]) * s;
+	}
+
+	return Quaternion(temp[0], temp[1], temp[2], temp[3]);
+}
+
+static const Basis _ortho_bases[24] = {
+	Basis(1, 0, 0, 0, 1, 0, 0, 0, 1),
+	Basis(0, -1, 0, 1, 0, 0, 0, 0, 1),
+	Basis(-1, 0, 0, 0, -1, 0, 0, 0, 1),
+	Basis(0, 1, 0, -1, 0, 0, 0, 0, 1),
+	Basis(1, 0, 0, 0, 0, -1, 0, 1, 0),
+	Basis(0, 0, 1, 1, 0, 0, 0, 1, 0),
+	Basis(-1, 0, 0, 0, 0, 1, 0, 1, 0),
+	Basis(0, 0, -1, -1, 0, 0, 0, 1, 0),
+	Basis(1, 0, 0, 0, -1, 0, 0, 0, -1),
+	Basis(0, 1, 0, 1, 0, 0, 0, 0, -1),
+	Basis(-1, 0, 0, 0, 1, 0, 0, 0, -1),
+	Basis(0, -1, 0, -1, 0, 0, 0, 0, -1),
+	Basis(1, 0, 0, 0, 0, 1, 0, -1, 0),
+	Basis(0, 0, -1, 1, 0, 0, 0, -1, 0),
+	Basis(-1, 0, 0, 0, 0, -1, 0, -1, 0),
+	Basis(0, 0, 1, -1, 0, 0, 0, -1, 0),
+	Basis(0, 0, 1, 0, 1, 0, -1, 0, 0),
+	Basis(0, -1, 0, 0, 0, 1, -1, 0, 0),
+	Basis(0, 0, -1, 0, -1, 0, -1, 0, 0),
+	Basis(0, 1, 0, 0, 0, -1, -1, 0, 0),
+	Basis(0, 0, 1, 0, -1, 0, 1, 0, 0),
+	Basis(0, 1, 0, 0, 0, 1, 1, 0, 0),
+	Basis(0, 0, -1, 0, 1, 0, 1, 0, 0),
+	Basis(0, -1, 0, 0, 0, -1, 1, 0, 0)
+};
+
+int Basis::get_orthogonal_index() const {
+	//could be sped up if i come up with a way
+	Basis orth = *this;
+	for (int i = 0; i < 3; i++) {
+		for (int j = 0; j < 3; j++) {
+			real_t v = orth[i][j];
+			if (v > 0.5) {
+				v = 1.0;
+			} else if (v < -0.5) {
+				v = -1.0;
+			} else {
+				v = 0;
+			}
+
+			orth[i][j] = v;
+		}
+	}
+
+	for (int i = 0; i < 24; i++) {
+		if (_ortho_bases[i] == orth) {
+			return i;
+		}
+	}
+
+	return 0;
+}
+
+void Basis::set_orthogonal_index(int p_index) {
+	//there only exist 24 orthogonal bases in r3
+	ERR_FAIL_INDEX(p_index, 24);
+
+	*this = _ortho_bases[p_index];
+}
+
+void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
+	/* checking this is a bad idea, because obtaining from scaled transform is a valid use case
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND(!is_rotation());
+#endif
+*/
+	real_t angle, x, y, z; // variables for result
+	real_t epsilon = 0.01; // margin to allow for rounding errors
+	real_t epsilon2 = 0.1; // margin to distinguish between 0 and 180 degrees
+
+	if ((Math::abs(elements[1][0] - elements[0][1]) < epsilon) && (Math::abs(elements[2][0] - elements[0][2]) < epsilon) && (Math::abs(elements[2][1] - elements[1][2]) < epsilon)) {
+		// singularity found
+		// first check for identity matrix which must have +1 for all terms
+		//  in leading diagonaland zero in other terms
+		if ((Math::abs(elements[1][0] + elements[0][1]) < epsilon2) && (Math::abs(elements[2][0] + elements[0][2]) < epsilon2) && (Math::abs(elements[2][1] + elements[1][2]) < epsilon2) && (Math::abs(elements[0][0] + elements[1][1] + elements[2][2] - 3) < epsilon2)) {
+			// this singularity is identity matrix so angle = 0
+			r_axis = Vector3(0, 1, 0);
+			r_angle = 0;
+			return;
+		}
+		// otherwise this singularity is angle = 180
+		angle = Math_PI;
+		real_t xx = (elements[0][0] + 1) / 2;
+		real_t yy = (elements[1][1] + 1) / 2;
+		real_t zz = (elements[2][2] + 1) / 2;
+		real_t xy = (elements[1][0] + elements[0][1]) / 4;
+		real_t xz = (elements[2][0] + elements[0][2]) / 4;
+		real_t yz = (elements[2][1] + elements[1][2]) / 4;
+		if ((xx > yy) && (xx > zz)) { // elements[0][0] is the largest diagonal term
+			if (xx < epsilon) {
+				x = 0;
+				y = Math_SQRT12;
+				z = Math_SQRT12;
+			} else {
+				x = Math::sqrt(xx);
+				y = xy / x;
+				z = xz / x;
+			}
+		} else if (yy > zz) { // elements[1][1] is the largest diagonal term
+			if (yy < epsilon) {
+				x = Math_SQRT12;
+				y = 0;
+				z = Math_SQRT12;
+			} else {
+				y = Math::sqrt(yy);
+				x = xy / y;
+				z = yz / y;
+			}
+		} else { // elements[2][2] is the largest diagonal term so base result on this
+			if (zz < epsilon) {
+				x = Math_SQRT12;
+				y = Math_SQRT12;
+				z = 0;
+			} else {
+				z = Math::sqrt(zz);
+				x = xz / z;
+				y = yz / z;
+			}
+		}
+		r_axis = Vector3(x, y, z);
+		r_angle = angle;
+		return;
+	}
+	// as we have reached here there are no singularities so we can handle normally
+	real_t s = Math::sqrt((elements[1][2] - elements[2][1]) * (elements[1][2] - elements[2][1]) + (elements[2][0] - elements[0][2]) * (elements[2][0] - elements[0][2]) + (elements[0][1] - elements[1][0]) * (elements[0][1] - elements[1][0])); // s=|axis||sin(angle)|, used to normalise
+
+	angle = Math::acos((elements[0][0] + elements[1][1] + elements[2][2] - 1) / 2);
+	if (angle < 0) {
+		s = -s;
+	}
+	x = (elements[2][1] - elements[1][2]) / s;
+	y = (elements[0][2] - elements[2][0]) / s;
+	z = (elements[1][0] - elements[0][1]) / s;
+
+	r_axis = Vector3(x, y, z);
+	r_angle = angle;
+}
+
+void Basis::set_quat(const Quaternion &p_quat) {
+	real_t d = p_quat.length_squared();
+	real_t s = 2.0 / d;
+	real_t xs = p_quat.x * s, ys = p_quat.y * s, zs = p_quat.z * s;
+	real_t wx = p_quat.w * xs, wy = p_quat.w * ys, wz = p_quat.w * zs;
+	real_t xx = p_quat.x * xs, xy = p_quat.x * ys, xz = p_quat.x * zs;
+	real_t yy = p_quat.y * ys, yz = p_quat.y * zs, zz = p_quat.z * zs;
+	set(1.0 - (yy + zz), xy - wz, xz + wy,
+			xy + wz, 1.0 - (xx + zz), yz - wx,
+			xz - wy, yz + wx, 1.0 - (xx + yy));
+}
+
+void Basis::set_axis_angle(const Vector3 &p_axis, real_t p_phi) {
+// Rotation matrix from axis and angle, see https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_angle
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND(!p_axis.is_normalized());
+#endif
+	Vector3 axis_sq(p_axis.x * p_axis.x, p_axis.y * p_axis.y, p_axis.z * p_axis.z);
+	real_t cosine = Math::cos(p_phi);
+	elements[0][0] = axis_sq.x + cosine * (1.0 - axis_sq.x);
+	elements[1][1] = axis_sq.y + cosine * (1.0 - axis_sq.y);
+	elements[2][2] = axis_sq.z + cosine * (1.0 - axis_sq.z);
+
+	real_t sine = Math::sin(p_phi);
+	real_t t = 1 - cosine;
+
+	real_t xyzt = p_axis.x * p_axis.y * t;
+	real_t zyxs = p_axis.z * sine;
+	elements[0][1] = xyzt - zyxs;
+	elements[1][0] = xyzt + zyxs;
+
+	xyzt = p_axis.x * p_axis.z * t;
+	zyxs = p_axis.y * sine;
+	elements[0][2] = xyzt + zyxs;
+	elements[2][0] = xyzt - zyxs;
+
+	xyzt = p_axis.y * p_axis.z * t;
+	zyxs = p_axis.x * sine;
+	elements[1][2] = xyzt - zyxs;
+	elements[2][1] = xyzt + zyxs;
+}
+
+void Basis::set_axis_angle_scale(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale) {
+	set_diagonal(p_scale);
+	rotate(p_axis, p_phi);
+}
+
+void Basis::set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale) {
+	set_diagonal(p_scale);
+	rotate(p_euler);
+}
+
+void Basis::set_quat_scale(const Quaternion &p_quat, const Vector3 &p_scale) {
+	set_diagonal(p_scale);
+	rotate(p_quat);
+}
+
+void Basis::set_diagonal(const Vector3 &p_diag) {
+	elements[0][0] = p_diag.x;
+	elements[0][1] = 0;
+	elements[0][2] = 0;
+
+	elements[1][0] = 0;
+	elements[1][1] = p_diag.y;
+	elements[1][2] = 0;
+
+	elements[2][0] = 0;
+	elements[2][1] = 0;
+	elements[2][2] = p_diag.z;
+}
+
+Basis Basis::slerp(const Basis &p_to, const real_t &p_weight) const {
+	//consider scale
+	Quaternion from(*this);
+	Quaternion to(p_to);
+
+	Basis b(from.slerp(to, p_weight));
+	b.elements[0] *= Math::lerp(elements[0].length(), p_to.elements[0].length(), p_weight);
+	b.elements[1] *= Math::lerp(elements[1].length(), p_to.elements[1].length(), p_weight);
+	b.elements[2] *= Math::lerp(elements[2].length(), p_to.elements[2].length(), p_weight);
+
+	return b;
+}
+
+void Basis::rotate_sh(real_t *p_values) {
+	// code by John Hable
+	// http://filmicworlds.com/blog/simple-and-fast-spherical-harmonic-rotation/
+	// this code is Public Domain
+
+	const static real_t s_c3 = 0.94617469575; // (3*sqrt(5))/(4*sqrt(pi))
+	const static real_t s_c4 = -0.31539156525; // (-sqrt(5))/(4*sqrt(pi))
+	const static real_t s_c5 = 0.54627421529; // (sqrt(15))/(4*sqrt(pi))
+
+	const static real_t s_c_scale = 1.0 / 0.91529123286551084;
+	const static real_t s_c_scale_inv = 0.91529123286551084;
+
+	const static real_t s_rc2 = 1.5853309190550713 * s_c_scale;
+	const static real_t s_c4_div_c3 = s_c4 / s_c3;
+	const static real_t s_c4_div_c3_x2 = (s_c4 / s_c3) * 2.0;
+
+	const static real_t s_scale_dst2 = s_c3 * s_c_scale_inv;
+	const static real_t s_scale_dst4 = s_c5 * s_c_scale_inv;
+
+	real_t src[9] = { p_values[0], p_values[1], p_values[2], p_values[3], p_values[4], p_values[5], p_values[6], p_values[7], p_values[8] };
+
+	real_t m00 = elements[0][0];
+	real_t m01 = elements[0][1];
+	real_t m02 = elements[0][2];
+	real_t m10 = elements[1][0];
+	real_t m11 = elements[1][1];
+	real_t m12 = elements[1][2];
+	real_t m20 = elements[2][0];
+	real_t m21 = elements[2][1];
+	real_t m22 = elements[2][2];
+
+	p_values[0] = src[0];
+	p_values[1] = m11 * src[1] - m12 * src[2] + m10 * src[3];
+	p_values[2] = -m21 * src[1] + m22 * src[2] - m20 * src[3];
+	p_values[3] = m01 * src[1] - m02 * src[2] + m00 * src[3];
+
+	real_t sh0 = src[7] + src[8] + src[8] - src[5];
+	real_t sh1 = src[4] + s_rc2 * src[6] + src[7] + src[8];
+	real_t sh2 = src[4];
+	real_t sh3 = -src[7];
+	real_t sh4 = -src[5];
+
+	// Rotations.  R0 and R1 just use the raw matrix columns
+	real_t r2x = m00 + m01;
+	real_t r2y = m10 + m11;
+	real_t r2z = m20 + m21;
+
+	real_t r3x = m00 + m02;
+	real_t r3y = m10 + m12;
+	real_t r3z = m20 + m22;
+
+	real_t r4x = m01 + m02;
+	real_t r4y = m11 + m12;
+	real_t r4z = m21 + m22;
+
+	// dense matrix multiplication one column at a time
+
+	// column 0
+	real_t sh0_x = sh0 * m00;
+	real_t sh0_y = sh0 * m10;
+	real_t d0 = sh0_x * m10;
+	real_t d1 = sh0_y * m20;
+	real_t d2 = sh0 * (m20 * m20 + s_c4_div_c3);
+	real_t d3 = sh0_x * m20;
+	real_t d4 = sh0_x * m00 - sh0_y * m10;
+
+	// column 1
+	real_t sh1_x = sh1 * m02;
+	real_t sh1_y = sh1 * m12;
+	d0 += sh1_x * m12;
+	d1 += sh1_y * m22;
+	d2 += sh1 * (m22 * m22 + s_c4_div_c3);
+	d3 += sh1_x * m22;
+	d4 += sh1_x * m02 - sh1_y * m12;
+
+	// column 2
+	real_t sh2_x = sh2 * r2x;
+	real_t sh2_y = sh2 * r2y;
+	d0 += sh2_x * r2y;
+	d1 += sh2_y * r2z;
+	d2 += sh2 * (r2z * r2z + s_c4_div_c3_x2);
+	d3 += sh2_x * r2z;
+	d4 += sh2_x * r2x - sh2_y * r2y;
+
+	// column 3
+	real_t sh3_x = sh3 * r3x;
+	real_t sh3_y = sh3 * r3y;
+	d0 += sh3_x * r3y;
+	d1 += sh3_y * r3z;
+	d2 += sh3 * (r3z * r3z + s_c4_div_c3_x2);
+	d3 += sh3_x * r3z;
+	d4 += sh3_x * r3x - sh3_y * r3y;
+
+	// column 4
+	real_t sh4_x = sh4 * r4x;
+	real_t sh4_y = sh4 * r4y;
+	d0 += sh4_x * r4y;
+	d1 += sh4_y * r4z;
+	d2 += sh4 * (r4z * r4z + s_c4_div_c3_x2);
+	d3 += sh4_x * r4z;
+	d4 += sh4_x * r4x - sh4_y * r4y;
+
+	// extra multipliers
+	p_values[4] = d0;
+	p_values[5] = -d1;
+	p_values[6] = d2 * s_scale_dst2;
+	p_values[7] = -d3;
+	p_values[8] = d4 * s_scale_dst4;
+}
+
+} // namespace godot

src/variant/char_string.cpp

@@ -192,6 +192,14 @@ bool String::operator!=(const char32_t *p_str) const {
 	return *this != String(p_str);
 }
 
+const char32_t &String::operator[](int p_index) const {
+	return *internal::interface->string_operator_index_const((GDNativeStringPtr) this, p_index);
+}
+
+char32_t &String::operator[](int p_index) {
+	return *internal::interface->string_operator_index((GDNativeStringPtr) this, p_index);
+}
+
 bool operator==(const char *p_chr, const String &p_str) {
 	return p_str == String(p_chr);
 }

src/variant/color.cpp

@@ -0,0 +1,532 @@
+#include <godot_cpp/core/error_macros.hpp>
+#include <godot_cpp/variant/color.hpp>
+#include <godot_cpp/variant/color_names.inc.hpp>
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+uint32_t Color::to_argb32() const {
+	uint32_t c = (uint8_t)Math::round(a * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(r * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(g * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(b * 255);
+
+	return c;
+}
+
+uint32_t Color::to_abgr32() const {
+	uint32_t c = (uint8_t)Math::round(a * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(b * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(g * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(r * 255);
+
+	return c;
+}
+
+uint32_t Color::to_rgba32() const {
+	uint32_t c = (uint8_t)Math::round(r * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(g * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(b * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(a * 255);
+
+	return c;
+}
+
+uint64_t Color::to_abgr64() const {
+	uint64_t c = (uint16_t)Math::round(a * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(b * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(g * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(r * 65535);
+
+	return c;
+}
+
+uint64_t Color::to_argb64() const {
+	uint64_t c = (uint16_t)Math::round(a * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(r * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(g * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(b * 65535);
+
+	return c;
+}
+
+uint64_t Color::to_rgba64() const {
+	uint64_t c = (uint16_t)Math::round(r * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(g * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(b * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(a * 65535);
+
+	return c;
+}
+
+float Color::get_h() const {
+	float min = Math::min(r, g);
+	min = Math::min(min, b);
+	float max = Math::max(r, g);
+	max = Math::max(max, b);
+
+	float delta = max - min;
+
+	if (delta == 0) {
+		return 0;
+	}
+
+	float h;
+	if (r == max) {
+		h = (g - b) / delta; // between yellow & magenta
+	} else if (g == max) {
+		h = 2 + (b - r) / delta; // between cyan & yellow
+	} else {
+		h = 4 + (r - g) / delta; // between magenta & cyan
+	}
+
+	h /= 6.0;
+	if (h < 0) {
+		h += 1.0;
+	}
+
+	return h;
+}
+
+float Color::get_s() const {
+	float min = Math::min(r, g);
+	min = Math::min(min, b);
+	float max = Math::max(r, g);
+	max = Math::max(max, b);
+
+	float delta = max - min;
+
+	return (max != 0) ? (delta / max) : 0;
+}
+
+float Color::get_v() const {
+	float max = Math::max(r, g);
+	max = Math::max(max, b);
+	return max;
+}
+
+void Color::set_hsv(float p_h, float p_s, float p_v, float p_alpha) {
+	int i;
+	float f, p, q, t;
+	a = p_alpha;
+
+	if (p_s == 0) {
+		// Achromatic (grey)
+		r = g = b = p_v;
+		return;
+	}
+
+	p_h *= 6.0;
+	p_h = Math::fmod(p_h, 6);
+	i = Math::floor(p_h);
+
+	f = p_h - i;
+	p = p_v * (1 - p_s);
+	q = p_v * (1 - p_s * f);
+	t = p_v * (1 - p_s * (1 - f));
+
+	switch (i) {
+		case 0: // Red is the dominant color
+			r = p_v;
+			g = t;
+			b = p;
+			break;
+		case 1: // Green is the dominant color
+			r = q;
+			g = p_v;
+			b = p;
+			break;
+		case 2:
+			r = p;
+			g = p_v;
+			b = t;
+			break;
+		case 3: // Blue is the dominant color
+			r = p;
+			g = q;
+			b = p_v;
+			break;
+		case 4:
+			r = t;
+			g = p;
+			b = p_v;
+			break;
+		default: // (5) Red is the dominant color
+			r = p_v;
+			g = p;
+			b = q;
+			break;
+	}
+}
+
+bool Color::is_equal_approx(const Color &p_color) const {
+	return Math::is_equal_approx(r, p_color.r) && Math::is_equal_approx(g, p_color.g) && Math::is_equal_approx(b, p_color.b) && Math::is_equal_approx(a, p_color.a);
+}
+
+void Color::invert() {
+	r = 1.0 - r;
+	g = 1.0 - g;
+	b = 1.0 - b;
+}
+
+Color Color::hex(uint32_t p_hex) {
+	float a = (p_hex & 0xFF) / 255.0;
+	p_hex >>= 8;
+	float b = (p_hex & 0xFF) / 255.0;
+	p_hex >>= 8;
+	float g = (p_hex & 0xFF) / 255.0;
+	p_hex >>= 8;
+	float r = (p_hex & 0xFF) / 255.0;
+
+	return Color(r, g, b, a);
+}
+
+Color Color::hex64(uint64_t p_hex) {
+	float a = (p_hex & 0xFFFF) / 65535.0;
+	p_hex >>= 16;
+	float b = (p_hex & 0xFFFF) / 65535.0;
+	p_hex >>= 16;
+	float g = (p_hex & 0xFFFF) / 65535.0;
+	p_hex >>= 16;
+	float r = (p_hex & 0xFFFF) / 65535.0;
+
+	return Color(r, g, b, a);
+}
+
+Color Color::from_rgbe9995(uint32_t p_rgbe) {
+	float r = p_rgbe & 0x1ff;
+	float g = (p_rgbe >> 9) & 0x1ff;
+	float b = (p_rgbe >> 18) & 0x1ff;
+	float e = (p_rgbe >> 27);
+	float m = Math::pow(2, e - 15.0 - 9.0);
+
+	float rd = r * m;
+	float gd = g * m;
+	float bd = b * m;
+
+	return Color(rd, gd, bd, 1.0f);
+}
+
+static int _parse_col4(const String &p_str, int p_ofs) {
+	char character = p_str[p_ofs];
+
+	if (character >= '0' && character <= '9') {
+		return character - '0';
+	} else if (character >= 'a' && character <= 'f') {
+		return character + (10 - 'a');
+	} else if (character >= 'A' && character <= 'F') {
+		return character + (10 - 'A');
+	}
+	return -1;
+}
+
+static int _parse_col8(const String &p_str, int p_ofs) {
+	return _parse_col4(p_str, p_ofs) * 16 + _parse_col4(p_str, p_ofs + 1);
+}
+
+Color Color::inverted() const {
+	Color c = *this;
+	c.invert();
+	return c;
+}
+
+Color Color::html(const String &p_rgba) {
+	String color = p_rgba;
+	if (color.length() == 0) {
+		return Color();
+	}
+	if (color[0] == '#') {
+		color = color.substr(1);
+	}
+
+	// If enabled, use 1 hex digit per channel instead of 2.
+	// Other sizes aren't in the HTML/CSS spec but we could add them if desired.
+	bool is_shorthand = color.length() < 5;
+	bool alpha = false;
+
+	if (color.length() == 8) {
+		alpha = true;
+	} else if (color.length() == 6) {
+		alpha = false;
+	} else if (color.length() == 4) {
+		alpha = true;
+	} else if (color.length() == 3) {
+		alpha = false;
+	} else {
+		ERR_FAIL_V(Color());
+	}
+
+	float r, g, b, a = 1.0;
+	if (is_shorthand) {
+		r = _parse_col4(color, 0) / 15.0;
+		g = _parse_col4(color, 1) / 15.0;
+		b = _parse_col4(color, 2) / 15.0;
+		if (alpha) {
+			a = _parse_col4(color, 3) / 15.0;
+		}
+	} else {
+		r = _parse_col8(color, 0) / 255.0;
+		g = _parse_col8(color, 2) / 255.0;
+		b = _parse_col8(color, 4) / 255.0;
+		if (alpha) {
+			a = _parse_col8(color, 6) / 255.0;
+		}
+	}
+	ERR_FAIL_COND_V(r < 0, Color());
+	ERR_FAIL_COND_V(g < 0, Color());
+	ERR_FAIL_COND_V(b < 0, Color());
+	ERR_FAIL_COND_V(a < 0, Color());
+
+	return Color(r, g, b, a);
+}
+
+bool Color::html_is_valid(const String &p_color) {
+	String color = p_color;
+
+	if (color.length() == 0) {
+		return false;
+	}
+	if (color[0] == '#') {
+		color = color.substr(1);
+	}
+
+	// Check if the amount of hex digits is valid.
+	int len = color.length();
+	if (!(len == 3 || len == 4 || len == 6 || len == 8)) {
+		return false;
+	}
+
+	// Check if each hex digit is valid.
+	for (int i = 0; i < len; i++) {
+		if (_parse_col4(color, i) == -1) {
+			return false;
+		}
+	}
+
+	return true;
+}
+
+Color Color::named(const String &p_name) {
+	int idx = find_named_color(p_name);
+	if (idx == -1) {
+		ERR_FAIL_V(Color());
+		return Color();
+	}
+	return get_named_color(idx);
+}
+
+Color Color::named(const String &p_name, const Color &p_default) {
+	int idx = find_named_color(p_name);
+	if (idx == -1) {
+		return p_default;
+	}
+	return get_named_color(idx);
+}
+
+int Color::find_named_color(const String &p_name) {
+	String name = p_name;
+	// Normalize name
+	name = name.replace(" ", "");
+	name = name.replace("-", "");
+	name = name.replace("_", "");
+	name = name.replace("'", "");
+	name = name.replace(".", "");
+	name = name.to_lower();
+
+	int idx = 0;
+	while (named_colors[idx].name != nullptr) {
+		if (name == String(named_colors[idx].name)) {
+			return idx;
+		}
+		idx++;
+	}
+
+	return -1;
+}
+
+int Color::get_named_color_count() {
+	int idx = 0;
+	while (named_colors[idx].name != nullptr) {
+		idx++;
+	}
+	return idx;
+}
+
+String Color::get_named_color_name(int p_idx) {
+	return named_colors[p_idx].name;
+}
+
+Color Color::get_named_color(int p_idx) {
+	return named_colors[p_idx].color;
+}
+
+// For a version that errors on invalid values instead of returning
+// a default color, use the Color(String) constructor instead.
+Color Color::from_string(const String &p_string, const Color &p_default) {
+	if (html_is_valid(p_string)) {
+		return html(p_string);
+	} else {
+		return named(p_string, p_default);
+	}
+}
+
+String _to_hex(float p_val) {
+	int v = Math::round(p_val * 255);
+	v = Math::clamp(v, 0, 255);
+	String ret;
+
+	for (int i = 0; i < 2; i++) {
+		char32_t c[2] = { 0, 0 };
+		int lv = v & 0xF;
+		if (lv < 10) {
+			c[0] = '0' + lv;
+		} else {
+			c[0] = 'a' + lv - 10;
+		}
+
+		v >>= 4;
+		String cs = (const char32_t *)c;
+		ret = cs + ret;
+	}
+
+	return ret;
+}
+
+String Color::to_html(bool p_alpha) const {
+	String txt;
+	txt = txt + _to_hex(g);
+	txt = txt + _to_hex(b);
+	txt = txt + _to_hex(r);
+	if (p_alpha) {
+		txt = txt + _to_hex(a);
+	}
+	return txt;
+}
+
+Color Color::from_hsv(float p_h, float p_s, float p_v, float p_a) {
+	Color result;
+	result.set_hsv(p_h, p_s, p_v, p_a);
+	return result;
+}
+
+Color::operator String() const {
+	return String::num(r, 3) + ", " + String::num(g, 3) + ", " + String::num(b, 3) + ", " + String::num(a, 3);
+}
+
+Color Color::operator+(const Color &p_color) const {
+	return Color(
+			r + p_color.r,
+			g + p_color.g,
+			b + p_color.b,
+			a + p_color.a);
+}
+
+void Color::operator+=(const Color &p_color) {
+	r = r + p_color.r;
+	g = g + p_color.g;
+	b = b + p_color.b;
+	a = a + p_color.a;
+}
+
+Color Color::operator-(const Color &p_color) const {
+	return Color(
+			r - p_color.r,
+			g - p_color.g,
+			b - p_color.b,
+			a - p_color.a);
+}
+
+void Color::operator-=(const Color &p_color) {
+	r = r - p_color.r;
+	g = g - p_color.g;
+	b = b - p_color.b;
+	a = a - p_color.a;
+}
+
+Color Color::operator*(const Color &p_color) const {
+	return Color(
+			r * p_color.r,
+			g * p_color.g,
+			b * p_color.b,
+			a * p_color.a);
+}
+
+Color Color::operator*(float p_scalar) const {
+	return Color(
+			r * p_scalar,
+			g * p_scalar,
+			b * p_scalar,
+			a * p_scalar);
+}
+
+void Color::operator*=(const Color &p_color) {
+	r = r * p_color.r;
+	g = g * p_color.g;
+	b = b * p_color.b;
+	a = a * p_color.a;
+}
+
+void Color::operator*=(float p_scalar) {
+	r = r * p_scalar;
+	g = g * p_scalar;
+	b = b * p_scalar;
+	a = a * p_scalar;
+}
+
+Color Color::operator/(const Color &p_color) const {
+	return Color(
+			r / p_color.r,
+			g / p_color.g,
+			b / p_color.b,
+			a / p_color.a);
+}
+
+Color Color::operator/(float p_scalar) const {
+	return Color(
+			r / p_scalar,
+			g / p_scalar,
+			b / p_scalar,
+			a / p_scalar);
+}
+
+void Color::operator/=(const Color &p_color) {
+	r = r / p_color.r;
+	g = g / p_color.g;
+	b = b / p_color.b;
+	a = a / p_color.a;
+}
+
+void Color::operator/=(float p_scalar) {
+	r = r / p_scalar;
+	g = g / p_scalar;
+	b = b / p_scalar;
+	a = a / p_scalar;
+}
+
+Color Color::operator-() const {
+	return Color(
+			1.0 - r,
+			1.0 - g,
+			1.0 - b,
+			1.0 - a);
+}
+
+} // namespace godot

src/variant/packed_arrays.cpp

@@ -0,0 +1,97 @@
+// extra functions for packed arrays
+
+#include <godot_cpp/godot.hpp>
+
+#include <godot_cpp/variant/packed_byte_array.hpp>
+#include <godot_cpp/variant/packed_color_array.hpp>
+#include <godot_cpp/variant/packed_float32_array.hpp>
+#include <godot_cpp/variant/packed_float64_array.hpp>
+#include <godot_cpp/variant/packed_int32_array.hpp>
+#include <godot_cpp/variant/packed_int64_array.hpp>
+#include <godot_cpp/variant/packed_string_array.hpp>
+#include <godot_cpp/variant/packed_vector2_array.hpp>
+#include <godot_cpp/variant/packed_vector3_array.hpp>
+
+namespace godot {
+
+const uint8_t &PackedByteArray::operator[](int p_index) const {
+	return *internal::interface->packed_byte_array_operator_index_const((GDNativeTypePtr *)this, p_index);
+}
+
+uint8_t &PackedByteArray::operator[](int p_index) {
+	return *internal::interface->packed_byte_array_operator_index((GDNativeTypePtr *)this, p_index);
+}
+
+const Color &PackedColorArray::operator[](int p_index) const {
+	const Color *color = (const Color *) internal::interface->packed_color_array_operator_index_const((GDNativeTypePtr *)this, p_index);
+	return *color;
+}
+
+Color &PackedColorArray::operator[](int p_index) {
+	Color *color = (Color *) internal::interface->packed_color_array_operator_index((GDNativeTypePtr *)this, p_index);
+	return *color;
+}
+
+const float &PackedFloat32Array::operator[](int p_index) const {
+	return *internal::interface->packed_float32_array_operator_index_const((GDNativeTypePtr *)this, p_index);
+}
+
+float &PackedFloat32Array::operator[](int p_index) {
+	return *internal::interface->packed_float32_array_operator_index((GDNativeTypePtr *)this, p_index);
+}
+
+const double &PackedFloat64Array::operator[](int p_index) const {
+	return *internal::interface->packed_float64_array_operator_index_const((GDNativeTypePtr *)this, p_index);
+}
+
+double &PackedFloat64Array::operator[](int p_index) {
+	return *internal::interface->packed_float64_array_operator_index((GDNativeTypePtr *)this, p_index);
+}
+
+const int32_t &PackedInt32Array::operator[](int p_index) const {
+	return *internal::interface->packed_int32_array_operator_index_const((GDNativeTypePtr *)this, p_index);
+}
+
+int32_t &PackedInt32Array::operator[](int p_index) {
+	return *internal::interface->packed_int32_array_operator_index((GDNativeTypePtr *)this, p_index);
+}
+
+const int64_t &PackedInt64Array::operator[](int p_index) const {
+	return *internal::interface->packed_int64_array_operator_index_const((GDNativeTypePtr *)this, p_index);
+}
+
+int64_t &PackedInt64Array::operator[](int p_index) {
+	return *internal::interface->packed_int64_array_operator_index((GDNativeTypePtr *)this, p_index);
+}
+
+const String &PackedStringArray::operator[](int p_index) const {
+	const String *string = (const String *) internal::interface->packed_string_array_operator_index_const((GDNativeTypePtr *)this, p_index);
+	return *string;
+}
+
+String &PackedStringArray::operator[](int p_index) {
+	String *string = (String *) internal::interface->packed_string_array_operator_index((GDNativeTypePtr *)this, p_index);
+	return *string;
+}
+
+const Vector2 &PackedVector2Array::operator[](int p_index) const {
+	const Vector2 *vec = (const Vector2 *) internal::interface->packed_vector2_array_operator_index_const((GDNativeTypePtr *)this, p_index);
+	return *vec;
+}
+
+Vector2 &PackedVector2Array::operator[](int p_index) {
+	Vector2 *vec = (Vector2 *) internal::interface->packed_vector2_array_operator_index((GDNativeTypePtr *)this, p_index);
+	return *vec;
+}
+
+const Vector3 &PackedVector3Array::operator[](int p_index) const {
+	const Vector3 *vec = (const Vector3 *) internal::interface->packed_vector3_array_operator_index_const((GDNativeTypePtr *)this, p_index);
+	return *vec;
+}
+
+Vector3 &PackedVector3Array::operator[](int p_index) {
+	Vector3 *vec = (Vector3 *) internal::interface->packed_vector3_array_operator_index((GDNativeTypePtr *)this, p_index);
+	return *vec;
+}
+
+} // namespace godot

src/variant/plane.cpp

@@ -0,0 +1,127 @@
+#include <godot_cpp/variant/plane.hpp>
+
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+void Plane::set_normal(const Vector3 &p_normal) {
+	normal = p_normal;
+}
+
+void Plane::normalize() {
+	real_t l = normal.length();
+	if (l == 0) {
+		*this = Plane(0, 0, 0, 0);
+		return;
+	}
+	normal /= l;
+	d /= l;
+}
+
+Plane Plane::normalized() const {
+	Plane p = *this;
+	p.normalize();
+	return p;
+}
+
+Vector3 Plane::get_any_perpendicular_normal() const {
+	static const Vector3 p1 = Vector3(1, 0, 0);
+	static const Vector3 p2 = Vector3(0, 1, 0);
+	Vector3 p;
+
+	if (Math::abs(normal.dot(p1)) > 0.99) { // if too similar to p1
+		p = p2; // use p2
+	} else {
+		p = p1; // use p1
+	}
+
+	p -= normal * normal.dot(p);
+	p.normalize();
+
+	return p;
+}
+
+/* intersections */
+
+bool Plane::intersect_3(const Plane &p_plane1, const Plane &p_plane2, Vector3 *r_result) const {
+	const Plane &p_plane0 = *this;
+	Vector3 normal0 = p_plane0.normal;
+	Vector3 normal1 = p_plane1.normal;
+	Vector3 normal2 = p_plane2.normal;
+
+	real_t denom = vec3_cross(normal0, normal1).dot(normal2);
+
+	if (Math::is_zero_approx(denom)) {
+		return false;
+	}
+
+	if (r_result) {
+		*r_result = ((vec3_cross(normal1, normal2) * p_plane0.d) +
+							(vec3_cross(normal2, normal0) * p_plane1.d) +
+							(vec3_cross(normal0, normal1) * p_plane2.d)) /
+					denom;
+	}
+
+	return true;
+}
+
+bool Plane::intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection) const {
+	Vector3 segment = p_dir;
+	real_t den = normal.dot(segment);
+
+	//printf("den is %i\n",den);
+	if (Math::is_zero_approx(den)) {
+		return false;
+	}
+
+	real_t dist = (normal.dot(p_from) - d) / den;
+	//printf("dist is %i\n",dist);
+
+	if (dist > CMP_EPSILON) { //this is a ray, before the emitting pos (p_from) doesn't exist
+
+		return false;
+	}
+
+	dist = -dist;
+	*p_intersection = p_from + segment * dist;
+
+	return true;
+}
+
+bool Plane::intersects_segment(const Vector3 &p_begin, const Vector3 &p_end, Vector3 *p_intersection) const {
+	Vector3 segment = p_begin - p_end;
+	real_t den = normal.dot(segment);
+
+	//printf("den is %i\n",den);
+	if (Math::is_zero_approx(den)) {
+		return false;
+	}
+
+	real_t dist = (normal.dot(p_begin) - d) / den;
+	//printf("dist is %i\n",dist);
+
+	if (dist < -CMP_EPSILON || dist > (1.0 + CMP_EPSILON)) {
+		return false;
+	}
+
+	dist = -dist;
+	*p_intersection = p_begin + segment * dist;
+
+	return true;
+}
+
+/* misc */
+
+bool Plane::is_equal_approx_any_side(const Plane &p_plane) const {
+	return (normal.is_equal_approx(p_plane.normal) && Math::is_equal_approx(d, p_plane.d)) || (normal.is_equal_approx(-p_plane.normal) && Math::is_equal_approx(d, -p_plane.d));
+}
+
+bool Plane::is_equal_approx(const Plane &p_plane) const {
+	return normal.is_equal_approx(p_plane.normal) && Math::is_equal_approx(d, p_plane.d);
+}
+
+Plane::operator String() const {
+	return normal.operator String() + ", " + String::num(d,3);
+}
+
+} // namespace godot

src/variant/quaternion.cpp

@@ -0,0 +1,203 @@
+#include <godot_cpp/variant/quaternion.hpp>
+
+#include <godot_cpp/variant/basis.hpp>
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+// get_euler_xyz returns a vector containing the Euler angles in the format
+// (ax,ay,az), where ax is the angle of rotation around x axis,
+// and similar for other axes.
+// This implementation uses XYZ convention (Z is the first rotation).
+Vector3 Quaternion::get_euler_xyz() const {
+	Basis m(*this);
+	return m.get_euler_xyz();
+}
+
+// get_euler_yxz returns a vector containing the Euler angles in the format
+// (ax,ay,az), where ax is the angle of rotation around x axis,
+// and similar for other axes.
+// This implementation uses YXZ convention (Z is the first rotation).
+Vector3 Quaternion::get_euler_yxz() const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!is_normalized(), Vector3(0, 0, 0));
+#endif
+	Basis m(*this);
+	return m.get_euler_yxz();
+}
+
+void Quaternion::operator*=(const Quaternion &p_q) {
+	x = w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y;
+	y = w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z;
+	z = w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x;
+	w = w * p_q.w - x * p_q.x - y * p_q.y - z * p_q.z;
+}
+
+Quaternion Quaternion::operator*(const Quaternion &p_q) const {
+	Quaternion r = *this;
+	r *= p_q;
+	return r;
+}
+
+bool Quaternion::is_equal_approx(const Quaternion &p_quat) const {
+	return Math::is_equal_approx(x, p_quat.x) && Math::is_equal_approx(y, p_quat.y) && Math::is_equal_approx(z, p_quat.z) && Math::is_equal_approx(w, p_quat.w);
+}
+
+real_t Quaternion::length() const {
+	return Math::sqrt(length_squared());
+}
+
+void Quaternion::normalize() {
+	*this /= length();
+}
+
+Quaternion Quaternion::normalized() const {
+	return *this / length();
+}
+
+bool Quaternion::is_normalized() const {
+	return Math::is_equal_approx(length_squared(), 1.0, UNIT_EPSILON); //use less epsilon
+}
+
+Quaternion Quaternion::inverse() const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!is_normalized(), Quaternion());
+#endif
+	return Quaternion(-x, -y, -z, w);
+}
+
+Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!is_normalized(), Quaternion());
+	ERR_FAIL_COND_V(!p_to.is_normalized(), Quaternion());
+#endif
+	Quaternion to1;
+	real_t omega, cosom, sinom, scale0, scale1;
+
+	// calc cosine
+	cosom = dot(p_to);
+
+	// adjust signs (if necessary)
+	if (cosom < 0.0) {
+		cosom = -cosom;
+		to1.x = -p_to.x;
+		to1.y = -p_to.y;
+		to1.z = -p_to.z;
+		to1.w = -p_to.w;
+	} else {
+		to1.x = p_to.x;
+		to1.y = p_to.y;
+		to1.z = p_to.z;
+		to1.w = p_to.w;
+	}
+
+	// calculate coefficients
+
+	if ((1.0 - cosom) > CMP_EPSILON) {
+		// standard case (slerp)
+		omega = Math::acos(cosom);
+		sinom = Math::sin(omega);
+		scale0 = Math::sin((1.0 - p_weight) * omega) / sinom;
+		scale1 = Math::sin(p_weight * omega) / sinom;
+	} else {
+		// "from" and "to" quaternions are very close
+		//  ... so we can do a linear interpolation
+		scale0 = 1.0 - p_weight;
+		scale1 = p_weight;
+	}
+	// calculate final values
+	return Quaternion(
+			scale0 * x + scale1 * to1.x,
+			scale0 * y + scale1 * to1.y,
+			scale0 * z + scale1 * to1.z,
+			scale0 * w + scale1 * to1.w);
+}
+
+Quaternion Quaternion::slerpni(const Quaternion &p_to, const real_t &p_weight) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!is_normalized(), Quaternion());
+	ERR_FAIL_COND_V(!p_to.is_normalized(), Quaternion());
+#endif
+	const Quaternion &from = *this;
+
+	real_t dot = from.dot(p_to);
+
+	if (Math::abs(dot) > 0.9999) {
+		return from;
+	}
+
+	real_t theta = Math::acos(dot),
+		   sinT = 1.0 / Math::sin(theta),
+		   newFactor = Math::sin(p_weight * theta) * sinT,
+		   invFactor = Math::sin((1.0 - p_weight) * theta) * sinT;
+
+	return Quaternion(invFactor * from.x + newFactor * p_to.x,
+			invFactor * from.y + newFactor * p_to.y,
+			invFactor * from.z + newFactor * p_to.z,
+			invFactor * from.w + newFactor * p_to.w);
+}
+
+Quaternion Quaternion::cubic_slerp(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!is_normalized(), Quaternion());
+	ERR_FAIL_COND_V(!p_b.is_normalized(), Quaternion());
+#endif
+	//the only way to do slerp :|
+	real_t t2 = (1.0 - p_weight) * p_weight * 2;
+	Quaternion sp = this->slerp(p_b, p_weight);
+	Quaternion sq = p_pre_a.slerpni(p_post_b, p_weight);
+	return sp.slerpni(sq, t2);
+}
+
+Quaternion::operator String() const {
+	return String::num(x, 5) + ", " + String::num(y, 5) + ", " + String::num(z, 5) + ", " + String::num(w, 5);
+}
+
+Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND(!p_axis.is_normalized());
+#endif
+	real_t d = p_axis.length();
+	if (d == 0) {
+		x = 0;
+		y = 0;
+		z = 0;
+		w = 0;
+	} else {
+		real_t sin_angle = Math::sin(p_angle * 0.5);
+		real_t cos_angle = Math::cos(p_angle * 0.5);
+		real_t s = sin_angle / d;
+		x = p_axis.x * s;
+		y = p_axis.y * s;
+		z = p_axis.z * s;
+		w = cos_angle;
+	}
+}
+
+// Euler constructor expects a vector containing the Euler angles in the format
+// (ax, ay, az), where ax is the angle of rotation around x axis,
+// and similar for other axes.
+// This implementation uses YXZ convention (Z is the first rotation).
+Quaternion::Quaternion(const Vector3 &p_euler) {
+	real_t half_a1 = p_euler.y * 0.5;
+	real_t half_a2 = p_euler.x * 0.5;
+	real_t half_a3 = p_euler.z * 0.5;
+
+	// R = Y(a1).X(a2).Z(a3) convention for Euler angles.
+	// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
+	// a3 is the angle of the first rotation, following the notation in this reference.
+
+	real_t cos_a1 = Math::cos(half_a1);
+	real_t sin_a1 = Math::sin(half_a1);
+	real_t cos_a2 = Math::cos(half_a2);
+	real_t sin_a2 = Math::sin(half_a2);
+	real_t cos_a3 = Math::cos(half_a3);
+	real_t sin_a3 = Math::sin(half_a3);
+
+	x = sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3;
+	y = sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3;
+	z = -sin_a1 * sin_a2 * cos_a3 + cos_a1 * cos_a2 * sin_a3;
+	w = sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3;
+}
+
+} // namespace godot

src/variant/rect2.cpp

@@ -0,0 +1,241 @@
+#include <godot_cpp/variant/rect2.hpp>
+
+#include <godot_cpp/variant/transform2d.hpp>
+
+namespace godot {
+
+bool Rect2::is_equal_approx(const Rect2 &p_rect) const {
+	return position.is_equal_approx(p_rect.position) && size.is_equal_approx(p_rect.size);
+}
+
+bool Rect2::intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos, Point2 *r_normal) const {
+	real_t min = 0, max = 1;
+	int axis = 0;
+	real_t sign = 0;
+
+	for (int i = 0; i < 2; i++) {
+		real_t seg_from = p_from[i];
+		real_t seg_to = p_to[i];
+		real_t box_begin = position[i];
+		real_t box_end = box_begin + size[i];
+		real_t cmin, cmax;
+		real_t csign;
+
+		if (seg_from < seg_to) {
+			if (seg_from > box_end || seg_to < box_begin) {
+				return false;
+			}
+			real_t length = seg_to - seg_from;
+			cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
+			cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;
+			csign = -1.0;
+
+		} else {
+			if (seg_to > box_end || seg_from < box_begin) {
+				return false;
+			}
+			real_t length = seg_to - seg_from;
+			cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
+			cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
+			csign = 1.0;
+		}
+
+		if (cmin > min) {
+			min = cmin;
+			axis = i;
+			sign = csign;
+		}
+		if (cmax < max) {
+			max = cmax;
+		}
+		if (max < min) {
+			return false;
+		}
+	}
+
+	Vector2 rel = p_to - p_from;
+
+	if (r_normal) {
+		Vector2 normal;
+		normal[axis] = sign;
+		*r_normal = normal;
+	}
+
+	if (r_pos) {
+		*r_pos = p_from + rel * min;
+	}
+
+	return true;
+}
+
+bool Rect2::intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const {
+	//SAT intersection between local and transformed rect2
+
+	Vector2 xf_points[4] = {
+		p_xform.xform(p_rect.position),
+		p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)),
+		p_xform.xform(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
+		p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
+	};
+
+	real_t low_limit;
+
+	//base rect2 first (faster)
+
+	if (xf_points[0].y > position.y) {
+		goto next1;
+	}
+	if (xf_points[1].y > position.y) {
+		goto next1;
+	}
+	if (xf_points[2].y > position.y) {
+		goto next1;
+	}
+	if (xf_points[3].y > position.y) {
+		goto next1;
+	}
+
+	return false;
+
+next1:
+
+	low_limit = position.y + size.y;
+
+	if (xf_points[0].y < low_limit) {
+		goto next2;
+	}
+	if (xf_points[1].y < low_limit) {
+		goto next2;
+	}
+	if (xf_points[2].y < low_limit) {
+		goto next2;
+	}
+	if (xf_points[3].y < low_limit) {
+		goto next2;
+	}
+
+	return false;
+
+next2:
+
+	if (xf_points[0].x > position.x) {
+		goto next3;
+	}
+	if (xf_points[1].x > position.x) {
+		goto next3;
+	}
+	if (xf_points[2].x > position.x) {
+		goto next3;
+	}
+	if (xf_points[3].x > position.x) {
+		goto next3;
+	}
+
+	return false;
+
+next3:
+
+	low_limit = position.x + size.x;
+
+	if (xf_points[0].x < low_limit) {
+		goto next4;
+	}
+	if (xf_points[1].x < low_limit) {
+		goto next4;
+	}
+	if (xf_points[2].x < low_limit) {
+		goto next4;
+	}
+	if (xf_points[3].x < low_limit) {
+		goto next4;
+	}
+
+	return false;
+
+next4:
+
+	Vector2 xf_points2[4] = {
+		position,
+		Vector2(position.x + size.x, position.y),
+		Vector2(position.x, position.y + size.y),
+		Vector2(position.x + size.x, position.y + size.y),
+	};
+
+	real_t maxa = p_xform.elements[0].dot(xf_points2[0]);
+	real_t mina = maxa;
+
+	real_t dp = p_xform.elements[0].dot(xf_points2[1]);
+	maxa = Math::max(dp, maxa);
+	mina = Math::min(dp, mina);
+
+	dp = p_xform.elements[0].dot(xf_points2[2]);
+	maxa = Math::max(dp, maxa);
+	mina = Math::min(dp, mina);
+
+	dp = p_xform.elements[0].dot(xf_points2[3]);
+	maxa = Math::max(dp, maxa);
+	mina = Math::min(dp, mina);
+
+	real_t maxb = p_xform.elements[0].dot(xf_points[0]);
+	real_t minb = maxb;
+
+	dp = p_xform.elements[0].dot(xf_points[1]);
+	maxb = Math::max(dp, maxb);
+	minb = Math::min(dp, minb);
+
+	dp = p_xform.elements[0].dot(xf_points[2]);
+	maxb = Math::max(dp, maxb);
+	minb = Math::min(dp, minb);
+
+	dp = p_xform.elements[0].dot(xf_points[3]);
+	maxb = Math::max(dp, maxb);
+	minb = Math::min(dp, minb);
+
+	if (mina > maxb) {
+		return false;
+	}
+	if (minb > maxa) {
+		return false;
+	}
+
+	maxa = p_xform.elements[1].dot(xf_points2[0]);
+	mina = maxa;
+
+	dp = p_xform.elements[1].dot(xf_points2[1]);
+	maxa = Math::max(dp, maxa);
+	mina = Math::min(dp, mina);
+
+	dp = p_xform.elements[1].dot(xf_points2[2]);
+	maxa = Math::max(dp, maxa);
+	mina = Math::min(dp, mina);
+
+	dp = p_xform.elements[1].dot(xf_points2[3]);
+	maxa = Math::max(dp, maxa);
+	mina = Math::min(dp, mina);
+
+	maxb = p_xform.elements[1].dot(xf_points[0]);
+	minb = maxb;
+
+	dp = p_xform.elements[1].dot(xf_points[1]);
+	maxb = Math::max(dp, maxb);
+	minb = Math::min(dp, minb);
+
+	dp = p_xform.elements[1].dot(xf_points[2]);
+	maxb = Math::max(dp, maxb);
+	minb = Math::min(dp, minb);
+
+	dp = p_xform.elements[1].dot(xf_points[3]);
+	maxb = Math::max(dp, maxb);
+	minb = Math::min(dp, minb);
+
+	if (mina > maxb) {
+		return false;
+	}
+	if (minb > maxa) {
+		return false;
+	}
+
+	return true;
+}
+
+} // namespace godot

src/variant/rect2i.cpp

@@ -0,0 +1,3 @@
+#include <godot_cpp/variant/rect2i.hpp>
+
+// No implementation left. This is here to add the header as a compiled unit.

src/variant/transform2d.cpp

@@ -0,0 +1,248 @@
+#include <godot_cpp/variant/transform2d.hpp>
+
+namespace godot {
+
+void Transform2D::invert() {
+	// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
+	// Transform2D::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
+	SWAP(elements[0][1], elements[1][0]);
+	elements[2] = basis_xform(-elements[2]);
+}
+
+Transform2D Transform2D::inverse() const {
+	Transform2D inv = *this;
+	inv.invert();
+	return inv;
+}
+
+void Transform2D::affine_invert() {
+	real_t det = basis_determinant();
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND(det == 0);
+#endif
+	real_t idet = 1.0 / det;
+
+	SWAP(elements[0][0], elements[1][1]);
+	elements[0] *= Vector2(idet, -idet);
+	elements[1] *= Vector2(-idet, idet);
+
+	elements[2] = basis_xform(-elements[2]);
+}
+
+Transform2D Transform2D::affine_inverse() const {
+	Transform2D inv = *this;
+	inv.affine_invert();
+	return inv;
+}
+
+void Transform2D::rotate(real_t p_phi) {
+	*this = Transform2D(p_phi, Vector2()) * (*this);
+}
+
+real_t Transform2D::get_skew() const {
+	real_t det = basis_determinant();
+	return Math::acos(elements[0].normalized().dot(Math::sign(det) * elements[1].normalized())) - Math_PI * 0.5;
+}
+
+void Transform2D::set_skew(float p_angle) {
+	real_t det = basis_determinant();
+	elements[1] = Math::sign(det) * elements[0].rotated((Math_PI * 0.5 + p_angle)).normalized() * elements[1].length();
+}
+
+real_t Transform2D::get_rotation() const {
+	return Math::atan2(elements[0].y, elements[0].x);
+}
+
+void Transform2D::set_rotation(real_t p_rot) {
+	Size2 scale = get_scale();
+	real_t cr = Math::cos(p_rot);
+	real_t sr = Math::sin(p_rot);
+	elements[0][0] = cr;
+	elements[0][1] = sr;
+	elements[1][0] = -sr;
+	elements[1][1] = cr;
+	set_scale(scale);
+}
+
+Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) {
+	real_t cr = Math::cos(p_rot);
+	real_t sr = Math::sin(p_rot);
+	elements[0][0] = cr;
+	elements[0][1] = sr;
+	elements[1][0] = -sr;
+	elements[1][1] = cr;
+	elements[2] = p_pos;
+}
+
+Size2 Transform2D::get_scale() const {
+	real_t det_sign = Math::sign(basis_determinant());
+	return Size2(elements[0].length(), det_sign * elements[1].length());
+}
+
+void Transform2D::set_scale(const Size2 &p_scale) {
+	elements[0].normalize();
+	elements[1].normalize();
+	elements[0] *= p_scale.x;
+	elements[1] *= p_scale.y;
+}
+
+void Transform2D::scale(const Size2 &p_scale) {
+	scale_basis(p_scale);
+	elements[2] *= p_scale;
+}
+
+void Transform2D::scale_basis(const Size2 &p_scale) {
+	elements[0][0] *= p_scale.x;
+	elements[0][1] *= p_scale.y;
+	elements[1][0] *= p_scale.x;
+	elements[1][1] *= p_scale.y;
+}
+
+void Transform2D::translate(real_t p_tx, real_t p_ty) {
+	translate(Vector2(p_tx, p_ty));
+}
+
+void Transform2D::translate(const Vector2 &p_translation) {
+	elements[2] += basis_xform(p_translation);
+}
+
+void Transform2D::orthonormalize() {
+	// Gram-Schmidt Process
+
+	Vector2 x = elements[0];
+	Vector2 y = elements[1];
+
+	x.normalize();
+	y = (y - x * (x.dot(y)));
+	y.normalize();
+
+	elements[0] = x;
+	elements[1] = y;
+}
+
+Transform2D Transform2D::orthonormalized() const {
+	Transform2D on = *this;
+	on.orthonormalize();
+	return on;
+}
+
+bool Transform2D::is_equal_approx(const Transform2D &p_transform) const {
+	return elements[0].is_equal_approx(p_transform.elements[0]) && elements[1].is_equal_approx(p_transform.elements[1]) && elements[2].is_equal_approx(p_transform.elements[2]);
+}
+
+bool Transform2D::operator==(const Transform2D &p_transform) const {
+	for (int i = 0; i < 3; i++) {
+		if (elements[i] != p_transform.elements[i]) {
+			return false;
+		}
+	}
+
+	return true;
+}
+
+bool Transform2D::operator!=(const Transform2D &p_transform) const {
+	for (int i = 0; i < 3; i++) {
+		if (elements[i] != p_transform.elements[i]) {
+			return true;
+		}
+	}
+
+	return false;
+}
+
+void Transform2D::operator*=(const Transform2D &p_transform) {
+	elements[2] = xform(p_transform.elements[2]);
+
+	real_t x0, x1, y0, y1;
+
+	x0 = tdotx(p_transform.elements[0]);
+	x1 = tdoty(p_transform.elements[0]);
+	y0 = tdotx(p_transform.elements[1]);
+	y1 = tdoty(p_transform.elements[1]);
+
+	elements[0][0] = x0;
+	elements[0][1] = x1;
+	elements[1][0] = y0;
+	elements[1][1] = y1;
+}
+
+Transform2D Transform2D::operator*(const Transform2D &p_transform) const {
+	Transform2D t = *this;
+	t *= p_transform;
+	return t;
+}
+
+Transform2D Transform2D::scaled(const Size2 &p_scale) const {
+	Transform2D copy = *this;
+	copy.scale(p_scale);
+	return copy;
+}
+
+Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
+	Transform2D copy = *this;
+	copy.scale_basis(p_scale);
+	return copy;
+}
+
+Transform2D Transform2D::untranslated() const {
+	Transform2D copy = *this;
+	copy.elements[2] = Vector2();
+	return copy;
+}
+
+Transform2D Transform2D::translated(const Vector2 &p_offset) const {
+	Transform2D copy = *this;
+	copy.translate(p_offset);
+	return copy;
+}
+
+Transform2D Transform2D::rotated(real_t p_phi) const {
+	Transform2D copy = *this;
+	copy.rotate(p_phi);
+	return copy;
+}
+
+real_t Transform2D::basis_determinant() const {
+	return elements[0].x * elements[1].y - elements[0].y * elements[1].x;
+}
+
+Transform2D Transform2D::interpolate_with(const Transform2D &p_transform, real_t p_c) const {
+	//extract parameters
+	Vector2 p1 = get_origin();
+	Vector2 p2 = p_transform.get_origin();
+
+	real_t r1 = get_rotation();
+	real_t r2 = p_transform.get_rotation();
+
+	Size2 s1 = get_scale();
+	Size2 s2 = p_transform.get_scale();
+
+	//slerp rotation
+	Vector2 v1(Math::cos(r1), Math::sin(r1));
+	Vector2 v2(Math::cos(r2), Math::sin(r2));
+
+	real_t dot = v1.dot(v2);
+
+	dot = Math::clamp(dot, (real_t)-1.0, (real_t)1.0);
+
+	Vector2 v;
+
+	if (dot > 0.9995) {
+		v = v1.lerp(v2, p_c).normalized(); //linearly interpolate to avoid numerical precision issues
+	} else {
+		real_t angle = p_c * Math::acos(dot);
+		Vector2 v3 = (v2 - v1 * dot).normalized();
+		v = v1 * Math::cos(angle) + v3 * Math::sin(angle);
+	}
+
+	//construct matrix
+	Transform2D res(Math::atan2(v.y, v.x), p1.lerp(p2, p_c));
+	res.scale_basis(s1.lerp(s2, p_c));
+	return res;
+}
+
+Transform2D::operator String() const {
+	return elements[0].operator String() + ", " + elements[1].operator String() + ", " + elements[2].operator String();
+}
+
+} // namespace godot

src/variant/transform3d.cpp

@@ -0,0 +1,185 @@
+#include <godot_cpp/variant/transform3d.hpp>
+
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+void Transform3D::affine_invert() {
+	basis.invert();
+	origin = basis.xform(-origin);
+}
+
+Transform3D Transform3D::affine_inverse() const {
+	Transform3D ret = *this;
+	ret.affine_invert();
+	return ret;
+}
+
+void Transform3D::invert() {
+	basis.transpose();
+	origin = basis.xform(-origin);
+}
+
+Transform3D Transform3D::inverse() const {
+	// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
+	// Transform3D::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
+	Transform3D ret = *this;
+	ret.invert();
+	return ret;
+}
+
+void Transform3D::rotate(const Vector3 &p_axis, real_t p_phi) {
+	*this = rotated(p_axis, p_phi);
+}
+
+Transform3D Transform3D::rotated(const Vector3 &p_axis, real_t p_phi) const {
+	return Transform3D(Basis(p_axis, p_phi), Vector3()) * (*this);
+}
+
+void Transform3D::rotate_basis(const Vector3 &p_axis, real_t p_phi) {
+	basis.rotate(p_axis, p_phi);
+}
+
+Transform3D Transform3D::looking_at(const Vector3 &p_target, const Vector3 &p_up) const {
+	Transform3D t = *this;
+	t.set_look_at(origin, p_target, p_up);
+	return t;
+}
+
+void Transform3D::set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up) {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND(p_eye == p_target);
+	ERR_FAIL_COND(p_up.length() == 0);
+#endif
+	// RefCounted: MESA source code
+	Vector3 v_x, v_y, v_z;
+
+	/* Make rotation matrix */
+
+	/* Z vector */
+	v_z = p_eye - p_target;
+
+	v_z.normalize();
+
+	v_y = p_up;
+
+	v_x = v_y.cross(v_z);
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND(v_x.length() == 0);
+#endif
+
+	/* Recompute Y = Z cross X */
+	v_y = v_z.cross(v_x);
+
+	v_x.normalize();
+	v_y.normalize();
+
+	basis.set(v_x, v_y, v_z);
+
+	origin = p_eye;
+}
+
+Transform3D Transform3D::interpolate_with(const Transform3D &p_transform, real_t p_c) const {
+	/* not sure if very "efficient" but good enough? */
+
+	Vector3 src_scale = basis.get_scale();
+	Quaternion src_rot = basis.get_rotation_quat();
+	Vector3 src_loc = origin;
+
+	Vector3 dst_scale = p_transform.basis.get_scale();
+	Quaternion dst_rot = p_transform.basis.get_rotation_quat();
+	Vector3 dst_loc = p_transform.origin;
+
+	Transform3D interp;
+	interp.basis.set_quat_scale(src_rot.slerp(dst_rot, p_c).normalized(), src_scale.lerp(dst_scale, p_c));
+	interp.origin = src_loc.lerp(dst_loc, p_c);
+
+	return interp;
+}
+
+void Transform3D::scale(const Vector3 &p_scale) {
+	basis.scale(p_scale);
+	origin *= p_scale;
+}
+
+Transform3D Transform3D::scaled(const Vector3 &p_scale) const {
+	Transform3D t = *this;
+	t.scale(p_scale);
+	return t;
+}
+
+void Transform3D::scale_basis(const Vector3 &p_scale) {
+	basis.scale(p_scale);
+}
+
+void Transform3D::translate(real_t p_tx, real_t p_ty, real_t p_tz) {
+	translate(Vector3(p_tx, p_ty, p_tz));
+}
+
+void Transform3D::translate(const Vector3 &p_translation) {
+	for (int i = 0; i < 3; i++) {
+		origin[i] += basis[i].dot(p_translation);
+	}
+}
+
+Transform3D Transform3D::translated(const Vector3 &p_translation) const {
+	Transform3D t = *this;
+	t.translate(p_translation);
+	return t;
+}
+
+void Transform3D::orthonormalize() {
+	basis.orthonormalize();
+}
+
+Transform3D Transform3D::orthonormalized() const {
+	Transform3D _copy = *this;
+	_copy.orthonormalize();
+	return _copy;
+}
+
+bool Transform3D::is_equal_approx(const Transform3D &p_transform) const {
+	return basis.is_equal_approx(p_transform.basis) && origin.is_equal_approx(p_transform.origin);
+}
+
+bool Transform3D::operator==(const Transform3D &p_transform) const {
+	return (basis == p_transform.basis && origin == p_transform.origin);
+}
+
+bool Transform3D::operator!=(const Transform3D &p_transform) const {
+	return (basis != p_transform.basis || origin != p_transform.origin);
+}
+
+void Transform3D::operator*=(const Transform3D &p_transform) {
+	origin = xform(p_transform.origin);
+	basis *= p_transform.basis;
+}
+
+Transform3D Transform3D::operator*(const Transform3D &p_transform) const {
+	Transform3D t = *this;
+	t *= p_transform;
+	return t;
+}
+
+Transform3D::operator String() const {
+	return basis.operator String() + " - " + origin.operator String();
+}
+
+Transform3D::Transform3D(const Basis &p_basis, const Vector3 &p_origin) :
+		basis(p_basis),
+		origin(p_origin) {
+}
+
+Transform3D::Transform3D(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z, const Vector3 &p_origin) :
+		origin(p_origin) {
+	basis.set_axis(0, p_x);
+	basis.set_axis(1, p_y);
+	basis.set_axis(2, p_z);
+}
+
+Transform3D::Transform3D(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t ox, real_t oy, real_t oz) {
+	basis = Basis(xx, xy, xz, yx, yy, yz, zx, zy, zz);
+	origin = Vector3(ox, oy, oz);
+}
+
+} // namespace godot

src/variant/variant.cpp

@@ -50,19 +50,6 @@ void Variant::init_bindings() {
 	}
 
 	String::init_bindings();
-	Vector2::init_bindings();
-	Vector2i::init_bindings();
-	Rect2::init_bindings();
-	Rect2i::init_bindings();
-	Vector3::init_bindings();
-	Vector3i::init_bindings();
-	Transform2D::init_bindings();
-	Plane::init_bindings();
-	Quaternion::init_bindings();
-	AABB::init_bindings();
-	Basis::init_bindings();
-	Transform3D::init_bindings();
-	Color::init_bindings();
 	StringName::init_bindings();
 	NodePath::init_bindings();
 	RID::init_bindings();

src/variant/vector2.cpp

@@ -0,0 +1,168 @@
+#include <godot_cpp/core/error_macros.hpp>
+#include <godot_cpp/variant/vector2.hpp>
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+Vector2::operator String() const {
+	return String::num(x, 5) + ", " + String::num(y, 5);
+}
+
+real_t Vector2::angle() const {
+	return Math::atan2(y, x);
+}
+
+real_t Vector2::length() const {
+	return Math::sqrt(x * x + y * y);
+}
+
+real_t Vector2::length_squared() const {
+	return x * x + y * y;
+}
+
+void Vector2::normalize() {
+	real_t l = x * x + y * y;
+	if (l != 0) {
+		l = Math::sqrt(l);
+		x /= l;
+		y /= l;
+	}
+}
+
+Vector2 Vector2::normalized() const {
+	Vector2 v = *this;
+	v.normalize();
+	return v;
+}
+
+bool Vector2::is_normalized() const {
+	// use length_squared() instead of length() to avoid sqrt(), makes it more stringent.
+	return Math::is_equal_approx(length_squared(), 1.0, UNIT_EPSILON);
+}
+
+real_t Vector2::distance_to(const Vector2 &p_vector2) const {
+	return Math::sqrt((x - p_vector2.x) * (x - p_vector2.x) + (y - p_vector2.y) * (y - p_vector2.y));
+}
+
+real_t Vector2::distance_squared_to(const Vector2 &p_vector2) const {
+	return (x - p_vector2.x) * (x - p_vector2.x) + (y - p_vector2.y) * (y - p_vector2.y);
+}
+
+real_t Vector2::angle_to(const Vector2 &p_vector2) const {
+	return Math::atan2(cross(p_vector2), dot(p_vector2));
+}
+
+real_t Vector2::angle_to_point(const Vector2 &p_vector2) const {
+	return Math::atan2(y - p_vector2.y, x - p_vector2.x);
+}
+
+real_t Vector2::dot(const Vector2 &p_other) const {
+	return x * p_other.x + y * p_other.y;
+}
+
+real_t Vector2::cross(const Vector2 &p_other) const {
+	return x * p_other.y - y * p_other.x;
+}
+
+Vector2 Vector2::sign() const {
+	return Vector2(Math::sign(x), Math::sign(y));
+}
+
+Vector2 Vector2::floor() const {
+	return Vector2(Math::floor(x), Math::floor(y));
+}
+
+Vector2 Vector2::ceil() const {
+	return Vector2(Math::ceil(x), Math::ceil(y));
+}
+
+Vector2 Vector2::round() const {
+	return Vector2(Math::round(x), Math::round(y));
+}
+
+Vector2 Vector2::rotated(real_t p_by) const {
+	real_t sine = Math::sin(p_by);
+	real_t cosi = Math::cos(p_by);
+	return Vector2(
+			x * cosi - y * sine,
+			x * sine + y * cosi);
+}
+
+Vector2 Vector2::posmod(const real_t p_mod) const {
+	return Vector2(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod));
+}
+
+Vector2 Vector2::posmodv(const Vector2 &p_modv) const {
+	return Vector2(Math::fposmod(x, p_modv.x), Math::fposmod(y, p_modv.y));
+}
+
+Vector2 Vector2::project(const Vector2 &p_to) const {
+	return p_to * (dot(p_to) / p_to.length_squared());
+}
+
+Vector2 Vector2::snapped(const Vector2 &p_step) const {
+	return Vector2(
+			Math::snapped(x, p_step.x),
+			Math::snapped(y, p_step.y));
+}
+
+Vector2 Vector2::clamped(real_t p_len) const {
+	real_t l = length();
+	Vector2 v = *this;
+	if (l > 0 && p_len < l) {
+		v /= l;
+		v *= p_len;
+	}
+
+	return v;
+}
+
+Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_weight) const {
+	Vector2 p0 = p_pre_a;
+	Vector2 p1 = *this;
+	Vector2 p2 = p_b;
+	Vector2 p3 = p_post_b;
+
+	real_t t = p_weight;
+	real_t t2 = t * t;
+	real_t t3 = t2 * t;
+
+	Vector2 out;
+	out = 0.5 * ((p1 * 2.0) +
+						(-p0 + p2) * t +
+						(2.0 * p0 - 5.0 * p1 + 4 * p2 - p3) * t2 +
+						(-p0 + 3.0 * p1 - 3.0 * p2 + p3) * t3);
+	return out;
+}
+
+Vector2 Vector2::move_toward(const Vector2 &p_to, const real_t p_delta) const {
+	Vector2 v = *this;
+	Vector2 vd = p_to - v;
+	real_t len = vd.length();
+	return len <= p_delta || len < CMP_EPSILON ? p_to : v + vd / len * p_delta;
+}
+
+// slide returns the component of the vector along the given plane, specified by its normal vector.
+Vector2 Vector2::slide(const Vector2 &p_normal) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!p_normal.is_normalized(), Vector2());
+#endif
+	return *this - p_normal * this->dot(p_normal);
+}
+
+Vector2 Vector2::bounce(const Vector2 &p_normal) const {
+	return -reflect(p_normal);
+}
+
+Vector2 Vector2::reflect(const Vector2 &p_normal) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V(!p_normal.is_normalized(), Vector2());
+#endif
+	return 2.0 * p_normal * this->dot(p_normal) - *this;
+}
+
+bool Vector2::is_equal_approx(const Vector2 &p_v) const {
+	return Math::is_equal_approx(x, p_v.x) && Math::is_equal_approx(y, p_v.y);
+}
+
+} // namespace godot

src/variant/vector2i.cpp

@@ -0,0 +1,80 @@
+#include <godot_cpp/core/error_macros.hpp>
+#include <godot_cpp/variant/vector2i.hpp>
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+Vector2i::operator String() const {
+	return String::num(x, 0) + ", " + String::num(y, 0);
+}
+
+Vector2i Vector2i::operator+(const Vector2i &p_v) const {
+	return Vector2i(x + p_v.x, y + p_v.y);
+}
+
+void Vector2i::operator+=(const Vector2i &p_v) {
+	x += p_v.x;
+	y += p_v.y;
+}
+
+Vector2i Vector2i::operator-(const Vector2i &p_v) const {
+	return Vector2i(x - p_v.x, y - p_v.y);
+}
+
+void Vector2i::operator-=(const Vector2i &p_v) {
+	x -= p_v.x;
+	y -= p_v.y;
+}
+
+Vector2i Vector2i::operator*(const Vector2i &p_v1) const {
+	return Vector2i(x * p_v1.x, y * p_v1.y);
+}
+
+Vector2i Vector2i::operator*(const int32_t &rvalue) const {
+	return Vector2i(x * rvalue, y * rvalue);
+}
+
+void Vector2i::operator*=(const int32_t &rvalue) {
+	x *= rvalue;
+	y *= rvalue;
+}
+
+Vector2i Vector2i::operator/(const Vector2i &p_v1) const {
+	return Vector2i(x / p_v1.x, y / p_v1.y);
+}
+
+Vector2i Vector2i::operator/(const int32_t &rvalue) const {
+	return Vector2i(x / rvalue, y / rvalue);
+}
+
+void Vector2i::operator/=(const int32_t &rvalue) {
+	x /= rvalue;
+	y /= rvalue;
+}
+
+Vector2i Vector2i::operator%(const Vector2i &p_v1) const {
+	return Vector2i(x % p_v1.x, y % p_v1.y);
+}
+
+Vector2i Vector2i::operator%(const int32_t &rvalue) const {
+	return Vector2i(x % rvalue, y % rvalue);
+}
+
+void Vector2i::operator%=(const int32_t &rvalue) {
+	x %= rvalue;
+	y %= rvalue;
+}
+
+Vector2i Vector2i::operator-() const {
+	return Vector2i(-x, -y);
+}
+
+bool Vector2i::operator==(const Vector2i &p_vec2) const {
+	return x == p_vec2.x && y == p_vec2.y;
+}
+
+bool Vector2i::operator!=(const Vector2i &p_vec2) const {
+	return x != p_vec2.x || y != p_vec2.y;
+}
+
+} // namespace godot

src/variant/vector3.cpp

@@ -0,0 +1,94 @@
+#include <godot_cpp/core/error_macros.hpp>
+#include <godot_cpp/variant/vector3.hpp>
+#include <godot_cpp/variant/basis.hpp>
+
+namespace godot {
+
+void Vector3::rotate(const Vector3 &p_axis, real_t p_phi) {
+	*this = Basis(p_axis, p_phi).xform(*this);
+}
+
+Vector3 Vector3::rotated(const Vector3 &p_axis, real_t p_phi) const {
+	Vector3 r = *this;
+	r.rotate(p_axis, p_phi);
+	return r;
+}
+
+void Vector3::set_axis(int p_axis, real_t p_value) {
+	ERR_FAIL_INDEX(p_axis, 3);
+	coord[p_axis] = p_value;
+}
+
+real_t Vector3::get_axis(int p_axis) const {
+	ERR_FAIL_INDEX_V(p_axis, 3, 0);
+	return operator[](p_axis);
+}
+
+int Vector3::min_axis() const {
+	return x < y ? (x < z ? 0 : 2) : (y < z ? 1 : 2);
+}
+
+int Vector3::max_axis() const {
+	return x < y ? (y < z ? 2 : 1) : (x < z ? 2 : 0);
+}
+
+void Vector3::snap(Vector3 p_step) {
+	x = Math::snapped(x, p_step.x);
+	y = Math::snapped(y, p_step.y);
+	z = Math::snapped(z, p_step.z);
+}
+
+Vector3 Vector3::snapped(Vector3 p_step) const {
+	Vector3 v = *this;
+	v.snap(p_step);
+	return v;
+}
+
+Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight) const {
+	Vector3 p0 = p_pre_a;
+	Vector3 p1 = *this;
+	Vector3 p2 = p_b;
+	Vector3 p3 = p_post_b;
+
+	real_t t = p_weight;
+	real_t t2 = t * t;
+	real_t t3 = t2 * t;
+
+	Vector3 out;
+	out = 0.5 * ((p1 * 2.0) +
+						(-p0 + p2) * t +
+						(2.0 * p0 - 5.0 * p1 + 4.0 * p2 - p3) * t2 +
+						(-p0 + 3.0 * p1 - 3.0 * p2 + p3) * t3);
+	return out;
+}
+
+Vector3 Vector3::move_toward(const Vector3 &p_to, const real_t p_delta) const {
+	Vector3 v = *this;
+	Vector3 vd = p_to - v;
+	real_t len = vd.length();
+	return len <= p_delta || len < CMP_EPSILON ? p_to : v + vd / len * p_delta;
+}
+
+Basis Vector3::outer(const Vector3 &p_b) const {
+	Vector3 row0(x * p_b.x, x * p_b.y, x * p_b.z);
+	Vector3 row1(y * p_b.x, y * p_b.y, y * p_b.z);
+	Vector3 row2(z * p_b.x, z * p_b.y, z * p_b.z);
+
+	return Basis(row0, row1, row2);
+}
+
+Basis Vector3::to_diagonal_matrix() const {
+	return Basis(x, 0, 0,
+			0, y, 0,
+			0, 0, z);
+}
+
+bool Vector3::is_equal_approx(const Vector3 &p_v) const {
+	return Math::is_equal_approx(x, p_v.x) && Math::is_equal_approx(y, p_v.y) && Math::is_equal_approx(z, p_v.z);
+}
+
+Vector3::operator String() const {
+	return (String::num(x, 5) + ", " + String::num(y, 5) + ", " + String::num(z, 5));
+}
+
+} // namespace godot

src/variant/vector3i.cpp

@@ -0,0 +1,29 @@
+#include <godot_cpp/core/error_macros.hpp>
+#include <godot_cpp/variant/vector3i.hpp>
+#include <godot_cpp/variant/string.hpp>
+
+namespace godot {
+
+void Vector3i::set_axis(int p_axis, int32_t p_value) {
+	ERR_FAIL_INDEX(p_axis, 3);
+	coord[p_axis] = p_value;
+}
+
+int32_t Vector3i::get_axis(int p_axis) const {
+	ERR_FAIL_INDEX_V(p_axis, 3, 0);
+	return operator[](p_axis);
+}
+
+int Vector3i::min_axis() const {
+	return x < y ? (x < z ? 0 : 2) : (y < z ? 1 : 2);
+}
+
+int Vector3i::max_axis() const {
+	return x < y ? (y < z ? 2 : 1) : (x < z ? 2 : 0);
+}
+
+Vector3i::operator String() const {
+	return (String::num(x, 0) + ", " + String::num(y, 0) + ", " + String::num(z, 5));
+}
+
+} // namespace godot