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+/**********************************************************************************************
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+*
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+* raymath v1.2 - Math functions to work with Vector3, Matrix and Quaternions
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+*
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+* CONFIGURATION:
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+*
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+* #define RAYMATH_IMPLEMENTATION
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+* Generates the implementation of the library into the included file.
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+* If not defined, the library is in header only mode and can be included in other headers
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+* or source files without problems. But only ONE file should hold the implementation.
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+*
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+* #define RAYMATH_HEADER_ONLY
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+* Define static inline functions code, so #include header suffices for use.
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+* This may use up lots of memory.
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+*
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+* #define RAYMATH_STANDALONE
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+* Avoid raylib.h header inclusion in this file.
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+* Vector3 and Matrix data types are defined internally in raymath module.
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+*
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+*
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+* LICENSE: zlib/libpng
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+*
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+* Copyright (c) 2015-2020 Ramon Santamaria (@raysan5)
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+*
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+* This software is provided "as-is", without any express or implied warranty. In no event
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+* will the authors be held liable for any damages arising from the use of this software.
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+*
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+* Permission is granted to anyone to use this software for any purpose, including commercial
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+* applications, and to alter it and redistribute it freely, subject to the following restrictions:
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+*
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+* 1. The origin of this software must not be misrepresented; you must not claim that you
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+* wrote the original software. If you use this software in a product, an acknowledgment
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+* in the product documentation would be appreciated but is not required.
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+*
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+* 2. Altered source versions must be plainly marked as such, and must not be misrepresented
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+* as being the original software.
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+*
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+* 3. This notice may not be removed or altered from any source distribution.
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+*
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+**********************************************************************************************/
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+
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+#ifndef RAYMATH_H
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+#define RAYMATH_H
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+
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+//#define RAYMATH_STANDALONE // NOTE: To use raymath as standalone lib, just uncomment this line
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+//#define RAYMATH_HEADER_ONLY // NOTE: To compile functions as static inline, uncomment this line
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+
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+#ifndef RAYMATH_STANDALONE
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+ #include "raylib.h" // Required for structs: Vector3, Matrix
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+#endif
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+
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+#if defined(RAYMATH_IMPLEMENTATION) && defined(RAYMATH_HEADER_ONLY)
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+ #error "Specifying both RAYMATH_IMPLEMENTATION and RAYMATH_HEADER_ONLY is contradictory"
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+#endif
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+
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+#if defined(RAYMATH_IMPLEMENTATION)
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+ #if defined(_WIN32) && defined(BUILD_LIBTYPE_SHARED)
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+ #define RMDEF __declspec(dllexport) extern inline // We are building raylib as a Win32 shared library (.dll).
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+ #elif defined(_WIN32) && defined(USE_LIBTYPE_SHARED)
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+ #define RMDEF __declspec(dllimport) // We are using raylib as a Win32 shared library (.dll)
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+ #else
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+ #define RMDEF extern inline // Provide external definition
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+ #endif
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+#elif defined(RAYMATH_HEADER_ONLY)
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+ #define RMDEF static inline // Functions may be inlined, no external out-of-line definition
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+#else
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+ #if defined(__TINYC__)
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+ #define RMDEF static inline // plain inline not supported by tinycc (See issue #435)
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+ #else
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+ #define RMDEF inline // Functions may be inlined or external definition used
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+ #endif
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+#endif
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+
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+//----------------------------------------------------------------------------------
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+// Defines and Macros
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+//----------------------------------------------------------------------------------
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+#ifndef PI
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+ #define PI 3.14159265358979323846
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+#endif
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+
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+#ifndef DEG2RAD
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+ #define DEG2RAD (PI/180.0f)
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+#endif
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+
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+#ifndef RAD2DEG
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+ #define RAD2DEG (180.0f/PI)
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+#endif
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+
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+// Return float vector for Matrix
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+#ifndef MatrixToFloat
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+ #define MatrixToFloat(mat) (MatrixToFloatV(mat).v)
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+#endif
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+
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+// Return float vector for Vector3
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+#ifndef Vector3ToFloat
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+ #define Vector3ToFloat(vec) (Vector3ToFloatV(vec).v)
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+#endif
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+
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+//----------------------------------------------------------------------------------
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+// Types and Structures Definition
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+//----------------------------------------------------------------------------------
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+
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+#if defined(RAYMATH_STANDALONE)
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+ // Vector2 type
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+ typedef struct Vector2 {
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+ float x;
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+ float y;
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+ } Vector2;
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+
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+ // Vector3 type
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+ typedef struct Vector3 {
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+ float x;
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+ float y;
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+ float z;
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+ } Vector3;
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+
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+ // Quaternion type
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+ typedef struct Quaternion {
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+ float x;
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+ float y;
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+ float z;
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+ float w;
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+ } Quaternion;
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+
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+ // Matrix type (OpenGL style 4x4 - right handed, column major)
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+ typedef struct Matrix {
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+ float m0, m4, m8, m12;
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+ float m1, m5, m9, m13;
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+ float m2, m6, m10, m14;
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+ float m3, m7, m11, m15;
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+ } Matrix;
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+#endif
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+
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+// NOTE: Helper types to be used instead of array return types for *ToFloat functions
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+typedef struct float3 { float v[3]; } float3;
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+typedef struct float16 { float v[16]; } float16;
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+
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+#include <math.h> // Required for: sinf(), cosf(), sqrtf(), tan(), fabs()
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+
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+//----------------------------------------------------------------------------------
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+// Module Functions Definition - Utils math
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+//----------------------------------------------------------------------------------
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+
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+// Clamp float value
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+RMDEF float Clamp(float value, float min, float max)
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+{
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+ const float res = value < min ? min : value;
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+ return res > max ? max : res;
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+}
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+
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+// Calculate linear interpolation between two floats
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+RMDEF float Lerp(float start, float end, float amount)
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+{
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+ return start + amount*(end - start);
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+}
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+
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+//----------------------------------------------------------------------------------
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+// Module Functions Definition - Vector2 math
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+//----------------------------------------------------------------------------------
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+
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+// Vector with components value 0.0f
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+RMDEF Vector2 Vector2Zero(void)
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+{
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+ Vector2 result = { 0.0f, 0.0f };
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+ return result;
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+}
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+
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+// Vector with components value 1.0f
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+RMDEF Vector2 Vector2One(void)
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+{
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+ Vector2 result = { 1.0f, 1.0f };
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+ return result;
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+}
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+
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+// Add two vectors (v1 + v2)
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+RMDEF Vector2 Vector2Add(Vector2 v1, Vector2 v2)
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+{
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+ Vector2 result = { v1.x + v2.x, v1.y + v2.y };
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+ return result;
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+}
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+
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+// Add vector and float value
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+RMDEF Vector2 Vector2AddValue(Vector2 v, float add)
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+{
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+ Vector2 result = { v.x + add, v.y + add };
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+ return result;
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+}
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+
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+// Subtract two vectors (v1 - v2)
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+RMDEF Vector2 Vector2Subtract(Vector2 v1, Vector2 v2)
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+{
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+ Vector2 result = { v1.x - v2.x, v1.y - v2.y };
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+ return result;
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+}
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+
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+// Subtract vector by float value
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+RMDEF Vector2 Vector2SubtractValue(Vector2 v, float sub)
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+{
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+ Vector2 result = { v.x - sub, v.y - sub };
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+ return result;
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+}
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+
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+// Calculate vector length
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+RMDEF float Vector2Length(Vector2 v)
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+{
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+ float result = sqrtf((v.x*v.x) + (v.y*v.y));
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+ return result;
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+}
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+
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+// Calculate two vectors dot product
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+RMDEF float Vector2DotProduct(Vector2 v1, Vector2 v2)
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+{
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+ float result = (v1.x*v2.x + v1.y*v2.y);
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+ return result;
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+}
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+
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+// Calculate distance between two vectors
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+RMDEF float Vector2Distance(Vector2 v1, Vector2 v2)
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+{
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+ float result = sqrtf((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y));
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+ return result;
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+}
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+
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+// Calculate angle from two vectors in X-axis
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+RMDEF float Vector2Angle(Vector2 v1, Vector2 v2)
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+{
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+ float result = atan2f(v2.y - v1.y, v2.x - v1.x)*(180.0f/PI);
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+ if (result < 0) result += 360.0f;
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+ return result;
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+}
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+
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+// Scale vector (multiply by value)
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+RMDEF Vector2 Vector2Scale(Vector2 v, float scale)
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+{
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+ Vector2 result = { v.x*scale, v.y*scale };
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+ return result;
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+}
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+
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+// Multiply vector by vector
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+RMDEF Vector2 Vector2Multiply(Vector2 v1, Vector2 v2)
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+{
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+ Vector2 result = { v1.x*v2.x, v1.y*v2.y };
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+ return result;
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+}
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+
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+// Negate vector
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+RMDEF Vector2 Vector2Negate(Vector2 v)
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+{
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+ Vector2 result = { -v.x, -v.y };
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+ return result;
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+}
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+
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+// Divide vector by vector
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+RMDEF Vector2 Vector2Divide(Vector2 v1, Vector2 v2)
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+{
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+ Vector2 result = { v1.x/v2.x, v1.y/v2.y };
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+ return result;
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+}
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+
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+// Normalize provided vector
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+RMDEF Vector2 Vector2Normalize(Vector2 v)
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+{
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+ Vector2 result = Vector2Scale(v, 1/Vector2Length(v));
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+ return result;
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+}
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+
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+// Calculate linear interpolation between two vectors
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+RMDEF Vector2 Vector2Lerp(Vector2 v1, Vector2 v2, float amount)
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+{
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+ Vector2 result = { 0 };
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+
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+ result.x = v1.x + amount*(v2.x - v1.x);
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+ result.y = v1.y + amount*(v2.y - v1.y);
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+
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+ return result;
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+}
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+
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+// Rotate Vector by float in Degrees.
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+RMDEF Vector2 Vector2Rotate(Vector2 v, float degs)
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+{
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+ float rads = degs*DEG2RAD;
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+ Vector2 result = {v.x * cosf(rads) - v.y * sinf(rads) , v.x * sinf(rads) + v.y * cosf(rads) };
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+ return result;
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+}
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+
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+//----------------------------------------------------------------------------------
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+// Module Functions Definition - Vector3 math
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+//----------------------------------------------------------------------------------
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+
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+// Vector with components value 0.0f
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+RMDEF Vector3 Vector3Zero(void)
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+{
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+ Vector3 result = { 0.0f, 0.0f, 0.0f };
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+ return result;
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+}
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+
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+// Vector with components value 1.0f
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+RMDEF Vector3 Vector3One(void)
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+{
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+ Vector3 result = { 1.0f, 1.0f, 1.0f };
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+ return result;
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+}
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+
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+// Add two vectors
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+RMDEF Vector3 Vector3Add(Vector3 v1, Vector3 v2)
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+{
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+ Vector3 result = { v1.x + v2.x, v1.y + v2.y, v1.z + v2.z };
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+ return result;
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+}
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+
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+// Add vector and float value
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+RMDEF Vector3 Vector3AddValue(Vector3 v, float add)
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+{
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+ Vector3 result = { v.x + add, v.y + add, v.z + add };
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+ return result;
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+}
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+
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+// Subtract two vectors
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+RMDEF Vector3 Vector3Subtract(Vector3 v1, Vector3 v2)
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+{
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+ Vector3 result = { v1.x - v2.x, v1.y - v2.y, v1.z - v2.z };
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+ return result;
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+}
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+
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+// Subtract vector by float value
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+RMDEF Vector3 Vector3SubtractValue(Vector3 v, float sub)
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+{
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+ Vector3 result = { v.x - sub, v.y - sub, v.z - sub };
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+ return result;
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+}
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+
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+// Multiply vector by scalar
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+RMDEF Vector3 Vector3Scale(Vector3 v, float scalar)
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+{
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+ Vector3 result = { v.x*scalar, v.y*scalar, v.z*scalar };
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+ return result;
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+}
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+
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+// Multiply vector by vector
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+RMDEF Vector3 Vector3Multiply(Vector3 v1, Vector3 v2)
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+{
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+ Vector3 result = { v1.x*v2.x, v1.y*v2.y, v1.z*v2.z };
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+ return result;
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+}
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+
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+// Calculate two vectors cross product
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+RMDEF Vector3 Vector3CrossProduct(Vector3 v1, Vector3 v2)
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+{
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+ Vector3 result = { v1.y*v2.z - v1.z*v2.y, v1.z*v2.x - v1.x*v2.z, v1.x*v2.y - v1.y*v2.x };
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+ return result;
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+}
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+
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+// Calculate one vector perpendicular vector
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+RMDEF Vector3 Vector3Perpendicular(Vector3 v)
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+{
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+ Vector3 result = { 0 };
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+
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+ float min = (float) fabs(v.x);
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+ Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f};
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+
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+ if (fabs(v.y) < min)
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+ {
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+ min = (float) fabs(v.y);
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+ Vector3 tmp = {0.0f, 1.0f, 0.0f};
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+ cardinalAxis = tmp;
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+ }
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+
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+ if (fabs(v.z) < min)
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+ {
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+ Vector3 tmp = {0.0f, 0.0f, 1.0f};
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+ cardinalAxis = tmp;
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+ }
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+
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+ result = Vector3CrossProduct(v, cardinalAxis);
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+
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+ return result;
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+}
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+
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+// Calculate vector length
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+RMDEF float Vector3Length(const Vector3 v)
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+{
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+ float result = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
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+ return result;
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+}
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+
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+// Calculate two vectors dot product
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+RMDEF float Vector3DotProduct(Vector3 v1, Vector3 v2)
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+{
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+ float result = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z);
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+ return result;
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+}
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+
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+// Calculate distance between two vectors
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+RMDEF float Vector3Distance(Vector3 v1, Vector3 v2)
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+{
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+ float dx = v2.x - v1.x;
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+ float dy = v2.y - v1.y;
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+ float dz = v2.z - v1.z;
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+ float result = sqrtf(dx*dx + dy*dy + dz*dz);
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+ return result;
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+}
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+
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+// Negate provided vector (invert direction)
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+RMDEF Vector3 Vector3Negate(Vector3 v)
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+{
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+ Vector3 result = { -v.x, -v.y, -v.z };
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+ return result;
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+}
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+
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+// Divide vector by vector
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+RMDEF Vector3 Vector3Divide(Vector3 v1, Vector3 v2)
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+{
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+ Vector3 result = { v1.x/v2.x, v1.y/v2.y, v1.z/v2.z };
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+ return result;
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+}
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+
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+// Normalize provided vector
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|
|
+RMDEF Vector3 Vector3Normalize(Vector3 v)
|
|
|
+{
|
|
|
+ Vector3 result = v;
|
|
|
+
|
|
|
+ float length, ilength;
|
|
|
+ length = Vector3Length(v);
|
|
|
+ if (length == 0.0f) length = 1.0f;
|
|
|
+ ilength = 1.0f/length;
|
|
|
+
|
|
|
+ result.x *= ilength;
|
|
|
+ result.y *= ilength;
|
|
|
+ result.z *= ilength;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Orthonormalize provided vectors
|
|
|
+// Makes vectors normalized and orthogonal to each other
|
|
|
+// Gram-Schmidt function implementation
|
|
|
+RMDEF void Vector3OrthoNormalize(Vector3 *v1, Vector3 *v2)
|
|
|
+{
|
|
|
+ *v1 = Vector3Normalize(*v1);
|
|
|
+ Vector3 vn = Vector3CrossProduct(*v1, *v2);
|
|
|
+ vn = Vector3Normalize(vn);
|
|
|
+ *v2 = Vector3CrossProduct(vn, *v1);
|
|
|
+}
|
|
|
+
|
|
|
+// Transforms a Vector3 by a given Matrix
|
|
|
+RMDEF Vector3 Vector3Transform(Vector3 v, Matrix mat)
|
|
|
+{
|
|
|
+ Vector3 result = { 0 };
|
|
|
+ float x = v.x;
|
|
|
+ float y = v.y;
|
|
|
+ float z = v.z;
|
|
|
+
|
|
|
+ result.x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12;
|
|
|
+ result.y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13;
|
|
|
+ result.z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Transform a vector by quaternion rotation
|
|
|
+RMDEF Vector3 Vector3RotateByQuaternion(Vector3 v, Quaternion q)
|
|
|
+{
|
|
|
+ Vector3 result = { 0 };
|
|
|
+
|
|
|
+ result.x = v.x*(q.x*q.x + q.w*q.w - q.y*q.y - q.z*q.z) + v.y*(2*q.x*q.y - 2*q.w*q.z) + v.z*(2*q.x*q.z + 2*q.w*q.y);
|
|
|
+ result.y = v.x*(2*q.w*q.z + 2*q.x*q.y) + v.y*(q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z) + v.z*(-2*q.w*q.x + 2*q.y*q.z);
|
|
|
+ result.z = v.x*(-2*q.w*q.y + 2*q.x*q.z) + v.y*(2*q.w*q.x + 2*q.y*q.z)+ v.z*(q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Calculate linear interpolation between two vectors
|
|
|
+RMDEF Vector3 Vector3Lerp(Vector3 v1, Vector3 v2, float amount)
|
|
|
+{
|
|
|
+ Vector3 result = { 0 };
|
|
|
+
|
|
|
+ result.x = v1.x + amount*(v2.x - v1.x);
|
|
|
+ result.y = v1.y + amount*(v2.y - v1.y);
|
|
|
+ result.z = v1.z + amount*(v2.z - v1.z);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Calculate reflected vector to normal
|
|
|
+RMDEF Vector3 Vector3Reflect(Vector3 v, Vector3 normal)
|
|
|
+{
|
|
|
+ // I is the original vector
|
|
|
+ // N is the normal of the incident plane
|
|
|
+ // R = I - (2*N*( DotProduct[ I,N] ))
|
|
|
+
|
|
|
+ Vector3 result = { 0 };
|
|
|
+
|
|
|
+ float dotProduct = Vector3DotProduct(v, normal);
|
|
|
+
|
|
|
+ result.x = v.x - (2.0f*normal.x)*dotProduct;
|
|
|
+ result.y = v.y - (2.0f*normal.y)*dotProduct;
|
|
|
+ result.z = v.z - (2.0f*normal.z)*dotProduct;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Return min value for each pair of components
|
|
|
+RMDEF Vector3 Vector3Min(Vector3 v1, Vector3 v2)
|
|
|
+{
|
|
|
+ Vector3 result = { 0 };
|
|
|
+
|
|
|
+ result.x = fminf(v1.x, v2.x);
|
|
|
+ result.y = fminf(v1.y, v2.y);
|
|
|
+ result.z = fminf(v1.z, v2.z);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Return max value for each pair of components
|
|
|
+RMDEF Vector3 Vector3Max(Vector3 v1, Vector3 v2)
|
|
|
+{
|
|
|
+ Vector3 result = { 0 };
|
|
|
+
|
|
|
+ result.x = fmaxf(v1.x, v2.x);
|
|
|
+ result.y = fmaxf(v1.y, v2.y);
|
|
|
+ result.z = fmaxf(v1.z, v2.z);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Compute barycenter coordinates (u, v, w) for point p with respect to triangle (a, b, c)
|
|
|
+// NOTE: Assumes P is on the plane of the triangle
|
|
|
+RMDEF Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c)
|
|
|
+{
|
|
|
+ //Vector v0 = b - a, v1 = c - a, v2 = p - a;
|
|
|
+
|
|
|
+ Vector3 v0 = Vector3Subtract(b, a);
|
|
|
+ Vector3 v1 = Vector3Subtract(c, a);
|
|
|
+ Vector3 v2 = Vector3Subtract(p, a);
|
|
|
+ float d00 = Vector3DotProduct(v0, v0);
|
|
|
+ float d01 = Vector3DotProduct(v0, v1);
|
|
|
+ float d11 = Vector3DotProduct(v1, v1);
|
|
|
+ float d20 = Vector3DotProduct(v2, v0);
|
|
|
+ float d21 = Vector3DotProduct(v2, v1);
|
|
|
+
|
|
|
+ float denom = d00*d11 - d01*d01;
|
|
|
+
|
|
|
+ Vector3 result = { 0 };
|
|
|
+
|
|
|
+ result.y = (d11*d20 - d01*d21)/denom;
|
|
|
+ result.z = (d00*d21 - d01*d20)/denom;
|
|
|
+ result.x = 1.0f - (result.z + result.y);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns Vector3 as float array
|
|
|
+RMDEF float3 Vector3ToFloatV(Vector3 v)
|
|
|
+{
|
|
|
+ float3 buffer = { 0 };
|
|
|
+
|
|
|
+ buffer.v[0] = v.x;
|
|
|
+ buffer.v[1] = v.y;
|
|
|
+ buffer.v[2] = v.z;
|
|
|
+
|
|
|
+ return buffer;
|
|
|
+}
|
|
|
+
|
|
|
+//----------------------------------------------------------------------------------
|
|
|
+// Module Functions Definition - Matrix math
|
|
|
+//----------------------------------------------------------------------------------
|
|
|
+
|
|
|
+// Compute matrix determinant
|
|
|
+RMDEF float MatrixDeterminant(Matrix mat)
|
|
|
+{
|
|
|
+ // Cache the matrix values (speed optimization)
|
|
|
+ float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3;
|
|
|
+ float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7;
|
|
|
+ float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11;
|
|
|
+ float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15;
|
|
|
+
|
|
|
+ float result = a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 +
|
|
|
+ a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 +
|
|
|
+ a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 +
|
|
|
+ a30*a11*a02*a23 - a10*a31*a02*a23 - a30*a01*a12*a23 + a00*a31*a12*a23 +
|
|
|
+ a10*a01*a32*a23 - a00*a11*a32*a23 - a20*a11*a02*a33 + a10*a21*a02*a33 +
|
|
|
+ a20*a01*a12*a33 - a00*a21*a12*a33 - a10*a01*a22*a33 + a00*a11*a22*a33;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns the trace of the matrix (sum of the values along the diagonal)
|
|
|
+RMDEF float MatrixTrace(Matrix mat)
|
|
|
+{
|
|
|
+ float result = (mat.m0 + mat.m5 + mat.m10 + mat.m15);
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Transposes provided matrix
|
|
|
+RMDEF Matrix MatrixTranspose(Matrix mat)
|
|
|
+{
|
|
|
+ Matrix result = { 0 };
|
|
|
+
|
|
|
+ result.m0 = mat.m0;
|
|
|
+ result.m1 = mat.m4;
|
|
|
+ result.m2 = mat.m8;
|
|
|
+ result.m3 = mat.m12;
|
|
|
+ result.m4 = mat.m1;
|
|
|
+ result.m5 = mat.m5;
|
|
|
+ result.m6 = mat.m9;
|
|
|
+ result.m7 = mat.m13;
|
|
|
+ result.m8 = mat.m2;
|
|
|
+ result.m9 = mat.m6;
|
|
|
+ result.m10 = mat.m10;
|
|
|
+ result.m11 = mat.m14;
|
|
|
+ result.m12 = mat.m3;
|
|
|
+ result.m13 = mat.m7;
|
|
|
+ result.m14 = mat.m11;
|
|
|
+ result.m15 = mat.m15;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Invert provided matrix
|
|
|
+RMDEF Matrix MatrixInvert(Matrix mat)
|
|
|
+{
|
|
|
+ Matrix result = { 0 };
|
|
|
+
|
|
|
+ // Cache the matrix values (speed optimization)
|
|
|
+ float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3;
|
|
|
+ float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7;
|
|
|
+ float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11;
|
|
|
+ float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15;
|
|
|
+
|
|
|
+ float b00 = a00*a11 - a01*a10;
|
|
|
+ float b01 = a00*a12 - a02*a10;
|
|
|
+ float b02 = a00*a13 - a03*a10;
|
|
|
+ float b03 = a01*a12 - a02*a11;
|
|
|
+ float b04 = a01*a13 - a03*a11;
|
|
|
+ float b05 = a02*a13 - a03*a12;
|
|
|
+ float b06 = a20*a31 - a21*a30;
|
|
|
+ float b07 = a20*a32 - a22*a30;
|
|
|
+ float b08 = a20*a33 - a23*a30;
|
|
|
+ float b09 = a21*a32 - a22*a31;
|
|
|
+ float b10 = a21*a33 - a23*a31;
|
|
|
+ float b11 = a22*a33 - a23*a32;
|
|
|
+
|
|
|
+ // Calculate the invert determinant (inlined to avoid double-caching)
|
|
|
+ float invDet = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06);
|
|
|
+
|
|
|
+ result.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet;
|
|
|
+ result.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet;
|
|
|
+ result.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet;
|
|
|
+ result.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet;
|
|
|
+ result.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet;
|
|
|
+ result.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet;
|
|
|
+ result.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet;
|
|
|
+ result.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet;
|
|
|
+ result.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet;
|
|
|
+ result.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet;
|
|
|
+ result.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet;
|
|
|
+ result.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet;
|
|
|
+ result.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet;
|
|
|
+ result.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet;
|
|
|
+ result.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet;
|
|
|
+ result.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Normalize provided matrix
|
|
|
+RMDEF Matrix MatrixNormalize(Matrix mat)
|
|
|
+{
|
|
|
+ Matrix result = { 0 };
|
|
|
+
|
|
|
+ float det = MatrixDeterminant(mat);
|
|
|
+
|
|
|
+ result.m0 = mat.m0/det;
|
|
|
+ result.m1 = mat.m1/det;
|
|
|
+ result.m2 = mat.m2/det;
|
|
|
+ result.m3 = mat.m3/det;
|
|
|
+ result.m4 = mat.m4/det;
|
|
|
+ result.m5 = mat.m5/det;
|
|
|
+ result.m6 = mat.m6/det;
|
|
|
+ result.m7 = mat.m7/det;
|
|
|
+ result.m8 = mat.m8/det;
|
|
|
+ result.m9 = mat.m9/det;
|
|
|
+ result.m10 = mat.m10/det;
|
|
|
+ result.m11 = mat.m11/det;
|
|
|
+ result.m12 = mat.m12/det;
|
|
|
+ result.m13 = mat.m13/det;
|
|
|
+ result.m14 = mat.m14/det;
|
|
|
+ result.m15 = mat.m15/det;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns identity matrix
|
|
|
+RMDEF Matrix MatrixIdentity(void)
|
|
|
+{
|
|
|
+ Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f,
|
|
|
+ 0.0f, 1.0f, 0.0f, 0.0f,
|
|
|
+ 0.0f, 0.0f, 1.0f, 0.0f,
|
|
|
+ 0.0f, 0.0f, 0.0f, 1.0f };
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Add two matrices
|
|
|
+RMDEF Matrix MatrixAdd(Matrix left, Matrix right)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ result.m0 = left.m0 + right.m0;
|
|
|
+ result.m1 = left.m1 + right.m1;
|
|
|
+ result.m2 = left.m2 + right.m2;
|
|
|
+ result.m3 = left.m3 + right.m3;
|
|
|
+ result.m4 = left.m4 + right.m4;
|
|
|
+ result.m5 = left.m5 + right.m5;
|
|
|
+ result.m6 = left.m6 + right.m6;
|
|
|
+ result.m7 = left.m7 + right.m7;
|
|
|
+ result.m8 = left.m8 + right.m8;
|
|
|
+ result.m9 = left.m9 + right.m9;
|
|
|
+ result.m10 = left.m10 + right.m10;
|
|
|
+ result.m11 = left.m11 + right.m11;
|
|
|
+ result.m12 = left.m12 + right.m12;
|
|
|
+ result.m13 = left.m13 + right.m13;
|
|
|
+ result.m14 = left.m14 + right.m14;
|
|
|
+ result.m15 = left.m15 + right.m15;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Subtract two matrices (left - right)
|
|
|
+RMDEF Matrix MatrixSubtract(Matrix left, Matrix right)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ result.m0 = left.m0 - right.m0;
|
|
|
+ result.m1 = left.m1 - right.m1;
|
|
|
+ result.m2 = left.m2 - right.m2;
|
|
|
+ result.m3 = left.m3 - right.m3;
|
|
|
+ result.m4 = left.m4 - right.m4;
|
|
|
+ result.m5 = left.m5 - right.m5;
|
|
|
+ result.m6 = left.m6 - right.m6;
|
|
|
+ result.m7 = left.m7 - right.m7;
|
|
|
+ result.m8 = left.m8 - right.m8;
|
|
|
+ result.m9 = left.m9 - right.m9;
|
|
|
+ result.m10 = left.m10 - right.m10;
|
|
|
+ result.m11 = left.m11 - right.m11;
|
|
|
+ result.m12 = left.m12 - right.m12;
|
|
|
+ result.m13 = left.m13 - right.m13;
|
|
|
+ result.m14 = left.m14 - right.m14;
|
|
|
+ result.m15 = left.m15 - right.m15;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns translation matrix
|
|
|
+RMDEF Matrix MatrixTranslate(float x, float y, float z)
|
|
|
+{
|
|
|
+ Matrix result = { 1.0f, 0.0f, 0.0f, x,
|
|
|
+ 0.0f, 1.0f, 0.0f, y,
|
|
|
+ 0.0f, 0.0f, 1.0f, z,
|
|
|
+ 0.0f, 0.0f, 0.0f, 1.0f };
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Create rotation matrix from axis and angle
|
|
|
+// NOTE: Angle should be provided in radians
|
|
|
+RMDEF Matrix MatrixRotate(Vector3 axis, float angle)
|
|
|
+{
|
|
|
+ Matrix result = { 0 };
|
|
|
+
|
|
|
+ float x = axis.x, y = axis.y, z = axis.z;
|
|
|
+
|
|
|
+ float length = sqrtf(x*x + y*y + z*z);
|
|
|
+
|
|
|
+ if ((length != 1.0f) && (length != 0.0f))
|
|
|
+ {
|
|
|
+ length = 1.0f/length;
|
|
|
+ x *= length;
|
|
|
+ y *= length;
|
|
|
+ z *= length;
|
|
|
+ }
|
|
|
+
|
|
|
+ float sinres = sinf(angle);
|
|
|
+ float cosres = cosf(angle);
|
|
|
+ float t = 1.0f - cosres;
|
|
|
+
|
|
|
+ result.m0 = x*x*t + cosres;
|
|
|
+ result.m1 = y*x*t + z*sinres;
|
|
|
+ result.m2 = z*x*t - y*sinres;
|
|
|
+ result.m3 = 0.0f;
|
|
|
+
|
|
|
+ result.m4 = x*y*t - z*sinres;
|
|
|
+ result.m5 = y*y*t + cosres;
|
|
|
+ result.m6 = z*y*t + x*sinres;
|
|
|
+ result.m7 = 0.0f;
|
|
|
+
|
|
|
+ result.m8 = x*z*t + y*sinres;
|
|
|
+ result.m9 = y*z*t - x*sinres;
|
|
|
+ result.m10 = z*z*t + cosres;
|
|
|
+ result.m11 = 0.0f;
|
|
|
+
|
|
|
+ result.m12 = 0.0f;
|
|
|
+ result.m13 = 0.0f;
|
|
|
+ result.m14 = 0.0f;
|
|
|
+ result.m15 = 1.0f;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns xyz-rotation matrix (angles in radians)
|
|
|
+RMDEF Matrix MatrixRotateXYZ(Vector3 ang)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ float cosz = cosf(-ang.z);
|
|
|
+ float sinz = sinf(-ang.z);
|
|
|
+ float cosy = cosf(-ang.y);
|
|
|
+ float siny = sinf(-ang.y);
|
|
|
+ float cosx = cosf(-ang.x);
|
|
|
+ float sinx = sinf(-ang.x);
|
|
|
+
|
|
|
+ result.m0 = cosz * cosy;
|
|
|
+ result.m4 = (cosz * siny * sinx) - (sinz * cosx);
|
|
|
+ result.m8 = (cosz * siny * cosx) + (sinz * sinx);
|
|
|
+
|
|
|
+ result.m1 = sinz * cosy;
|
|
|
+ result.m5 = (sinz * siny * sinx) + (cosz * cosx);
|
|
|
+ result.m9 = (sinz * siny * cosx) - (cosz * sinx);
|
|
|
+
|
|
|
+ result.m2 = -siny;
|
|
|
+ result.m6 = cosy * sinx;
|
|
|
+ result.m10= cosy * cosx;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns x-rotation matrix (angle in radians)
|
|
|
+RMDEF Matrix MatrixRotateX(float angle)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ float cosres = cosf(angle);
|
|
|
+ float sinres = sinf(angle);
|
|
|
+
|
|
|
+ result.m5 = cosres;
|
|
|
+ result.m6 = -sinres;
|
|
|
+ result.m9 = sinres;
|
|
|
+ result.m10 = cosres;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns y-rotation matrix (angle in radians)
|
|
|
+RMDEF Matrix MatrixRotateY(float angle)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ float cosres = cosf(angle);
|
|
|
+ float sinres = sinf(angle);
|
|
|
+
|
|
|
+ result.m0 = cosres;
|
|
|
+ result.m2 = sinres;
|
|
|
+ result.m8 = -sinres;
|
|
|
+ result.m10 = cosres;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns z-rotation matrix (angle in radians)
|
|
|
+RMDEF Matrix MatrixRotateZ(float angle)
|
|
|
+{
|
|
|
+ Matrix result = MatrixIdentity();
|
|
|
+
|
|
|
+ float cosres = cosf(angle);
|
|
|
+ float sinres = sinf(angle);
|
|
|
+
|
|
|
+ result.m0 = cosres;
|
|
|
+ result.m1 = -sinres;
|
|
|
+ result.m4 = sinres;
|
|
|
+ result.m5 = cosres;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns scaling matrix
|
|
|
+RMDEF Matrix MatrixScale(float x, float y, float z)
|
|
|
+{
|
|
|
+ Matrix result = { x, 0.0f, 0.0f, 0.0f,
|
|
|
+ 0.0f, y, 0.0f, 0.0f,
|
|
|
+ 0.0f, 0.0f, z, 0.0f,
|
|
|
+ 0.0f, 0.0f, 0.0f, 1.0f };
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns two matrix multiplication
|
|
|
+// NOTE: When multiplying matrices... the order matters!
|
|
|
+RMDEF Matrix MatrixMultiply(Matrix left, Matrix right)
|
|
|
+{
|
|
|
+ Matrix result = { 0 };
|
|
|
+
|
|
|
+ result.m0 = left.m0*right.m0 + left.m1*right.m4 + left.m2*right.m8 + left.m3*right.m12;
|
|
|
+ result.m1 = left.m0*right.m1 + left.m1*right.m5 + left.m2*right.m9 + left.m3*right.m13;
|
|
|
+ result.m2 = left.m0*right.m2 + left.m1*right.m6 + left.m2*right.m10 + left.m3*right.m14;
|
|
|
+ result.m3 = left.m0*right.m3 + left.m1*right.m7 + left.m2*right.m11 + left.m3*right.m15;
|
|
|
+ result.m4 = left.m4*right.m0 + left.m5*right.m4 + left.m6*right.m8 + left.m7*right.m12;
|
|
|
+ result.m5 = left.m4*right.m1 + left.m5*right.m5 + left.m6*right.m9 + left.m7*right.m13;
|
|
|
+ result.m6 = left.m4*right.m2 + left.m5*right.m6 + left.m6*right.m10 + left.m7*right.m14;
|
|
|
+ result.m7 = left.m4*right.m3 + left.m5*right.m7 + left.m6*right.m11 + left.m7*right.m15;
|
|
|
+ result.m8 = left.m8*right.m0 + left.m9*right.m4 + left.m10*right.m8 + left.m11*right.m12;
|
|
|
+ result.m9 = left.m8*right.m1 + left.m9*right.m5 + left.m10*right.m9 + left.m11*right.m13;
|
|
|
+ result.m10 = left.m8*right.m2 + left.m9*right.m6 + left.m10*right.m10 + left.m11*right.m14;
|
|
|
+ result.m11 = left.m8*right.m3 + left.m9*right.m7 + left.m10*right.m11 + left.m11*right.m15;
|
|
|
+ result.m12 = left.m12*right.m0 + left.m13*right.m4 + left.m14*right.m8 + left.m15*right.m12;
|
|
|
+ result.m13 = left.m12*right.m1 + left.m13*right.m5 + left.m14*right.m9 + left.m15*right.m13;
|
|
|
+ result.m14 = left.m12*right.m2 + left.m13*right.m6 + left.m14*right.m10 + left.m15*right.m14;
|
|
|
+ result.m15 = left.m12*right.m3 + left.m13*right.m7 + left.m14*right.m11 + left.m15*right.m15;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns perspective projection matrix
|
|
|
+RMDEF Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far)
|
|
|
+{
|
|
|
+ Matrix result = { 0 };
|
|
|
+
|
|
|
+ float rl = (float)(right - left);
|
|
|
+ float tb = (float)(top - bottom);
|
|
|
+ float fn = (float)(far - near);
|
|
|
+
|
|
|
+ result.m0 = ((float) near*2.0f)/rl;
|
|
|
+ result.m1 = 0.0f;
|
|
|
+ result.m2 = 0.0f;
|
|
|
+ result.m3 = 0.0f;
|
|
|
+
|
|
|
+ result.m4 = 0.0f;
|
|
|
+ result.m5 = ((float) near*2.0f)/tb;
|
|
|
+ result.m6 = 0.0f;
|
|
|
+ result.m7 = 0.0f;
|
|
|
+
|
|
|
+ result.m8 = ((float)right + (float)left)/rl;
|
|
|
+ result.m9 = ((float)top + (float)bottom)/tb;
|
|
|
+ result.m10 = -((float)far + (float)near)/fn;
|
|
|
+ result.m11 = -1.0f;
|
|
|
+
|
|
|
+ result.m12 = 0.0f;
|
|
|
+ result.m13 = 0.0f;
|
|
|
+ result.m14 = -((float)far*(float)near*2.0f)/fn;
|
|
|
+ result.m15 = 0.0f;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns perspective projection matrix
|
|
|
+// NOTE: Angle should be provided in radians
|
|
|
+RMDEF Matrix MatrixPerspective(double fovy, double aspect, double near, double far)
|
|
|
+{
|
|
|
+ double top = near*tan(fovy*0.5);
|
|
|
+ double right = top*aspect;
|
|
|
+ Matrix result = MatrixFrustum(-right, right, -top, top, near, far);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns orthographic projection matrix
|
|
|
+RMDEF Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far)
|
|
|
+{
|
|
|
+ Matrix result = { 0 };
|
|
|
+
|
|
|
+ float rl = (float)(right - left);
|
|
|
+ float tb = (float)(top - bottom);
|
|
|
+ float fn = (float)(far - near);
|
|
|
+
|
|
|
+ result.m0 = 2.0f/rl;
|
|
|
+ result.m1 = 0.0f;
|
|
|
+ result.m2 = 0.0f;
|
|
|
+ result.m3 = 0.0f;
|
|
|
+ result.m4 = 0.0f;
|
|
|
+ result.m5 = 2.0f/tb;
|
|
|
+ result.m6 = 0.0f;
|
|
|
+ result.m7 = 0.0f;
|
|
|
+ result.m8 = 0.0f;
|
|
|
+ result.m9 = 0.0f;
|
|
|
+ result.m10 = -2.0f/fn;
|
|
|
+ result.m11 = 0.0f;
|
|
|
+ result.m12 = -((float)left + (float)right)/rl;
|
|
|
+ result.m13 = -((float)top + (float)bottom)/tb;
|
|
|
+ result.m14 = -((float)far + (float)near)/fn;
|
|
|
+ result.m15 = 1.0f;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns camera look-at matrix (view matrix)
|
|
|
+RMDEF Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up)
|
|
|
+{
|
|
|
+ Matrix result = { 0 };
|
|
|
+
|
|
|
+ Vector3 z = Vector3Subtract(eye, target);
|
|
|
+ z = Vector3Normalize(z);
|
|
|
+ Vector3 x = Vector3CrossProduct(up, z);
|
|
|
+ x = Vector3Normalize(x);
|
|
|
+ Vector3 y = Vector3CrossProduct(z, x);
|
|
|
+ y = Vector3Normalize(y);
|
|
|
+
|
|
|
+ result.m0 = x.x;
|
|
|
+ result.m1 = x.y;
|
|
|
+ result.m2 = x.z;
|
|
|
+ result.m3 = 0.0f;
|
|
|
+ result.m4 = y.x;
|
|
|
+ result.m5 = y.y;
|
|
|
+ result.m6 = y.z;
|
|
|
+ result.m7 = 0.0f;
|
|
|
+ result.m8 = z.x;
|
|
|
+ result.m9 = z.y;
|
|
|
+ result.m10 = z.z;
|
|
|
+ result.m11 = 0.0f;
|
|
|
+ result.m12 = eye.x;
|
|
|
+ result.m13 = eye.y;
|
|
|
+ result.m14 = eye.z;
|
|
|
+ result.m15 = 1.0f;
|
|
|
+
|
|
|
+ result = MatrixInvert(result);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns float array of matrix data
|
|
|
+RMDEF float16 MatrixToFloatV(Matrix mat)
|
|
|
+{
|
|
|
+ float16 buffer = { 0 };
|
|
|
+
|
|
|
+ buffer.v[0] = mat.m0;
|
|
|
+ buffer.v[1] = mat.m1;
|
|
|
+ buffer.v[2] = mat.m2;
|
|
|
+ buffer.v[3] = mat.m3;
|
|
|
+ buffer.v[4] = mat.m4;
|
|
|
+ buffer.v[5] = mat.m5;
|
|
|
+ buffer.v[6] = mat.m6;
|
|
|
+ buffer.v[7] = mat.m7;
|
|
|
+ buffer.v[8] = mat.m8;
|
|
|
+ buffer.v[9] = mat.m9;
|
|
|
+ buffer.v[10] = mat.m10;
|
|
|
+ buffer.v[11] = mat.m11;
|
|
|
+ buffer.v[12] = mat.m12;
|
|
|
+ buffer.v[13] = mat.m13;
|
|
|
+ buffer.v[14] = mat.m14;
|
|
|
+ buffer.v[15] = mat.m15;
|
|
|
+
|
|
|
+ return buffer;
|
|
|
+}
|
|
|
+
|
|
|
+//----------------------------------------------------------------------------------
|
|
|
+// Module Functions Definition - Quaternion math
|
|
|
+//----------------------------------------------------------------------------------
|
|
|
+
|
|
|
+// Add two quaternions
|
|
|
+RMDEF Quaternion QuaternionAdd(Quaternion q1, Quaternion q2)
|
|
|
+{
|
|
|
+ Quaternion result = {q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w};
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Add quaternion and float value
|
|
|
+RMDEF Quaternion QuaternionAddValue(Quaternion q, float add)
|
|
|
+{
|
|
|
+ Quaternion result = {q.x + add, q.y + add, q.z + add, q.w + add};
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Subtract two quaternions
|
|
|
+RMDEF Quaternion QuaternionSubtract(Quaternion q1, Quaternion q2)
|
|
|
+{
|
|
|
+ Quaternion result = {q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w};
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Subtract quaternion and float value
|
|
|
+RMDEF Quaternion QuaternionSubtractValue(Quaternion q, float sub)
|
|
|
+{
|
|
|
+ Quaternion result = {q.x - sub, q.y - sub, q.z - sub, q.w - sub};
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns identity quaternion
|
|
|
+RMDEF Quaternion QuaternionIdentity(void)
|
|
|
+{
|
|
|
+ Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f };
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Computes the length of a quaternion
|
|
|
+RMDEF float QuaternionLength(Quaternion q)
|
|
|
+{
|
|
|
+ float result = (float)sqrt(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Normalize provided quaternion
|
|
|
+RMDEF Quaternion QuaternionNormalize(Quaternion q)
|
|
|
+{
|
|
|
+ Quaternion result = { 0 };
|
|
|
+
|
|
|
+ float length, ilength;
|
|
|
+ length = QuaternionLength(q);
|
|
|
+ if (length == 0.0f) length = 1.0f;
|
|
|
+ ilength = 1.0f/length;
|
|
|
+
|
|
|
+ result.x = q.x*ilength;
|
|
|
+ result.y = q.y*ilength;
|
|
|
+ result.z = q.z*ilength;
|
|
|
+ result.w = q.w*ilength;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Invert provided quaternion
|
|
|
+RMDEF Quaternion QuaternionInvert(Quaternion q)
|
|
|
+{
|
|
|
+ Quaternion result = q;
|
|
|
+ float length = QuaternionLength(q);
|
|
|
+ float lengthSq = length*length;
|
|
|
+
|
|
|
+ if (lengthSq != 0.0)
|
|
|
+ {
|
|
|
+ float i = 1.0f/lengthSq;
|
|
|
+
|
|
|
+ result.x *= -i;
|
|
|
+ result.y *= -i;
|
|
|
+ result.z *= -i;
|
|
|
+ result.w *= i;
|
|
|
+ }
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Calculate two quaternion multiplication
|
|
|
+RMDEF Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2)
|
|
|
+{
|
|
|
+ Quaternion result = { 0 };
|
|
|
+
|
|
|
+ float qax = q1.x, qay = q1.y, qaz = q1.z, qaw = q1.w;
|
|
|
+ float qbx = q2.x, qby = q2.y, qbz = q2.z, qbw = q2.w;
|
|
|
+
|
|
|
+ result.x = qax*qbw + qaw*qbx + qay*qbz - qaz*qby;
|
|
|
+ result.y = qay*qbw + qaw*qby + qaz*qbx - qax*qbz;
|
|
|
+ result.z = qaz*qbw + qaw*qbz + qax*qby - qay*qbx;
|
|
|
+ result.w = qaw*qbw - qax*qbx - qay*qby - qaz*qbz;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Scale quaternion by float value
|
|
|
+RMDEF Quaternion QuaternionScale(Quaternion q, float mul)
|
|
|
+{
|
|
|
+ Quaternion result = { 0 };
|
|
|
+
|
|
|
+ float qax = q.x, qay = q.y, qaz = q.z, qaw = q.w;
|
|
|
+
|
|
|
+ result.x = qax * mul + qaw * mul + qay * mul - qaz * mul;
|
|
|
+ result.y = qay * mul + qaw * mul + qaz * mul - qax * mul;
|
|
|
+ result.z = qaz * mul + qaw * mul + qax * mul - qay * mul;
|
|
|
+ result.w = qaw * mul - qax * mul - qay * mul - qaz * mul;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Divide two quaternions
|
|
|
+RMDEF Quaternion QuaternionDivide(Quaternion q1, Quaternion q2)
|
|
|
+{
|
|
|
+ Quaternion result = {q1.x / q2.x, q1.y / q2.y, q1.z / q2.z, q1.w / q2.w};
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Calculate linear interpolation between two quaternions
|
|
|
+RMDEF Quaternion QuaternionLerp(Quaternion q1, Quaternion q2, float amount)
|
|
|
+{
|
|
|
+ Quaternion result = { 0 };
|
|
|
+
|
|
|
+ result.x = q1.x + amount*(q2.x - q1.x);
|
|
|
+ result.y = q1.y + amount*(q2.y - q1.y);
|
|
|
+ result.z = q1.z + amount*(q2.z - q1.z);
|
|
|
+ result.w = q1.w + amount*(q2.w - q1.w);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Calculate slerp-optimized interpolation between two quaternions
|
|
|
+RMDEF Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount)
|
|
|
+{
|
|
|
+ Quaternion result = QuaternionLerp(q1, q2, amount);
|
|
|
+ result = QuaternionNormalize(result);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Calculates spherical linear interpolation between two quaternions
|
|
|
+RMDEF Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount)
|
|
|
+{
|
|
|
+ Quaternion result = { 0 };
|
|
|
+
|
|
|
+ float cosHalfTheta = q1.x*q2.x + q1.y*q2.y + q1.z*q2.z + q1.w*q2.w;
|
|
|
+
|
|
|
+ if (fabs(cosHalfTheta) >= 1.0f) result = q1;
|
|
|
+ else if (cosHalfTheta > 0.95f) result = QuaternionNlerp(q1, q2, amount);
|
|
|
+ else
|
|
|
+ {
|
|
|
+ float halfTheta = acosf(cosHalfTheta);
|
|
|
+ float sinHalfTheta = sqrtf(1.0f - cosHalfTheta*cosHalfTheta);
|
|
|
+
|
|
|
+ if (fabs(sinHalfTheta) < 0.001f)
|
|
|
+ {
|
|
|
+ result.x = (q1.x*0.5f + q2.x*0.5f);
|
|
|
+ result.y = (q1.y*0.5f + q2.y*0.5f);
|
|
|
+ result.z = (q1.z*0.5f + q2.z*0.5f);
|
|
|
+ result.w = (q1.w*0.5f + q2.w*0.5f);
|
|
|
+ }
|
|
|
+ else
|
|
|
+ {
|
|
|
+ float ratioA = sinf((1 - amount)*halfTheta)/sinHalfTheta;
|
|
|
+ float ratioB = sinf(amount*halfTheta)/sinHalfTheta;
|
|
|
+
|
|
|
+ result.x = (q1.x*ratioA + q2.x*ratioB);
|
|
|
+ result.y = (q1.y*ratioA + q2.y*ratioB);
|
|
|
+ result.z = (q1.z*ratioA + q2.z*ratioB);
|
|
|
+ result.w = (q1.w*ratioA + q2.w*ratioB);
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Calculate quaternion based on the rotation from one vector to another
|
|
|
+RMDEF Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to)
|
|
|
+{
|
|
|
+ Quaternion result = { 0 };
|
|
|
+
|
|
|
+ float cos2Theta = Vector3DotProduct(from, to);
|
|
|
+ Vector3 cross = Vector3CrossProduct(from, to);
|
|
|
+
|
|
|
+ result.x = cross.x;
|
|
|
+ result.y = cross.y;
|
|
|
+ result.z = cross.y;
|
|
|
+ result.w = 1.0f + cos2Theta; // NOTE: Added QuaternioIdentity()
|
|
|
+
|
|
|
+ // Normalize to essentially nlerp the original and identity to 0.5
|
|
|
+ result = QuaternionNormalize(result);
|
|
|
+
|
|
|
+ // Above lines are equivalent to:
|
|
|
+ //Quaternion result = QuaternionNlerp(q, QuaternionIdentity(), 0.5f);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns a quaternion for a given rotation matrix
|
|
|
+RMDEF Quaternion QuaternionFromMatrix(Matrix mat)
|
|
|
+{
|
|
|
+ Quaternion result = { 0 };
|
|
|
+
|
|
|
+ float trace = MatrixTrace(mat);
|
|
|
+
|
|
|
+ if (trace > 0.0f)
|
|
|
+ {
|
|
|
+ float s = sqrtf(trace + 1)*2.0f;
|
|
|
+ float invS = 1.0f/s;
|
|
|
+
|
|
|
+ result.w = s*0.25f;
|
|
|
+ result.x = (mat.m6 - mat.m9)*invS;
|
|
|
+ result.y = (mat.m8 - mat.m2)*invS;
|
|
|
+ result.z = (mat.m1 - mat.m4)*invS;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ {
|
|
|
+ float m00 = mat.m0, m11 = mat.m5, m22 = mat.m10;
|
|
|
+
|
|
|
+ if (m00 > m11 && m00 > m22)
|
|
|
+ {
|
|
|
+ float s = (float)sqrt(1.0f + m00 - m11 - m22)*2.0f;
|
|
|
+ float invS = 1.0f/s;
|
|
|
+
|
|
|
+ result.w = (mat.m6 - mat.m9)*invS;
|
|
|
+ result.x = s*0.25f;
|
|
|
+ result.y = (mat.m4 + mat.m1)*invS;
|
|
|
+ result.z = (mat.m8 + mat.m2)*invS;
|
|
|
+ }
|
|
|
+ else if (m11 > m22)
|
|
|
+ {
|
|
|
+ float s = sqrtf(1.0f + m11 - m00 - m22)*2.0f;
|
|
|
+ float invS = 1.0f/s;
|
|
|
+
|
|
|
+ result.w = (mat.m8 - mat.m2)*invS;
|
|
|
+ result.x = (mat.m4 + mat.m1)*invS;
|
|
|
+ result.y = s*0.25f;
|
|
|
+ result.z = (mat.m9 + mat.m6)*invS;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ {
|
|
|
+ float s = sqrtf(1.0f + m22 - m00 - m11)*2.0f;
|
|
|
+ float invS = 1.0f/s;
|
|
|
+
|
|
|
+ result.w = (mat.m1 - mat.m4)*invS;
|
|
|
+ result.x = (mat.m8 + mat.m2)*invS;
|
|
|
+ result.y = (mat.m9 + mat.m6)*invS;
|
|
|
+ result.z = s*0.25f;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns a matrix for a given quaternion
|
|
|
+RMDEF Matrix QuaternionToMatrix(Quaternion q)
|
|
|
+{
|
|
|
+ Matrix result = { 0 };
|
|
|
+
|
|
|
+ float x = q.x, y = q.y, z = q.z, w = q.w;
|
|
|
+
|
|
|
+ float x2 = x + x;
|
|
|
+ float y2 = y + y;
|
|
|
+ float z2 = z + z;
|
|
|
+
|
|
|
+ float length = QuaternionLength(q);
|
|
|
+ float lengthSquared = length*length;
|
|
|
+
|
|
|
+ float xx = x*x2/lengthSquared;
|
|
|
+ float xy = x*y2/lengthSquared;
|
|
|
+ float xz = x*z2/lengthSquared;
|
|
|
+
|
|
|
+ float yy = y*y2/lengthSquared;
|
|
|
+ float yz = y*z2/lengthSquared;
|
|
|
+ float zz = z*z2/lengthSquared;
|
|
|
+
|
|
|
+ float wx = w*x2/lengthSquared;
|
|
|
+ float wy = w*y2/lengthSquared;
|
|
|
+ float wz = w*z2/lengthSquared;
|
|
|
+
|
|
|
+ result.m0 = 1.0f - (yy + zz);
|
|
|
+ result.m1 = xy - wz;
|
|
|
+ result.m2 = xz + wy;
|
|
|
+ result.m3 = 0.0f;
|
|
|
+ result.m4 = xy + wz;
|
|
|
+ result.m5 = 1.0f - (xx + zz);
|
|
|
+ result.m6 = yz - wx;
|
|
|
+ result.m7 = 0.0f;
|
|
|
+ result.m8 = xz - wy;
|
|
|
+ result.m9 = yz + wx;
|
|
|
+ result.m10 = 1.0f - (xx + yy);
|
|
|
+ result.m11 = 0.0f;
|
|
|
+ result.m12 = 0.0f;
|
|
|
+ result.m13 = 0.0f;
|
|
|
+ result.m14 = 0.0f;
|
|
|
+ result.m15 = 1.0f;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns rotation quaternion for an angle and axis
|
|
|
+// NOTE: angle must be provided in radians
|
|
|
+RMDEF Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle)
|
|
|
+{
|
|
|
+ Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f };
|
|
|
+
|
|
|
+ if (Vector3Length(axis) != 0.0f)
|
|
|
+
|
|
|
+ angle *= 0.5f;
|
|
|
+
|
|
|
+ axis = Vector3Normalize(axis);
|
|
|
+
|
|
|
+ float sinres = sinf(angle);
|
|
|
+ float cosres = cosf(angle);
|
|
|
+
|
|
|
+ result.x = axis.x*sinres;
|
|
|
+ result.y = axis.y*sinres;
|
|
|
+ result.z = axis.z*sinres;
|
|
|
+ result.w = cosres;
|
|
|
+
|
|
|
+ result = QuaternionNormalize(result);
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns the rotation angle and axis for a given quaternion
|
|
|
+RMDEF void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle)
|
|
|
+{
|
|
|
+ if (fabs(q.w) > 1.0f) q = QuaternionNormalize(q);
|
|
|
+
|
|
|
+ Vector3 resAxis = { 0.0f, 0.0f, 0.0f };
|
|
|
+ float resAngle = 2.0f*acosf(q.w);
|
|
|
+ float den = sqrtf(1.0f - q.w*q.w);
|
|
|
+
|
|
|
+ if (den > 0.0001f)
|
|
|
+ {
|
|
|
+ resAxis.x = q.x/den;
|
|
|
+ resAxis.y = q.y/den;
|
|
|
+ resAxis.z = q.z/den;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ {
|
|
|
+ // This occurs when the angle is zero.
|
|
|
+ // Not a problem: just set an arbitrary normalized axis.
|
|
|
+ resAxis.x = 1.0f;
|
|
|
+ }
|
|
|
+
|
|
|
+ *outAxis = resAxis;
|
|
|
+ *outAngle = resAngle;
|
|
|
+}
|
|
|
+
|
|
|
+// Returns he quaternion equivalent to Euler angles
|
|
|
+RMDEF Quaternion QuaternionFromEuler(float roll, float pitch, float yaw)
|
|
|
+{
|
|
|
+ Quaternion q = { 0 };
|
|
|
+
|
|
|
+ float x0 = cosf(roll*0.5f);
|
|
|
+ float x1 = sinf(roll*0.5f);
|
|
|
+ float y0 = cosf(pitch*0.5f);
|
|
|
+ float y1 = sinf(pitch*0.5f);
|
|
|
+ float z0 = cosf(yaw*0.5f);
|
|
|
+ float z1 = sinf(yaw*0.5f);
|
|
|
+
|
|
|
+ q.x = x1*y0*z0 - x0*y1*z1;
|
|
|
+ q.y = x0*y1*z0 + x1*y0*z1;
|
|
|
+ q.z = x0*y0*z1 - x1*y1*z0;
|
|
|
+ q.w = x0*y0*z0 + x1*y1*z1;
|
|
|
+
|
|
|
+ return q;
|
|
|
+}
|
|
|
+
|
|
|
+// Return the Euler angles equivalent to quaternion (roll, pitch, yaw)
|
|
|
+// NOTE: Angles are returned in a Vector3 struct in degrees
|
|
|
+RMDEF Vector3 QuaternionToEuler(Quaternion q)
|
|
|
+{
|
|
|
+ Vector3 result = { 0 };
|
|
|
+
|
|
|
+ // roll (x-axis rotation)
|
|
|
+ float x0 = 2.0f*(q.w*q.x + q.y*q.z);
|
|
|
+ float x1 = 1.0f - 2.0f*(q.x*q.x + q.y*q.y);
|
|
|
+ result.x = atan2f(x0, x1)*RAD2DEG;
|
|
|
+
|
|
|
+ // pitch (y-axis rotation)
|
|
|
+ float y0 = 2.0f*(q.w*q.y - q.z*q.x);
|
|
|
+ y0 = y0 > 1.0f ? 1.0f : y0;
|
|
|
+ y0 = y0 < -1.0f ? -1.0f : y0;
|
|
|
+ result.y = asinf(y0)*RAD2DEG;
|
|
|
+
|
|
|
+ // yaw (z-axis rotation)
|
|
|
+ float z0 = 2.0f*(q.w*q.z + q.x*q.y);
|
|
|
+ float z1 = 1.0f - 2.0f*(q.y*q.y + q.z*q.z);
|
|
|
+ result.z = atan2f(z0, z1)*RAD2DEG;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+// Transform a quaternion given a transformation matrix
|
|
|
+RMDEF Quaternion QuaternionTransform(Quaternion q, Matrix mat)
|
|
|
+{
|
|
|
+ Quaternion result = { 0 };
|
|
|
+
|
|
|
+ result.x = mat.m0*q.x + mat.m4*q.y + mat.m8*q.z + mat.m12*q.w;
|
|
|
+ result.y = mat.m1*q.x + mat.m5*q.y + mat.m9*q.z + mat.m13*q.w;
|
|
|
+ result.z = mat.m2*q.x + mat.m6*q.y + mat.m10*q.z + mat.m14*q.w;
|
|
|
+ result.w = mat.m3*q.x + mat.m7*q.y + mat.m11*q.z + mat.m15*q.w;
|
|
|
+
|
|
|
+ return result;
|
|
|
+}
|
|
|
+
|
|
|
+#endif // RAYMATH_H
|
raysan5