/*************************************************************************/ /* transform_2d.h */ /*************************************************************************/ /* This file is part of: */ /* GODOT ENGINE */ /* https://godotengine.org */ /*************************************************************************/ /* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur. */ /* Copyright (c) 2014-2021 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. */ /*************************************************************************/ #ifndef TRANSFORM_2D_H #define TRANSFORM_2D_H #include "core/math/rect2.h" // also includes vector2, math_funcs, and ustring #include "core/pool_vector.h" struct Transform2D { // Warning #1: basis of Transform2D is stored differently from Basis. In terms of elements array, the basis matrix looks like "on paper": // M = (elements[0][0] elements[1][0]) // (elements[0][1] elements[1][1]) // This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as elements[i]. // Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to elements[1][0] here. // This requires additional care when working with explicit indices. // See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading. // Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down, // and angle is measure from +X to +Y in a clockwise-fashion. Vector2 elements[3]; _FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return elements[0][0] * v.x + elements[1][0] * v.y; } _FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return elements[0][1] * v.x + elements[1][1] * v.y; } const Vector2 &operator[](int p_idx) const { return elements[p_idx]; } Vector2 &operator[](int p_idx) { return elements[p_idx]; } _FORCE_INLINE_ Vector2 get_axis(int p_axis) const { ERR_FAIL_INDEX_V(p_axis, 3, Vector2()); return elements[p_axis]; } _FORCE_INLINE_ void set_axis(int p_axis, const Vector2 &p_vec) { ERR_FAIL_INDEX(p_axis, 3); elements[p_axis] = p_vec; } void invert(); Transform2D inverse() const; void affine_invert(); Transform2D affine_inverse() const; void set_rotation(real_t p_rot); real_t get_rotation() const; _FORCE_INLINE_ void set_rotation_and_scale(real_t p_rot, const Size2 &p_scale); void rotate(real_t p_phi); void scale(const Size2 &p_scale); void scale_basis(const Size2 &p_scale); void translate(real_t p_tx, real_t p_ty); void translate(const Vector2 &p_translation); real_t basis_determinant() const; Size2 get_scale() const; void set_scale(const Size2 &p_scale); _FORCE_INLINE_ const Vector2 &get_origin() const { return elements[2]; } _FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { elements[2] = p_origin; } Transform2D scaled(const Size2 &p_scale) const; Transform2D basis_scaled(const Size2 &p_scale) const; Transform2D translated(const Vector2 &p_offset) const; Transform2D rotated(real_t p_phi) const; Transform2D untranslated() const; void orthonormalize(); Transform2D orthonormalized() const; bool is_equal_approx(const Transform2D &p_transform) const; bool operator==(const Transform2D &p_transform) const; bool operator!=(const Transform2D &p_transform) const; void operator*=(const Transform2D &p_transform); Transform2D operator*(const Transform2D &p_transform) const; Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const; _FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const; _FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const; _FORCE_INLINE_ Vector2 xform(const Vector2 &p_vec) const; _FORCE_INLINE_ Vector2 xform_inv(const Vector2 &p_vec) const; _FORCE_INLINE_ Rect2 xform(const Rect2 &p_rect) const; _FORCE_INLINE_ Rect2 xform_inv(const Rect2 &p_rect) const; _FORCE_INLINE_ PoolVector xform(const PoolVector &p_array) const; _FORCE_INLINE_ PoolVector xform_inv(const PoolVector &p_array) const; operator String() const; Transform2D(real_t xx, real_t xy, real_t yx, real_t yy, real_t ox, real_t oy) { elements[0][0] = xx; elements[0][1] = xy; elements[1][0] = yx; elements[1][1] = yy; elements[2][0] = ox; elements[2][1] = oy; } Transform2D(real_t p_rot, const Vector2 &p_pos); Transform2D() { elements[0][0] = 1.0; elements[1][1] = 1.0; } }; Vector2 Transform2D::basis_xform(const Vector2 &p_vec) const { return Vector2( tdotx(p_vec), tdoty(p_vec)); } Vector2 Transform2D::basis_xform_inv(const Vector2 &p_vec) const { return Vector2( elements[0].dot(p_vec), elements[1].dot(p_vec)); } Vector2 Transform2D::xform(const Vector2 &p_vec) const { return Vector2( tdotx(p_vec), tdoty(p_vec)) + elements[2]; } Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const { Vector2 v = p_vec - elements[2]; return Vector2( elements[0].dot(v), elements[1].dot(v)); } Rect2 Transform2D::xform(const Rect2 &p_rect) const { Vector2 x = elements[0] * p_rect.size.x; Vector2 y = elements[1] * p_rect.size.y; Vector2 pos = xform(p_rect.position); Rect2 new_rect; new_rect.position = pos; new_rect.expand_to(pos + x); new_rect.expand_to(pos + y); new_rect.expand_to(pos + x + y); return new_rect; } void Transform2D::set_rotation_and_scale(real_t p_rot, const Size2 &p_scale) { elements[0][0] = Math::cos(p_rot) * p_scale.x; elements[1][1] = Math::cos(p_rot) * p_scale.y; elements[1][0] = -Math::sin(p_rot) * p_scale.y; elements[0][1] = Math::sin(p_rot) * p_scale.x; } Rect2 Transform2D::xform_inv(const Rect2 &p_rect) const { Vector2 ends[4] = { xform_inv(p_rect.position), xform_inv(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)), xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)), xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)) }; Rect2 new_rect; new_rect.position = ends[0]; new_rect.expand_to(ends[1]); new_rect.expand_to(ends[2]); new_rect.expand_to(ends[3]); return new_rect; } PoolVector Transform2D::xform(const PoolVector &p_array) const { PoolVector array; array.resize(p_array.size()); PoolVector::Read r = p_array.read(); PoolVector::Write w = array.write(); for (int i = 0; i < p_array.size(); ++i) { w[i] = xform(r[i]); } return array; } PoolVector Transform2D::xform_inv(const PoolVector &p_array) const { PoolVector array; array.resize(p_array.size()); PoolVector::Read r = p_array.read(); PoolVector::Write w = array.write(); for (int i = 0; i < p_array.size(); ++i) { w[i] = xform_inv(r[i]); } return array; } #endif // TRANSFORM_2D_H