Merge pull request #69111 from TokageItLab/put-together-interpolations

Refactor interpolating functions in some classes to use `Math` class

core/math/color.h

@@ -105,12 +105,10 @@ struct _NO_DISCARD_ Color {
 
 	_FORCE_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));
-
+		res.r = Math::lerp(res.r, p_to.r, p_weight);
+		res.g = Math::lerp(res.g, p_to.g, p_weight);
+		res.b = Math::lerp(res.b, p_to.b, p_weight);
+		res.a = Math::lerp(res.a, p_to.a, p_weight);
 		return res;
 	}
 

core/math/vector2.h

@@ -243,10 +243,8 @@ _FORCE_INLINE_ bool Vector2::operator!=(const Vector2 &p_vec2) const {
 
 Vector2 Vector2::lerp(const Vector2 &p_to, const real_t p_weight) const {
 	Vector2 res = *this;
-
-	res.x += (p_weight * (p_to.x - x));
-	res.y += (p_weight * (p_to.y - y));
-
+	res.x = Math::lerp(res.x, p_to.x, p_weight);
+	res.y = Math::lerp(res.y, p_to.y, p_weight);
 	return res;
 }
 
@@ -279,27 +277,16 @@ Vector2 Vector2::cubic_interpolate_in_time(const Vector2 &p_b, const Vector2 &p_
 
 Vector2 Vector2::bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const {
 	Vector2 res = *this;
-
-	/* Formula from Wikipedia article on Bezier curves. */
-	real_t omt = (1.0 - p_t);
-	real_t omt2 = omt * omt;
-	real_t omt3 = omt2 * omt;
-	real_t t2 = p_t * p_t;
-	real_t t3 = t2 * p_t;
-
-	return res * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
+	res.x = Math::bezier_interpolate(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
+	res.y = Math::bezier_interpolate(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
+	return res;
 }
 
 Vector2 Vector2::bezier_derivative(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const {
 	Vector2 res = *this;
-
-	/* Formula from Wikipedia article on Bezier curves. */
-	real_t omt = (1.0 - p_t);
-	real_t omt2 = omt * omt;
-	real_t t2 = p_t * p_t;
-
-	Vector2 d = (p_control_1 - res) * 3.0 * omt2 + (p_control_2 - p_control_1) * 6.0 * omt * p_t + (p_end - p_control_2) * 3.0 * t2;
-	return d;
+	res.x = Math::bezier_derivative(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
+	res.y = Math::bezier_derivative(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
+	return res;
 }
 
 Vector2 Vector2::direction_to(const Vector2 &p_to) const {

core/math/vector3.h

@@ -209,10 +209,11 @@ Vector3 Vector3::round() const {
 }
 
 Vector3 Vector3::lerp(const Vector3 &p_to, const 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 res = *this;
+	res.x = Math::lerp(res.x, p_to.x, p_weight);
+	res.y = Math::lerp(res.y, p_to.y, p_weight);
+	res.z = Math::lerp(res.z, p_to.z, p_weight);
+	return res;
 }
 
 Vector3 Vector3::slerp(const Vector3 &p_to, const real_t p_weight) const {
@@ -255,27 +256,18 @@ Vector3 Vector3::cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_
 
 Vector3 Vector3::bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const {
 	Vector3 res = *this;
-
-	/* Formula from Wikipedia article on Bezier curves. */
-	real_t omt = (1.0 - p_t);
-	real_t omt2 = omt * omt;
-	real_t omt3 = omt2 * omt;
-	real_t t2 = p_t * p_t;
-	real_t t3 = t2 * p_t;
-
-	return res * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
+	res.x = Math::bezier_interpolate(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
+	res.y = Math::bezier_interpolate(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
+	res.z = Math::bezier_interpolate(res.z, p_control_1.z, p_control_2.z, p_end.z, p_t);
+	return res;
 }
 
 Vector3 Vector3::bezier_derivative(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const {
 	Vector3 res = *this;
-
-	/* Formula from Wikipedia article on Bezier curves. */
-	real_t omt = (1.0 - p_t);
-	real_t omt2 = omt * omt;
-	real_t t2 = p_t * p_t;
-
-	Vector3 d = (p_control_1 - res) * 3.0 * omt2 + (p_control_2 - p_control_1) * 6.0 * omt * p_t + (p_end - p_control_2) * 3.0 * t2;
-	return d;
+	res.x = Math::bezier_derivative(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
+	res.y = Math::bezier_derivative(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
+	res.z = Math::bezier_derivative(res.z, p_control_1.z, p_control_2.z, p_end.z, p_t);
+	return res;
 }
 
 real_t Vector3::distance_to(const Vector3 &p_to) const {

core/math/vector4.cpp

@@ -130,11 +130,12 @@ Vector4 Vector4::round() const {
 }
 
 Vector4 Vector4::lerp(const Vector4 &p_to, const real_t p_weight) const {
-	return Vector4(
-			x + (p_weight * (p_to.x - x)),
-			y + (p_weight * (p_to.y - y)),
-			z + (p_weight * (p_to.z - z)),
-			w + (p_weight * (p_to.w - w)));
+	Vector4 res = *this;
+	res.x = Math::lerp(res.x, p_to.x, p_weight);
+	res.y = Math::lerp(res.y, p_to.y, p_weight);
+	res.z = Math::lerp(res.z, p_to.z, p_weight);
+	res.w = Math::lerp(res.w, p_to.w, p_weight);
+	return res;
 }
 
 Vector4 Vector4::cubic_interpolate(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, const real_t p_weight) const {

modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs

@@ -249,14 +249,11 @@ namespace Godot
         /// <returns>The interpolated vector.</returns>
         public readonly Vector2 BezierInterpolate(Vector2 control1, Vector2 control2, Vector2 end, real_t t)
         {
-            // Formula from Wikipedia article on Bezier curves
-            real_t omt = 1 - t;
-            real_t omt2 = omt * omt;
-            real_t omt3 = omt2 * omt;
-            real_t t2 = t * t;
-            real_t t3 = t2 * t;
-
-            return this * omt3 + control1 * omt2 * t * 3 + control2 * omt * t2 * 3 + end * t3;
+            return new Vector2
+            (
+                Mathf.BezierInterpolate(x, control1.x, control2.x, end.x, t),
+                Mathf.BezierInterpolate(y, control1.y, control2.y, end.y, t)
+            );
         }
 
         /// <summary>

modules/mono/glue/GodotSharp/GodotSharp/Core/Vector3.cs

@@ -243,14 +243,12 @@ namespace Godot
         /// <returns>The interpolated vector.</returns>
         public readonly Vector3 BezierInterpolate(Vector3 control1, Vector3 control2, Vector3 end, real_t t)
         {
-            // Formula from Wikipedia article on Bezier curves
-            real_t omt = 1 - t;
-            real_t omt2 = omt * omt;
-            real_t omt3 = omt2 * omt;
-            real_t t2 = t * t;
-            real_t t3 = t2 * t;
-
-            return this * omt3 + control1 * omt2 * t * 3 + control2 * omt * t2 * 3 + end * t3;
+            return new Vector3
+            (
+                Mathf.BezierInterpolate(x, control1.x, control2.x, end.x, t),
+                Mathf.BezierInterpolate(y, control1.y, control2.y, end.y, t),
+                Mathf.BezierInterpolate(z, control1.z, control2.z, end.z, t)
+            );
         }
 
         /// <summary>

scene/resources/primitive_meshes.cpp

@@ -2779,13 +2779,7 @@ void TextMesh::_generate_glyph_mesh_data(const GlyphMeshKey &p_key, const Glyph
 				real_t step = CLAMP(curve_step / (p0 - p3).length(), 0.01, 0.5);
 				real_t t = step;
 				while (t < 1.0) {
-					real_t omt = (1.0 - t);
-					real_t omt2 = omt * omt;
-					real_t omt3 = omt2 * omt;
-					real_t t2 = t * t;
-					real_t t3 = t2 * t;
-
-					Vector2 point = p0 * omt3 + p1 * omt2 * t * 3.0 + p2 * omt * t2 * 3.0 + p3 * t3;
+					Vector2 point = p0.bezier_interpolate(p1, p2, p3, t);
 					Vector2 p = point * pixel_size + origin;
 					polygon.push_back(ContourPoint(p, false));
 					t += step;