1/**************************************************************************/
2/* transform_2d.h */
3/**************************************************************************/
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30
31#ifndef TRANSFORM_2D_H
32#define TRANSFORM_2D_H
33
34#include "core/math/math_funcs.h"
35#include "core/math/rect2.h"
36#include "core/math/vector2.h"
37#include "core/templates/vector.h"
38
39class String;
40
41struct _NO_DISCARD_ Transform2D {
42 // Warning #1: basis of Transform2D is stored differently from Basis. In terms of columns array, the basis matrix looks like "on paper":
43 // M = (columns[0][0] columns[1][0])
44 // (columns[0][1] columns[1][1])
45 // 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].
46 // 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.
47 // This requires additional care when working with explicit indices.
48 // See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading.
49
50 // Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down,
51 // and angle is measure from +X to +Y in a clockwise-fashion.
52
53 Vector2 columns[3];
54
55 _FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return columns[0][0] * v.x + columns[1][0] * v.y; }
56 _FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return columns[0][1] * v.x + columns[1][1] * v.y; }
57
58 const Vector2 &operator[](int p_idx) const { return columns[p_idx]; }
59 Vector2 &operator[](int p_idx) { return columns[p_idx]; }
60
61 void invert();
62 Transform2D inverse() const;
63
64 void affine_invert();
65 Transform2D affine_inverse() const;
66
67 void set_rotation(const real_t p_rot);
68 real_t get_rotation() const;
69 real_t get_skew() const;
70 void set_skew(const real_t p_angle);
71 _FORCE_INLINE_ void set_rotation_and_scale(const real_t p_rot, const Size2 &p_scale);
72 _FORCE_INLINE_ void set_rotation_scale_and_skew(const real_t p_rot, const Size2 &p_scale, const real_t p_skew);
73 void rotate(const real_t p_angle);
74
75 void scale(const Size2 &p_scale);
76 void scale_basis(const Size2 &p_scale);
77 void translate_local(const real_t p_tx, const real_t p_ty);
78 void translate_local(const Vector2 &p_translation);
79
80 real_t determinant() const;
81
82 Size2 get_scale() const;
83 void set_scale(const Size2 &p_scale);
84
85 _FORCE_INLINE_ const Vector2 &get_origin() const { return columns[2]; }
86 _FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { columns[2] = p_origin; }
87
88 Transform2D scaled(const Size2 &p_scale) const;
89 Transform2D scaled_local(const Size2 &p_scale) const;
90 Transform2D translated(const Vector2 &p_offset) const;
91 Transform2D translated_local(const Vector2 &p_offset) const;
92 Transform2D rotated(const real_t p_angle) const;
93 Transform2D rotated_local(const real_t p_angle) const;
94
95 Transform2D untranslated() const;
96
97 void orthonormalize();
98 Transform2D orthonormalized() const;
99 bool is_equal_approx(const Transform2D &p_transform) const;
100 bool is_finite() const;
101
102 Transform2D looking_at(const Vector2 &p_target) const;
103
104 bool operator==(const Transform2D &p_transform) const;
105 bool operator!=(const Transform2D &p_transform) const;
106
107 void operator*=(const Transform2D &p_transform);
108 Transform2D operator*(const Transform2D &p_transform) const;
109 void operator*=(const real_t p_val);
110 Transform2D operator*(const real_t p_val) const;
111
112 Transform2D interpolate_with(const Transform2D &p_transform, const real_t p_c) const;
113
114 _FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const;
115 _FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const;
116 _FORCE_INLINE_ Vector2 xform(const Vector2 &p_vec) const;
117 _FORCE_INLINE_ Vector2 xform_inv(const Vector2 &p_vec) const;
118 _FORCE_INLINE_ Rect2 xform(const Rect2 &p_rect) const;
119 _FORCE_INLINE_ Rect2 xform_inv(const Rect2 &p_rect) const;
120 _FORCE_INLINE_ Vector<Vector2> xform(const Vector<Vector2> &p_array) const;
121 _FORCE_INLINE_ Vector<Vector2> xform_inv(const Vector<Vector2> &p_array) const;
122
123 operator String() const;
124
125 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) {
126 columns[0][0] = xx;
127 columns[0][1] = xy;
128 columns[1][0] = yx;
129 columns[1][1] = yy;
130 columns[2][0] = ox;
131 columns[2][1] = oy;
132 }
133
134 Transform2D(const Vector2 &p_x, const Vector2 &p_y, const Vector2 &p_origin) {
135 columns[0] = p_x;
136 columns[1] = p_y;
137 columns[2] = p_origin;
138 }
139
140 Transform2D(const real_t p_rot, const Vector2 &p_pos);
141
142 Transform2D(const real_t p_rot, const Size2 &p_scale, const real_t p_skew, const Vector2 &p_pos);
143
144 Transform2D() {
145 columns[0][0] = 1.0;
146 columns[1][1] = 1.0;
147 }
148};
149
150Vector2 Transform2D::basis_xform(const Vector2 &p_vec) const {
151 return Vector2(
152 tdotx(p_vec),
153 tdoty(p_vec));
154}
155
156Vector2 Transform2D::basis_xform_inv(const Vector2 &p_vec) const {
157 return Vector2(
158 columns[0].dot(p_vec),
159 columns[1].dot(p_vec));
160}
161
162Vector2 Transform2D::xform(const Vector2 &p_vec) const {
163 return Vector2(
164 tdotx(p_vec),
165 tdoty(p_vec)) +
166 columns[2];
167}
168
169Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const {
170 Vector2 v = p_vec - columns[2];
171
172 return Vector2(
173 columns[0].dot(v),
174 columns[1].dot(v));
175}
176
177Rect2 Transform2D::xform(const Rect2 &p_rect) const {
178 Vector2 x = columns[0] * p_rect.size.x;
179 Vector2 y = columns[1] * p_rect.size.y;
180 Vector2 pos = xform(p_rect.position);
181
182 Rect2 new_rect;
183 new_rect.position = pos;
184 new_rect.expand_to(pos + x);
185 new_rect.expand_to(pos + y);
186 new_rect.expand_to(pos + x + y);
187 return new_rect;
188}
189
190void Transform2D::set_rotation_and_scale(const real_t p_rot, const Size2 &p_scale) {
191 columns[0][0] = Math::cos(p_rot) * p_scale.x;
192 columns[1][1] = Math::cos(p_rot) * p_scale.y;
193 columns[1][0] = -Math::sin(p_rot) * p_scale.y;
194 columns[0][1] = Math::sin(p_rot) * p_scale.x;
195}
196
197void Transform2D::set_rotation_scale_and_skew(const real_t p_rot, const Size2 &p_scale, const real_t p_skew) {
198 columns[0][0] = Math::cos(p_rot) * p_scale.x;
199 columns[1][1] = Math::cos(p_rot + p_skew) * p_scale.y;
200 columns[1][0] = -Math::sin(p_rot + p_skew) * p_scale.y;
201 columns[0][1] = Math::sin(p_rot) * p_scale.x;
202}
203
204Rect2 Transform2D::xform_inv(const Rect2 &p_rect) const {
205 Vector2 ends[4] = {
206 xform_inv(p_rect.position),
207 xform_inv(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
208 xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
209 xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y))
210 };
211
212 Rect2 new_rect;
213 new_rect.position = ends[0];
214 new_rect.expand_to(ends[1]);
215 new_rect.expand_to(ends[2]);
216 new_rect.expand_to(ends[3]);
217
218 return new_rect;
219}
220
221Vector<Vector2> Transform2D::xform(const Vector<Vector2> &p_array) const {
222 Vector<Vector2> array;
223 array.resize(p_array.size());
224
225 const Vector2 *r = p_array.ptr();
226 Vector2 *w = array.ptrw();
227
228 for (int i = 0; i < p_array.size(); ++i) {
229 w[i] = xform(r[i]);
230 }
231 return array;
232}
233
234Vector<Vector2> Transform2D::xform_inv(const Vector<Vector2> &p_array) const {
235 Vector<Vector2> array;
236 array.resize(p_array.size());
237
238 const Vector2 *r = p_array.ptr();
239 Vector2 *w = array.ptrw();
240
241 for (int i = 0; i < p_array.size(); ++i) {
242 w[i] = xform_inv(r[i]);
243 }
244 return array;
245}
246
247#endif // TRANSFORM_2D_H
248