godot/core/math/transform_2d.cpp
2024-03-04 18:17:10 +01:00

315 lines
9.7 KiB
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/**************************************************************************/
/* transform_2d.cpp */
/**************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/**************************************************************************/
/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
/* */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the */
/* "Software"), to deal in the Software without restriction, including */
/* without limitation the rights to use, copy, modify, merge, publish, */
/* distribute, sublicense, and/or sell copies of the Software, and to */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/**************************************************************************/
#include "transform_2d.h"
#include "core/string/ustring.h"
void Transform2D::invert() {
// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
// Transform2D::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
SWAP(columns[0][1], columns[1][0]);
columns[2] = basis_xform(-columns[2]);
}
Transform2D Transform2D::inverse() const {
Transform2D inv = *this;
inv.invert();
return inv;
}
void Transform2D::affine_invert() {
real_t det = determinant();
#ifdef MATH_CHECKS
ERR_FAIL_COND(det == 0);
#endif
real_t idet = 1.0f / det;
SWAP(columns[0][0], columns[1][1]);
columns[0] *= Vector2(idet, -idet);
columns[1] *= Vector2(-idet, idet);
columns[2] = basis_xform(-columns[2]);
}
Transform2D Transform2D::affine_inverse() const {
Transform2D inv = *this;
inv.affine_invert();
return inv;
}
void Transform2D::rotate(real_t p_angle) {
*this = Transform2D(p_angle, Vector2()) * (*this);
}
real_t Transform2D::get_skew() const {
real_t det = determinant();
return Math::acos(columns[0].normalized().dot(SIGN(det) * columns[1].normalized())) - (real_t)Math_PI * 0.5f;
}
void Transform2D::set_skew(real_t p_angle) {
real_t det = determinant();
columns[1] = SIGN(det) * columns[0].rotated(((real_t)Math_PI * 0.5f + p_angle)).normalized() * columns[1].length();
}
real_t Transform2D::get_rotation() const {
return Math::atan2(columns[0].y, columns[0].x);
}
void Transform2D::set_rotation(real_t p_rot) {
Size2 scale = get_scale();
real_t cr = Math::cos(p_rot);
real_t sr = Math::sin(p_rot);
columns[0][0] = cr;
columns[0][1] = sr;
columns[1][0] = -sr;
columns[1][1] = cr;
set_scale(scale);
}
Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) {
real_t cr = Math::cos(p_rot);
real_t sr = Math::sin(p_rot);
columns[0][0] = cr;
columns[0][1] = sr;
columns[1][0] = -sr;
columns[1][1] = cr;
columns[2] = p_pos;
}
Transform2D::Transform2D(real_t p_rot, const Size2 &p_scale, real_t p_skew, const Vector2 &p_pos) {
columns[0][0] = Math::cos(p_rot) * p_scale.x;
columns[1][1] = Math::cos(p_rot + p_skew) * p_scale.y;
columns[1][0] = -Math::sin(p_rot + p_skew) * p_scale.y;
columns[0][1] = Math::sin(p_rot) * p_scale.x;
columns[2] = p_pos;
}
Size2 Transform2D::get_scale() const {
real_t det_sign = SIGN(determinant());
return Size2(columns[0].length(), det_sign * columns[1].length());
}
void Transform2D::set_scale(const Size2 &p_scale) {
columns[0].normalize();
columns[1].normalize();
columns[0] *= p_scale.x;
columns[1] *= p_scale.y;
}
void Transform2D::scale(const Size2 &p_scale) {
scale_basis(p_scale);
columns[2] *= p_scale;
}
void Transform2D::scale_basis(const Size2 &p_scale) {
columns[0][0] *= p_scale.x;
columns[0][1] *= p_scale.y;
columns[1][0] *= p_scale.x;
columns[1][1] *= p_scale.y;
}
void Transform2D::translate_local(real_t p_tx, real_t p_ty) {
translate_local(Vector2(p_tx, p_ty));
}
void Transform2D::translate_local(const Vector2 &p_translation) {
columns[2] += basis_xform(p_translation);
}
void Transform2D::orthonormalize() {
// Gram-Schmidt Process
Vector2 x = columns[0];
Vector2 y = columns[1];
x.normalize();
y = y - x * x.dot(y);
y.normalize();
columns[0] = x;
columns[1] = y;
}
Transform2D Transform2D::orthonormalized() const {
Transform2D ortho = *this;
ortho.orthonormalize();
return ortho;
}
bool Transform2D::is_conformal() const {
// Non-flipped case.
if (Math::is_equal_approx(columns[0][0], columns[1][1]) && Math::is_equal_approx(columns[0][1], -columns[1][0])) {
return true;
}
// Flipped case.
if (Math::is_equal_approx(columns[0][0], -columns[1][1]) && Math::is_equal_approx(columns[0][1], columns[1][0])) {
return true;
}
return false;
}
bool Transform2D::is_equal_approx(const Transform2D &p_transform) const {
return columns[0].is_equal_approx(p_transform.columns[0]) && columns[1].is_equal_approx(p_transform.columns[1]) && columns[2].is_equal_approx(p_transform.columns[2]);
}
bool Transform2D::is_finite() const {
return columns[0].is_finite() && columns[1].is_finite() && columns[2].is_finite();
}
Transform2D Transform2D::looking_at(const Vector2 &p_target) const {
Transform2D return_trans = Transform2D(get_rotation(), get_origin());
Vector2 target_position = affine_inverse().xform(p_target);
return_trans.set_rotation(return_trans.get_rotation() + (target_position * get_scale()).angle());
return return_trans;
}
bool Transform2D::operator==(const Transform2D &p_transform) const {
for (int i = 0; i < 3; i++) {
if (columns[i] != p_transform.columns[i]) {
return false;
}
}
return true;
}
bool Transform2D::operator!=(const Transform2D &p_transform) const {
for (int i = 0; i < 3; i++) {
if (columns[i] != p_transform.columns[i]) {
return true;
}
}
return false;
}
void Transform2D::operator*=(const Transform2D &p_transform) {
columns[2] = xform(p_transform.columns[2]);
real_t x0, x1, y0, y1;
x0 = tdotx(p_transform.columns[0]);
x1 = tdoty(p_transform.columns[0]);
y0 = tdotx(p_transform.columns[1]);
y1 = tdoty(p_transform.columns[1]);
columns[0][0] = x0;
columns[0][1] = x1;
columns[1][0] = y0;
columns[1][1] = y1;
}
Transform2D Transform2D::operator*(const Transform2D &p_transform) const {
Transform2D t = *this;
t *= p_transform;
return t;
}
Transform2D Transform2D::scaled(const Size2 &p_scale) const {
// Equivalent to left multiplication
Transform2D copy = *this;
copy.scale(p_scale);
return copy;
}
Transform2D Transform2D::scaled_local(const Size2 &p_scale) const {
// Equivalent to right multiplication
return Transform2D(columns[0] * p_scale.x, columns[1] * p_scale.y, columns[2]);
}
Transform2D Transform2D::untranslated() const {
Transform2D copy = *this;
copy.columns[2] = Vector2();
return copy;
}
Transform2D Transform2D::translated(const Vector2 &p_offset) const {
// Equivalent to left multiplication
return Transform2D(columns[0], columns[1], columns[2] + p_offset);
}
Transform2D Transform2D::translated_local(const Vector2 &p_offset) const {
// Equivalent to right multiplication
return Transform2D(columns[0], columns[1], columns[2] + basis_xform(p_offset));
}
Transform2D Transform2D::rotated(real_t p_angle) const {
// Equivalent to left multiplication
return Transform2D(p_angle, Vector2()) * (*this);
}
Transform2D Transform2D::rotated_local(real_t p_angle) const {
// Equivalent to right multiplication
return (*this) * Transform2D(p_angle, Vector2()); // Could be optimized, because origin transform can be skipped.
}
real_t Transform2D::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_weight) const {
return Transform2D(
Math::lerp_angle(get_rotation(), p_transform.get_rotation(), p_weight),
get_scale().lerp(p_transform.get_scale(), p_weight),
Math::lerp_angle(get_skew(), p_transform.get_skew(), p_weight),
get_origin().lerp(p_transform.get_origin(), p_weight));
}
void Transform2D::operator*=(real_t p_val) {
columns[0] *= p_val;
columns[1] *= p_val;
columns[2] *= p_val;
}
Transform2D Transform2D::operator*(real_t p_val) const {
Transform2D ret(*this);
ret *= p_val;
return ret;
}
void Transform2D::operator/=(real_t p_val) {
columns[0] /= p_val;
columns[1] /= p_val;
columns[2] /= p_val;
}
Transform2D Transform2D::operator/(real_t p_val) const {
Transform2D ret(*this);
ret /= p_val;
return ret;
}
Transform2D::operator String() const {
return "[X: " + columns[0].operator String() +
", Y: " + columns[1].operator String() +
", O: " + columns[2].operator String() + "]";
}