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virtualx-engine/core/math/transform_2d.h
Rémi Verschelde d95794ec8a
One Copyright Update to rule them all 
As many open source projects have started doing it, we're removing the
current year from the copyright notice, so that we don't need to bump
it every year.

It seems like only the first year of publication is technically
relevant for copyright notices, and even that seems to be something
that many companies stopped listing altogether (in a version controlled
codebase, the commits are a much better source of date of publication
than a hardcoded copyright statement).

We also now list Godot Engine contributors first as we're collectively
the current maintainers of the project, and we clarify that the
"exclusive" copyright of the co-founders covers the timespan before
opensourcing (their further contributions are included as part of Godot
Engine contributors).

Also fixed "cf." Frenchism - it's meant as "refer to / see".
2023-01-05 13:25:55 +01:00

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/**************************************************************************/
/* transform_2d.h */
/**************************************************************************/
/* 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. */
/**************************************************************************/
#ifndef TRANSFORM_2D_H
#define TRANSFORM_2D_H
#include "core/math/math_funcs.h"
#include "core/math/rect2.h"
#include "core/math/vector2.h"
#include "core/templates/vector.h"
class String;
struct _NO_DISCARD_ Transform2D {
// Warning #1: basis of Transform2D is stored differently from Basis. In terms of columns array, the basis matrix looks like "on paper":
// M = (columns[0][0] columns[1][0])
// (columns[0][1] columns[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 columns[i].
// Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to columns[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 columns[3];
_FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return columns[0][0] * v.x + columns[1][0] * v.y; }
_FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return columns[0][1] * v.x + columns[1][1] * v.y; }
const Vector2 &operator[](int p_idx) const { return columns[p_idx]; }
Vector2 &operator[](int p_idx) { return columns[p_idx]; }
void invert();
Transform2D inverse() const;
void affine_invert();
Transform2D affine_inverse() const;
void set_rotation(const real_t p_rot);
real_t get_rotation() const;
real_t get_skew() const;
void set_skew(const real_t p_angle);
_FORCE_INLINE_ void set_rotation_and_scale(const real_t p_rot, const Size2 &p_scale);
_FORCE_INLINE_ void set_rotation_scale_and_skew(const real_t p_rot, const Size2 &p_scale, const real_t p_skew);
void rotate(const real_t p_angle);
void scale(const Size2 &p_scale);
void scale_basis(const Size2 &p_scale);
void translate_local(const real_t p_tx, const real_t p_ty);
void translate_local(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 columns[2]; }
_FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { columns[2] = p_origin; }
Transform2D basis_scaled(const Size2 &p_scale) const;
Transform2D scaled(const Size2 &p_scale) const;
Transform2D scaled_local(const Size2 &p_scale) const;
Transform2D translated(const Vector2 &p_offset) const;
Transform2D translated_local(const Vector2 &p_offset) const;
Transform2D rotated(const real_t p_angle) const;
Transform2D rotated_local(const real_t p_angle) const;
Transform2D untranslated() const;
void orthonormalize();
Transform2D orthonormalized() const;
bool is_equal_approx(const Transform2D &p_transform) const;
bool is_finite() const;
Transform2D looking_at(const Vector2 &p_target) 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;
void operator*=(const real_t p_val);
Transform2D operator*(const real_t p_val) const;
Transform2D interpolate_with(const Transform2D &p_transform, const 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_ Vector<Vector2> xform(const Vector<Vector2> &p_array) const;
_FORCE_INLINE_ Vector<Vector2> xform_inv(const Vector<Vector2> &p_array) const;
operator String() const;
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) {
columns[0][0] = xx;
columns[0][1] = xy;
columns[1][0] = yx;
columns[1][1] = yy;
columns[2][0] = ox;
columns[2][1] = oy;
}
Transform2D(const Vector2 &p_x, const Vector2 &p_y, const Vector2 &p_origin) {
columns[0] = p_x;
columns[1] = p_y;
columns[2] = p_origin;
}
Transform2D(const real_t p_rot, const Vector2 &p_pos);
Transform2D(const real_t p_rot, const Size2 &p_scale, const real_t p_skew, const Vector2 &p_pos);
Transform2D() {
columns[0][0] = 1.0;
columns[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(
columns[0].dot(p_vec),
columns[1].dot(p_vec));
}
Vector2 Transform2D::xform(const Vector2 &p_vec) const {
return Vector2(
tdotx(p_vec),
tdoty(p_vec)) +
columns[2];
}
Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const {
Vector2 v = p_vec - columns[2];
return Vector2(
columns[0].dot(v),
columns[1].dot(v));
}
Rect2 Transform2D::xform(const Rect2 &p_rect) const {
Vector2 x = columns[0] * p_rect.size.x;
Vector2 y = columns[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(const real_t p_rot, const Size2 &p_scale) {
columns[0][0] = Math::cos(p_rot) * p_scale.x;
columns[1][1] = Math::cos(p_rot) * p_scale.y;
columns[1][0] = -Math::sin(p_rot) * p_scale.y;
columns[0][1] = Math::sin(p_rot) * p_scale.x;
}
void Transform2D::set_rotation_scale_and_skew(const real_t p_rot, const Size2 &p_scale, const real_t p_skew) {
columns[0][0] = Math::cos(p_rot) * p_scale.x;
columns[1][1] = Math::cos(p_rot + p_skew) * p_scale.y;
columns[1][0] = -Math::sin(p_rot + p_skew) * p_scale.y;
columns[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;
}
Vector<Vector2> Transform2D::xform(const Vector<Vector2> &p_array) const {
Vector<Vector2> array;
array.resize(p_array.size());
const Vector2 *r = p_array.ptr();
Vector2 *w = array.ptrw();
for (int i = 0; i < p_array.size(); ++i) {
w[i] = xform(r[i]);
}
return array;
}
Vector<Vector2> Transform2D::xform_inv(const Vector<Vector2> &p_array) const {
Vector<Vector2> array;
array.resize(p_array.size());
const Vector2 *r = p_array.ptr();
Vector2 *w = array.ptrw();
for (int i = 0; i < p_array.size(); ++i) {
w[i] = xform_inv(r[i]);
}
return array;
}
#endif // TRANSFORM_2D_H
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