godot/core/math/transform_interpolator.cpp

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/*  transform_interpolator.cpp                                            */
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/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur.                  */
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#include "transform_interpolator.h"

#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.columns[0] = p_curr.columns[0];
		r_result.columns[1] = p_curr.columns[1];
		r_result.set_origin(p1.lerp(p2, 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 = v1.lerp(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), p1.lerp(p2, p_fraction));
	r_result.scale_basis(s1.lerp(s2, p_fraction));
}