Refactor bezier interpolation functions

5 files changed, 68 insertions, 17 deletions

diff --git a/core/math/math_funcs.h b/core/math/math_funcs.h
index c8a55341aa..53deb9bd42 100644
--- a/core/math/math_funcs.h
+++ b/core/math/math_funcs.h
@@ -253,6 +253,27 @@ public:
 						(-p_pre + 3.0f * p_from - 3.0f * p_to + p_post) * (p_weight * p_weight * p_weight));
 	}
 
+	static _ALWAYS_INLINE_ double bezier_interpolate(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) {
+		/* Formula from Wikipedia article on Bezier curves. */
+		double omt = (1.0 - p_t);
+		double omt2 = omt * omt;
+		double omt3 = omt2 * omt;
+		double t2 = p_t * p_t;
+		double t3 = t2 * p_t;
+
+		return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
+	}
+	static _ALWAYS_INLINE_ float bezier_interpolate(float p_start, float p_control_1, float p_control_2, float p_end, float p_t) {
+		/* Formula from Wikipedia article on Bezier curves. */
+		float omt = (1.0f - p_t);
+		float omt2 = omt * omt;
+		float omt3 = omt2 * omt;
+		float t2 = p_t * p_t;
+		float t3 = t2 * p_t;
+
+		return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0f + p_control_2 * omt * t2 * 3.0f + p_end * t3;
+	}
+
 	static _ALWAYS_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;
diff --git a/core/math/vector2.cpp b/core/math/vector2.cpp
index a27227905c..d9b5d55454 100644
--- a/core/math/vector2.cpp
+++ b/core/math/vector2.cpp
@@ -152,13 +152,6 @@ Vector2 Vector2::limit_length(const real_t p_len) const {
 	return v;
 }
 
-Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight) const {
-	Vector2 res = *this;
-	res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
-	res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
-	return res;
-}
-
 Vector2 Vector2::move_toward(const Vector2 &p_to, const real_t p_delta) const {
 	Vector2 v = *this;
 	Vector2 vd = p_to - v;
diff --git a/core/math/vector2.h b/core/math/vector2.h
index bd67299f33..91d3d3a56b 100644
--- a/core/math/vector2.h
+++ b/core/math/vector2.h
@@ -113,7 +113,9 @@ struct _NO_DISCARD_ Vector2 {
 
 	_FORCE_INLINE_ Vector2 lerp(const Vector2 &p_to, const real_t p_weight) const;
 	_FORCE_INLINE_ Vector2 slerp(const Vector2 &p_to, const real_t p_weight) const;
-	Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight) const;
+	_FORCE_INLINE_ Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight) const;
+	_FORCE_INLINE_ Vector2 bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const;
+
 	Vector2 move_toward(const Vector2 &p_to, const real_t p_delta) const;
 
 	Vector2 slide(const Vector2 &p_normal) const;
@@ -261,6 +263,26 @@ Vector2 Vector2::slerp(const Vector2 &p_to, const real_t p_weight) const {
 	return rotated(angle * p_weight) * (result_length / start_length);
 }
 
+Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight) const {
+	Vector2 res = *this;
+	res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
+	res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
+	return res;
+}
+
+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;
+}
+
 Vector2 Vector2::direction_to(const Vector2 &p_to) const {
 	Vector2 ret(p_to.x - x, p_to.y - y);
 	ret.normalize();
diff --git a/core/math/vector3.cpp b/core/math/vector3.cpp
index f94f39b7f2..d71d365053 100644
--- a/core/math/vector3.cpp
+++ b/core/math/vector3.cpp
@@ -85,14 +85,6 @@ Vector3 Vector3::limit_length(const real_t p_len) const {
 	return v;
 }
 
-Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const {
-	Vector3 res = *this;
-	res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
-	res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
-	res.z = Math::cubic_interpolate(res.z, p_b.z, p_pre_a.z, p_post_b.z, p_weight);
-	return res;
-}
-
 Vector3 Vector3::move_toward(const Vector3 &p_to, const real_t p_delta) const {
 	Vector3 v = *this;
 	Vector3 vd = p_to - v;
diff --git a/core/math/vector3.h b/core/math/vector3.h
index 8891532f42..970416234d 100644
--- a/core/math/vector3.h
+++ b/core/math/vector3.h
@@ -104,7 +104,9 @@ struct _NO_DISCARD_ Vector3 {
 
 	_FORCE_INLINE_ Vector3 lerp(const Vector3 &p_to, const real_t p_weight) const;
 	_FORCE_INLINE_ Vector3 slerp(const Vector3 &p_to, const real_t p_weight) const;
-	Vector3 cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const;
+	_FORCE_INLINE_ Vector3 cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const;
+	_FORCE_INLINE_ Vector3 bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const;
+
 	Vector3 move_toward(const Vector3 &p_to, const real_t p_delta) const;
 
 	Vector2 octahedron_encode() const;
@@ -227,6 +229,27 @@ Vector3 Vector3::slerp(const Vector3 &p_to, const real_t p_weight) const {
 	return rotated(cross(p_to).normalized(), angle * p_weight) * (result_length / start_length);
 }
 
+Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const {
+	Vector3 res = *this;
+	res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
+	res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
+	res.z = Math::cubic_interpolate(res.z, p_b.z, p_pre_a.z, p_post_b.z, p_weight);
+	return res;
+}
+
+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;
+}
+
 real_t Vector3::distance_to(const Vector3 &p_to) const {
 	return (p_to - *this).length();
 }