1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
|
/*************************************************************************/
/* transform_2d.h */
/*************************************************************************/
/* 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. */
/*************************************************************************/
#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<Vector2> xform(const PoolVector<Vector2> &p_array) const;
_FORCE_INLINE_ PoolVector<Vector2> xform_inv(const PoolVector<Vector2> &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<Vector2> Transform2D::xform(const PoolVector<Vector2> &p_array) const {
PoolVector<Vector2> array;
array.resize(p_array.size());
PoolVector<Vector2>::Read r = p_array.read();
PoolVector<Vector2>::Write w = array.write();
for (int i = 0; i < p_array.size(); ++i) {
w[i] = xform(r[i]);
}
return array;
}
PoolVector<Vector2> Transform2D::xform_inv(const PoolVector<Vector2> &p_array) const {
PoolVector<Vector2> array;
array.resize(p_array.size());
PoolVector<Vector2>::Read r = p_array.read();
PoolVector<Vector2>::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
|