/**************************************************************************/ /* 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 */ /* 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 = determinant(); #ifdef MATH_CHECKS ERR_FAIL_COND(det == 0); #endif real_t idet = 1 / 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_angle) { *this = Transform2D(p_angle, Vector2()) * (*this); } real_t Transform2D::get_rotation() const { return Math::atan2(elements[0].y, elements[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(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_angle) const { Transform2D copy = *this; copy.rotate(p_angle); return copy; } real_t Transform2D::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 = CLAMP(dot, -1, 1); Vector2 v; if (dot > 0.9995f) { 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]); }