a7f49ac9a1
Happy new year to the wonderful Godot community! We're starting a new decade with a well-established, non-profit, free and open source game engine, and tons of further improvements in the pipeline from hundreds of contributors. Godot will keep getting better, and we're looking forward to all the games that the community will keep developing and releasing with it.
286 lines
7.9 KiB
C++
286 lines
7.9 KiB
C++
/*************************************************************************/
|
|
/* transform_2d.cpp */
|
|
/*************************************************************************/
|
|
/* This file is part of: */
|
|
/* GODOT ENGINE */
|
|
/* https://godotengine.org */
|
|
/*************************************************************************/
|
|
/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur. */
|
|
/* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md). */
|
|
/* */
|
|
/* 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 */
|
|
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
|
|
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
|
|
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
|
|
/*************************************************************************/
|
|
|
|
#include "transform_2d.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(elements[0][1], elements[1][0]);
|
|
elements[2] = basis_xform(-elements[2]);
|
|
}
|
|
|
|
Transform2D Transform2D::inverse() const {
|
|
|
|
Transform2D inv = *this;
|
|
inv.invert();
|
|
return inv;
|
|
}
|
|
|
|
void Transform2D::affine_invert() {
|
|
|
|
real_t det = basis_determinant();
|
|
#ifdef MATH_CHECKS
|
|
ERR_FAIL_COND(det == 0);
|
|
#endif
|
|
real_t idet = 1.0 / det;
|
|
|
|
SWAP(elements[0][0], elements[1][1]);
|
|
elements[0] *= Vector2(idet, -idet);
|
|
elements[1] *= Vector2(-idet, idet);
|
|
|
|
elements[2] = basis_xform(-elements[2]);
|
|
}
|
|
|
|
Transform2D Transform2D::affine_inverse() const {
|
|
|
|
Transform2D inv = *this;
|
|
inv.affine_invert();
|
|
return inv;
|
|
}
|
|
|
|
void Transform2D::rotate(real_t p_phi) {
|
|
*this = Transform2D(p_phi, Vector2()) * (*this);
|
|
}
|
|
|
|
real_t Transform2D::get_rotation() const {
|
|
real_t det = basis_determinant();
|
|
Transform2D m = orthonormalized();
|
|
if (det < 0) {
|
|
m.scale_basis(Size2(1, -1)); // convention to separate rotation and reflection for 2D is to absorb a flip along y into scaling.
|
|
}
|
|
return Math::atan2(m[0].y, m[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);
|
|
elements[0][0] = cr;
|
|
elements[0][1] = sr;
|
|
elements[1][0] = -sr;
|
|
elements[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);
|
|
elements[0][0] = cr;
|
|
elements[0][1] = sr;
|
|
elements[1][0] = -sr;
|
|
elements[1][1] = cr;
|
|
elements[2] = p_pos;
|
|
}
|
|
|
|
Size2 Transform2D::get_scale() const {
|
|
real_t det_sign = SGN(basis_determinant());
|
|
return Size2(elements[0].length(), det_sign * elements[1].length());
|
|
}
|
|
|
|
void Transform2D::set_scale(const Size2 &p_scale) {
|
|
elements[0].normalize();
|
|
elements[1].normalize();
|
|
elements[0] *= p_scale.x;
|
|
elements[1] *= p_scale.y;
|
|
}
|
|
|
|
void Transform2D::scale(const Size2 &p_scale) {
|
|
scale_basis(p_scale);
|
|
elements[2] *= p_scale;
|
|
}
|
|
void Transform2D::scale_basis(const Size2 &p_scale) {
|
|
|
|
elements[0][0] *= p_scale.x;
|
|
elements[0][1] *= p_scale.y;
|
|
elements[1][0] *= p_scale.x;
|
|
elements[1][1] *= p_scale.y;
|
|
}
|
|
void Transform2D::translate(real_t p_tx, real_t p_ty) {
|
|
|
|
translate(Vector2(p_tx, p_ty));
|
|
}
|
|
void Transform2D::translate(const Vector2 &p_translation) {
|
|
|
|
elements[2] += basis_xform(p_translation);
|
|
}
|
|
|
|
void Transform2D::orthonormalize() {
|
|
|
|
// Gram-Schmidt Process
|
|
|
|
Vector2 x = elements[0];
|
|
Vector2 y = elements[1];
|
|
|
|
x.normalize();
|
|
y = (y - x * (x.dot(y)));
|
|
y.normalize();
|
|
|
|
elements[0] = x;
|
|
elements[1] = y;
|
|
}
|
|
|
|
Transform2D Transform2D::orthonormalized() const {
|
|
|
|
Transform2D on = *this;
|
|
on.orthonormalize();
|
|
return on;
|
|
}
|
|
|
|
bool Transform2D::is_equal_approx(const Transform2D &p_transform) const {
|
|
|
|
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]);
|
|
}
|
|
|
|
bool Transform2D::operator==(const Transform2D &p_transform) const {
|
|
|
|
for (int i = 0; i < 3; i++) {
|
|
if (elements[i] != p_transform.elements[i])
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
bool Transform2D::operator!=(const Transform2D &p_transform) const {
|
|
|
|
for (int i = 0; i < 3; i++) {
|
|
if (elements[i] != p_transform.elements[i])
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
void Transform2D::operator*=(const Transform2D &p_transform) {
|
|
|
|
elements[2] = xform(p_transform.elements[2]);
|
|
|
|
real_t x0, x1, y0, y1;
|
|
|
|
x0 = tdotx(p_transform.elements[0]);
|
|
x1 = tdoty(p_transform.elements[0]);
|
|
y0 = tdotx(p_transform.elements[1]);
|
|
y1 = tdoty(p_transform.elements[1]);
|
|
|
|
elements[0][0] = x0;
|
|
elements[0][1] = x1;
|
|
elements[1][0] = y0;
|
|
elements[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 {
|
|
|
|
Transform2D copy = *this;
|
|
copy.scale(p_scale);
|
|
return copy;
|
|
}
|
|
|
|
Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
|
|
|
|
Transform2D copy = *this;
|
|
copy.scale_basis(p_scale);
|
|
return copy;
|
|
}
|
|
|
|
Transform2D Transform2D::untranslated() const {
|
|
|
|
Transform2D copy = *this;
|
|
copy.elements[2] = Vector2();
|
|
return copy;
|
|
}
|
|
|
|
Transform2D Transform2D::translated(const Vector2 &p_offset) const {
|
|
|
|
Transform2D copy = *this;
|
|
copy.translate(p_offset);
|
|
return copy;
|
|
}
|
|
|
|
Transform2D Transform2D::rotated(real_t p_phi) const {
|
|
|
|
Transform2D copy = *this;
|
|
copy.rotate(p_phi);
|
|
return copy;
|
|
}
|
|
|
|
real_t Transform2D::basis_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 = (dot < -1.0) ? -1.0 : ((dot > 1.0) ? 1.0 : dot); //clamp dot to [-1,1]
|
|
|
|
Vector2 v;
|
|
|
|
if (dot > 0.9995) {
|
|
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]);
|
|
}
|