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287 lines
7.9 KiB
C++
287 lines
7.9 KiB
C++
/*************************************************************************/
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/* transform_2d.cpp */
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/*************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/*************************************************************************/
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/* Copyright (c) 2007-2019 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2019 Godot Engine contributors (cf. AUTHORS.md) */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/*************************************************************************/
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#include "transform_2d.h"
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void Transform2D::invert() {
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// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
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// Transform2D::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
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SWAP(elements[0][1], elements[1][0]);
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elements[2] = basis_xform(-elements[2]);
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}
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Transform2D Transform2D::inverse() const {
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Transform2D inv = *this;
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inv.invert();
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return inv;
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}
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void Transform2D::affine_invert() {
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real_t det = basis_determinant();
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#ifdef MATH_CHECKS
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ERR_FAIL_COND(det == 0);
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#endif
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real_t idet = 1.0 / det;
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SWAP(elements[0][0], elements[1][1]);
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elements[0] *= Vector2(idet, -idet);
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elements[1] *= Vector2(-idet, idet);
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elements[2] = basis_xform(-elements[2]);
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}
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Transform2D Transform2D::affine_inverse() const {
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Transform2D inv = *this;
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inv.affine_invert();
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return inv;
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}
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void Transform2D::rotate(real_t p_phi) {
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*this = Transform2D(p_phi, Vector2()) * (*this);
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}
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real_t Transform2D::get_rotation() const {
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real_t det = basis_determinant();
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Transform2D m = orthonormalized();
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if (det < 0) {
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m.scale_basis(Size2(1, -1)); // convention to separate rotation and reflection for 2D is to absorb a flip along y into scaling.
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}
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return Math::atan2(m[0].y, m[0].x);
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}
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void Transform2D::set_rotation(real_t p_rot) {
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Size2 scale = get_scale();
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real_t cr = Math::cos(p_rot);
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real_t sr = Math::sin(p_rot);
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elements[0][0] = cr;
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elements[0][1] = sr;
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elements[1][0] = -sr;
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elements[1][1] = cr;
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set_scale(scale);
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}
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Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) {
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real_t cr = Math::cos(p_rot);
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real_t sr = Math::sin(p_rot);
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elements[0][0] = cr;
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elements[0][1] = sr;
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elements[1][0] = -sr;
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elements[1][1] = cr;
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elements[2] = p_pos;
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}
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Size2 Transform2D::get_scale() const {
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real_t det_sign = SGN(basis_determinant());
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return Size2(elements[0].length(), det_sign * elements[1].length());
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}
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void Transform2D::set_scale(const Size2 &p_scale) {
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elements[0].normalize();
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elements[1].normalize();
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elements[0] *= p_scale.x;
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elements[1] *= p_scale.y;
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}
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void Transform2D::scale(const Size2 &p_scale) {
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scale_basis(p_scale);
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elements[2] *= p_scale;
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}
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void Transform2D::scale_basis(const Size2 &p_scale) {
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elements[0][0] *= p_scale.x;
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elements[0][1] *= p_scale.y;
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elements[1][0] *= p_scale.x;
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elements[1][1] *= p_scale.y;
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}
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void Transform2D::translate(real_t p_tx, real_t p_ty) {
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translate(Vector2(p_tx, p_ty));
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}
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void Transform2D::translate(const Vector2 &p_translation) {
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elements[2] += basis_xform(p_translation);
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}
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void Transform2D::orthonormalize() {
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// Gram-Schmidt Process
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Vector2 x = elements[0];
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Vector2 y = elements[1];
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x.normalize();
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y = (y - x * (x.dot(y)));
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y.normalize();
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elements[0] = x;
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elements[1] = y;
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}
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Transform2D Transform2D::orthonormalized() const {
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Transform2D on = *this;
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on.orthonormalize();
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return on;
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}
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bool Transform2D::is_equal_approx(const Transform2D &p_transform) const {
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return elements[0].is_equal_approx(p_transform.elements[0]) && elements[1].is_equal_approx(p_transform.elements[1]) && elements[2].is_equal_approx(p_transform.elements[2]);
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}
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bool Transform2D::operator==(const Transform2D &p_transform) const {
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for (int i = 0; i < 3; i++) {
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if (elements[i] != p_transform.elements[i])
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return false;
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}
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return true;
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}
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bool Transform2D::operator!=(const Transform2D &p_transform) const {
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for (int i = 0; i < 3; i++) {
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if (elements[i] != p_transform.elements[i])
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return true;
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}
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return false;
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}
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void Transform2D::operator*=(const Transform2D &p_transform) {
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elements[2] = xform(p_transform.elements[2]);
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real_t x0, x1, y0, y1;
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x0 = tdotx(p_transform.elements[0]);
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x1 = tdoty(p_transform.elements[0]);
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y0 = tdotx(p_transform.elements[1]);
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y1 = tdoty(p_transform.elements[1]);
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elements[0][0] = x0;
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elements[0][1] = x1;
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elements[1][0] = y0;
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elements[1][1] = y1;
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}
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Transform2D Transform2D::operator*(const Transform2D &p_transform) const {
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Transform2D t = *this;
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t *= p_transform;
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return t;
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}
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Transform2D Transform2D::scaled(const Size2 &p_scale) const {
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Transform2D copy = *this;
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copy.scale(p_scale);
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return copy;
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}
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Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
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Transform2D copy = *this;
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copy.scale_basis(p_scale);
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return copy;
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}
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Transform2D Transform2D::untranslated() const {
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Transform2D copy = *this;
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copy.elements[2] = Vector2();
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return copy;
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}
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Transform2D Transform2D::translated(const Vector2 &p_offset) const {
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Transform2D copy = *this;
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copy.translate(p_offset);
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return copy;
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}
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Transform2D Transform2D::rotated(real_t p_phi) const {
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Transform2D copy = *this;
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copy.rotate(p_phi);
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return copy;
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}
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real_t Transform2D::basis_determinant() const {
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return elements[0].x * elements[1].y - elements[0].y * elements[1].x;
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}
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Transform2D Transform2D::interpolate_with(const Transform2D &p_transform, real_t p_c) const {
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//extract parameters
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Vector2 p1 = get_origin();
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Vector2 p2 = p_transform.get_origin();
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real_t r1 = get_rotation();
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real_t r2 = p_transform.get_rotation();
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Size2 s1 = get_scale();
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Size2 s2 = p_transform.get_scale();
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//slerp rotation
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Vector2 v1(Math::cos(r1), Math::sin(r1));
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Vector2 v2(Math::cos(r2), Math::sin(r2));
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real_t dot = v1.dot(v2);
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dot = (dot < -1.0) ? -1.0 : ((dot > 1.0) ? 1.0 : dot); //clamp dot to [-1,1]
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Vector2 v;
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if (dot > 0.9995) {
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v = Vector2::linear_interpolate(v1, v2, p_c).normalized(); //linearly interpolate to avoid numerical precision issues
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} else {
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real_t angle = p_c * Math::acos(dot);
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Vector2 v3 = (v2 - v1 * dot).normalized();
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v = v1 * Math::cos(angle) + v3 * Math::sin(angle);
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}
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//construct matrix
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Transform2D res(Math::atan2(v.y, v.x), Vector2::linear_interpolate(p1, p2, p_c));
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res.scale_basis(Vector2::linear_interpolate(s1, s2, p_c));
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return res;
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}
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Transform2D::operator String() const {
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return String(String() + elements[0] + ", " + elements[1] + ", " + elements[2]);
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}
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