From 131880d444ab3675b68a32e36fc2520a90ac38b8 Mon Sep 17 00:00:00 2001
From: lawnjelly <lawnjelly@gmail.com>
Date: Tue, 2 Jul 2024 07:42:08 +0100
Subject: [PATCH] Physics Interpolation - Fix `Transform2D::interpolate_with()`

Ports the `interpolate_with()` routine from 4.x which works correctly with skew.
---
 core/math/transform_2d.cpp           | 35 ----------------------------
 core/math/transform_2d.h             |  8 ++++++-
 core/math/transform_interpolator.cpp | 34 ++-------------------------
 3 files changed, 9 insertions(+), 68 deletions(-)

diff --git a/core/math/transform_2d.cpp b/core/math/transform_2d.cpp
index 9df4894ac..7d5625684 100644
--- a/core/math/transform_2d.cpp
+++ b/core/math/transform_2d.cpp
@@ -295,41 +295,6 @@ real_t Transform2D::basis_determinant() const {
 	return columns[0].x * columns[1].y - columns[0].y * columns[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 = CLAMP(dot, -1, 1);
-
-	Vector2 v;
-
-	if (dot > 0.9995f) {
-		v = Vector2::linear_interpolate(v1, 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), Vector2::linear_interpolate(p1, p2, p_c));
-	res.scale_basis(Vector2::linear_interpolate(s1, s2, p_c));
-	return res;
-}
-
 Transform2D::operator String() const {
 	return "[X: " + columns[0].operator String() +
 			", Y: " + columns[1].operator String() +
diff --git a/core/math/transform_2d.h b/core/math/transform_2d.h
index a961d1be5..8148596b0 100644
--- a/core/math/transform_2d.h
+++ b/core/math/transform_2d.h
@@ -132,7 +132,13 @@ struct _NO_DISCARD_CLASS_ Transform2D {
 	void operator*=(const real_t p_val);
 	Transform2D operator*(const real_t p_val) const;
 
-	Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const;
+	Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const {
+		return Transform2D(
+				Math::lerp_angle(get_rotation(), p_transform.get_rotation(), p_c),
+				get_scale().linear_interpolate(p_transform.get_scale(), p_c),
+				Math::lerp_angle(get_skew(), p_transform.get_skew(), p_c),
+				get_origin().linear_interpolate(p_transform.get_origin(), p_c));
+	}
 
 	_FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const;
 	_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const;
diff --git a/core/math/transform_interpolator.cpp b/core/math/transform_interpolator.cpp
index 647954073..84a8597c2 100644
--- a/core/math/transform_interpolator.cpp
+++ b/core/math/transform_interpolator.cpp
@@ -44,46 +44,16 @@ void TransformInterpolator::interpolate_basis(const Basis &p_prev, const Basis &
 }
 
 void TransformInterpolator::interpolate_transform_2d(const Transform2D &p_prev, const Transform2D &p_curr, Transform2D &r_result, real_t p_fraction) {
-	// Extract parameters.
-	Vector2 p1 = p_prev.get_origin();
-	Vector2 p2 = p_curr.get_origin();
-
 	// Special case for physics interpolation, if flipping, don't interpolate basis.
 	// If the determinant polarity changes, the handedness of the coordinate system changes.
 	if (_sign(p_prev.basis_determinant()) != _sign(p_curr.basis_determinant())) {
 		r_result.columns[0] = p_curr.columns[0];
 		r_result.columns[1] = p_curr.columns[1];
-		r_result.set_origin(Vector2::linear_interpolate(p1, p2, p_fraction));
+		r_result.set_origin(Vector2::linear_interpolate(p_prev.get_origin(), p_curr.get_origin(), p_fraction));
 		return;
 	}
 
-	real_t r1 = p_prev.get_rotation();
-	real_t r2 = p_curr.get_rotation();
-
-	Size2 s1 = p_prev.get_scale();
-	Size2 s2 = p_curr.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 = CLAMP(dot, -1, 1);
-
-	Vector2 v;
-
-	if (dot > 0.9995f) {
-		v = Vector2::linear_interpolate(v1, v2, p_fraction).normalized(); // Linearly interpolate to avoid numerical precision issues.
-	} else {
-		real_t angle = p_fraction * Math::acos(dot);
-		Vector2 v3 = (v2 - v1 * dot).normalized();
-		v = v1 * Math::cos(angle) + v3 * Math::sin(angle);
-	}
-
-	// Construct matrix.
-	r_result = Transform2D(Math::atan2(v.y, v.x), Vector2::linear_interpolate(p1, p2, p_fraction));
-	r_result.scale_basis(Vector2::linear_interpolate(s1, s2, p_fraction));
+	r_result = p_prev.interpolate_with(p_curr, p_fraction);
 }
 
 void TransformInterpolator::interpolate_transform_via_method(const Transform &p_prev, const Transform &p_curr, Transform &r_result, real_t p_fraction, Method p_method) {