mirror of
https://github.com/godotengine/godot.git
synced 2024-12-15 10:12:40 +08:00
281 lines
7.7 KiB
C++
281 lines
7.7 KiB
C++
/*************************************************************************/
|
|
/* transform_2d.cpp */
|
|
/*************************************************************************/
|
|
/* This file is part of: */
|
|
/* GODOT ENGINE */
|
|
/* https://godotengine.org */
|
|
/*************************************************************************/
|
|
/* Copyright (c) 2007-2019 Juan Linietsky, Ariel Manzur. */
|
|
/* Copyright (c) 2014-2019 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(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::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]);
|
|
}
|