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249 lines
9.2 KiB
C++
249 lines
9.2 KiB
C++
/*************************************************************************/
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/* transform_2d.h */
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/*************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/*************************************************************************/
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/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md). */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/*************************************************************************/
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#ifndef TRANSFORM_2D_H
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#define TRANSFORM_2D_H
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#include "core/math/rect2.h" // also includes vector2, math_funcs, and ustring
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struct Transform2D {
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// Warning #1: basis of Transform2D is stored differently from Basis. In terms of elements array, the basis matrix looks like "on paper":
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// M = (elements[0][0] elements[1][0])
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// (elements[0][1] elements[1][1])
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// 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].
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// 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.
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// This requires additional care when working with explicit indices.
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// See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading.
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// Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down,
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// and angle is measure from +X to +Y in a clockwise-fashion.
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Vector2 elements[3];
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_FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return elements[0][0] * v.x + elements[1][0] * v.y; }
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_FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return elements[0][1] * v.x + elements[1][1] * v.y; }
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const Vector2 &operator[](int p_idx) const { return elements[p_idx]; }
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Vector2 &operator[](int p_idx) { return elements[p_idx]; }
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_FORCE_INLINE_ Vector2 get_axis(int p_axis) const {
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ERR_FAIL_INDEX_V(p_axis, 3, Vector2());
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return elements[p_axis];
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}
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_FORCE_INLINE_ void set_axis(int p_axis, const Vector2 &p_vec) {
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ERR_FAIL_INDEX(p_axis, 3);
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elements[p_axis] = p_vec;
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}
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void invert();
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Transform2D inverse() const;
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void affine_invert();
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Transform2D affine_inverse() const;
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void set_rotation(const real_t p_rot);
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real_t get_rotation() const;
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real_t get_skew() const;
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void set_skew(const real_t p_angle);
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_FORCE_INLINE_ void set_rotation_and_scale(const real_t p_rot, const Size2 &p_scale);
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_FORCE_INLINE_ void set_rotation_scale_and_skew(const real_t p_rot, const Size2 &p_scale, const real_t p_skew);
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void rotate(const real_t p_phi);
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void scale(const Size2 &p_scale);
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void scale_basis(const Size2 &p_scale);
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void translate(const real_t p_tx, const real_t p_ty);
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void translate(const Vector2 &p_translation);
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real_t basis_determinant() const;
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Size2 get_scale() const;
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void set_scale(const Size2 &p_scale);
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_FORCE_INLINE_ const Vector2 &get_origin() const { return elements[2]; }
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_FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { elements[2] = p_origin; }
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Transform2D scaled(const Size2 &p_scale) const;
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Transform2D basis_scaled(const Size2 &p_scale) const;
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Transform2D translated(const Vector2 &p_offset) const;
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Transform2D rotated(const real_t p_phi) const;
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Transform2D untranslated() const;
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void orthonormalize();
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Transform2D orthonormalized() const;
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bool is_equal_approx(const Transform2D &p_transform) const;
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Transform2D looking_at(const Vector2 &p_target) const;
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bool operator==(const Transform2D &p_transform) const;
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bool operator!=(const Transform2D &p_transform) const;
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void operator*=(const Transform2D &p_transform);
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Transform2D operator*(const Transform2D &p_transform) const;
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void operator*=(const real_t p_val);
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Transform2D operator*(const real_t p_val) const;
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Transform2D interpolate_with(const Transform2D &p_transform, const real_t p_c) const;
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_FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const;
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_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const;
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_FORCE_INLINE_ Vector2 xform(const Vector2 &p_vec) const;
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_FORCE_INLINE_ Vector2 xform_inv(const Vector2 &p_vec) const;
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_FORCE_INLINE_ Rect2 xform(const Rect2 &p_rect) const;
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_FORCE_INLINE_ Rect2 xform_inv(const Rect2 &p_rect) const;
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_FORCE_INLINE_ Vector<Vector2> xform(const Vector<Vector2> &p_array) const;
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_FORCE_INLINE_ Vector<Vector2> xform_inv(const Vector<Vector2> &p_array) const;
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operator String() const;
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Transform2D(const real_t xx, const real_t xy, const real_t yx, const real_t yy, const real_t ox, const real_t oy) {
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elements[0][0] = xx;
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elements[0][1] = xy;
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elements[1][0] = yx;
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elements[1][1] = yy;
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elements[2][0] = ox;
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elements[2][1] = oy;
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}
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Transform2D(const Vector2 &p_x, const Vector2 &p_y, const Vector2 &p_origin) {
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elements[0] = p_x;
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elements[1] = p_y;
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elements[2] = p_origin;
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}
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Transform2D(const real_t p_rot, const Vector2 &p_pos);
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Transform2D(const real_t p_rot, const Size2 &p_scale, const real_t p_skew, const Vector2 &p_pos);
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Transform2D() {
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elements[0][0] = 1.0;
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elements[1][1] = 1.0;
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}
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};
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Vector2 Transform2D::basis_xform(const Vector2 &p_vec) const {
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return Vector2(
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tdotx(p_vec),
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tdoty(p_vec));
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}
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Vector2 Transform2D::basis_xform_inv(const Vector2 &p_vec) const {
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return Vector2(
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elements[0].dot(p_vec),
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elements[1].dot(p_vec));
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}
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Vector2 Transform2D::xform(const Vector2 &p_vec) const {
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return Vector2(
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tdotx(p_vec),
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tdoty(p_vec)) +
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elements[2];
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}
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Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const {
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Vector2 v = p_vec - elements[2];
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return Vector2(
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elements[0].dot(v),
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elements[1].dot(v));
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}
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Rect2 Transform2D::xform(const Rect2 &p_rect) const {
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Vector2 x = elements[0] * p_rect.size.x;
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Vector2 y = elements[1] * p_rect.size.y;
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Vector2 pos = xform(p_rect.position);
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Rect2 new_rect;
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new_rect.position = pos;
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new_rect.expand_to(pos + x);
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new_rect.expand_to(pos + y);
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new_rect.expand_to(pos + x + y);
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return new_rect;
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}
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void Transform2D::set_rotation_and_scale(const real_t p_rot, const Size2 &p_scale) {
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elements[0][0] = Math::cos(p_rot) * p_scale.x;
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elements[1][1] = Math::cos(p_rot) * p_scale.y;
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elements[1][0] = -Math::sin(p_rot) * p_scale.y;
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elements[0][1] = Math::sin(p_rot) * p_scale.x;
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}
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void Transform2D::set_rotation_scale_and_skew(const real_t p_rot, const Size2 &p_scale, const real_t p_skew) {
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elements[0][0] = Math::cos(p_rot) * p_scale.x;
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elements[1][1] = Math::cos(p_rot + p_skew) * p_scale.y;
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elements[1][0] = -Math::sin(p_rot + p_skew) * p_scale.y;
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elements[0][1] = Math::sin(p_rot) * p_scale.x;
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}
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Rect2 Transform2D::xform_inv(const Rect2 &p_rect) const {
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Vector2 ends[4] = {
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xform_inv(p_rect.position),
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xform_inv(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
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xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
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xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y))
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};
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Rect2 new_rect;
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new_rect.position = ends[0];
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new_rect.expand_to(ends[1]);
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new_rect.expand_to(ends[2]);
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new_rect.expand_to(ends[3]);
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return new_rect;
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}
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Vector<Vector2> Transform2D::xform(const Vector<Vector2> &p_array) const {
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Vector<Vector2> array;
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array.resize(p_array.size());
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const Vector2 *r = p_array.ptr();
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Vector2 *w = array.ptrw();
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for (int i = 0; i < p_array.size(); ++i) {
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w[i] = xform(r[i]);
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}
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return array;
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}
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Vector<Vector2> Transform2D::xform_inv(const Vector<Vector2> &p_array) const {
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Vector<Vector2> array;
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array.resize(p_array.size());
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const Vector2 *r = p_array.ptr();
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Vector2 *w = array.ptrw();
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for (int i = 0; i < p_array.size(); ++i) {
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w[i] = xform_inv(r[i]);
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}
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return array;
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}
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#endif // TRANSFORM_2D_H
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