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Physics Interpolation - Fix `Transform2D::interpolate_with()` 

Ports the `interpolate_with()` routine from 4.x which works correctly with skew.
This commit is contained in:
lawnjelly 2024-07-02 07:42:08 +01:00
parent 98e24835ee
commit 250a7d8788
3 changed files with 31 additions and 68 deletions
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53
core/math/transform_2d.cpp
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@ -82,6 +82,24 @@ void Transform2D::set_rotation(real_t p_rot) {
set_scale(scale);
}
void Transform2D::set_skew(real_t p_angle) {
real_t det = determinant();
elements[1] = SGN(det) * elements[0].rotated(((real_t)Math_PI * 0.5f + p_angle)).normalized() * elements[1].length();
}
real_t Transform2D::get_skew() const {
real_t det = determinant();
return Math::acos(elements[0].normalized().dot(SGN(det) * elements[1].normalized())) - (real_t)Math_PI * 0.5f;
}
Transform2D::Transform2D(real_t p_rot, const Size2 &p_scale, real_t p_skew, const Vector2 &p_pos) {
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;
elements[2] = p_pos;
}
Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) {
real_t cr = Math::cos(p_rot);
real_t sr = Math::sin(p_rot);
@ -221,41 +239,6 @@ real_t Transform2D::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 = 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 String(String() + elements[0] + ", " + elements[1] + ", " + elements[2]);
}

12
core/math/transform_2d.h
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@ -71,6 +71,8 @@ struct _NO_DISCARD_CLASS_ Transform2D {
void set_rotation(real_t p_rot);
real_t get_rotation() const;
void set_skew(real_t p_angle);
real_t get_skew() const;
_FORCE_INLINE_ void set_rotation_and_scale(real_t p_rot, const Size2 &p_scale);
void rotate(real_t p_angle);
@ -104,7 +106,13 @@ struct _NO_DISCARD_CLASS_ Transform2D {
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;
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;
@ -127,6 +135,8 @@ struct _NO_DISCARD_CLASS_ Transform2D {
}
Transform2D(real_t p_rot, const Vector2 &p_pos);
Transform2D(real_t p_rot, const Size2 &p_scale, real_t p_skew, const Vector2 &p_pos);
Transform2D() {
elements[0][0] = 1.0;
elements[1][1] = 1.0;

34
core/math/transform_interpolator.cpp
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@ -33,46 +33,16 @@
#include "core/math/transform_2d.h"
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.determinant()) != _sign(p_curr.determinant())) {
r_result.elements[0] = p_curr.elements[0];
r_result.elements[1] = p_curr.elements[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(const Transform &p_prev, const Transform &p_curr, Transform &r_result, real_t p_fraction) {