1 /*************************************************************************/
2 /* transform.h */
3 /*************************************************************************/
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5 /* GODOT ENGINE */
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30
31 #ifndef TRANSFORM_H
32 #define TRANSFORM_H
33
34 #include "core/math/aabb.h"
35 #include "core/math/basis.h"
36 #include "core/math/plane.h"
37 #include "core/pool_vector.h"
38
39 class Transform {
40 public:
41 Basis basis;
42 Vector3 origin;
43
44 void invert();
45 Transform inverse() const;
46
47 void affine_invert();
48 Transform affine_inverse() const;
49
50 Transform rotated(const Vector3 &p_axis, real_t p_phi) const;
51
52 void rotate(const Vector3 &p_axis, real_t p_phi);
53 void rotate_basis(const Vector3 &p_axis, real_t p_phi);
54
55 void set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up);
56 Transform looking_at(const Vector3 &p_target, const Vector3 &p_up) const;
57
58 void scale(const Vector3 &p_scale);
59 Transform scaled(const Vector3 &p_scale) const;
60 void scale_basis(const Vector3 &p_scale);
61 void translate(real_t p_tx, real_t p_ty, real_t p_tz);
62 void translate(const Vector3 &p_translation);
63 Transform translated(const Vector3 &p_translation) const;
64
get_basis()65 const Basis &get_basis() const { return basis; }
set_basis(const Basis & p_basis)66 void set_basis(const Basis &p_basis) { basis = p_basis; }
67
get_origin()68 const Vector3 &get_origin() const { return origin; }
set_origin(const Vector3 & p_origin)69 void set_origin(const Vector3 &p_origin) { origin = p_origin; }
70
71 void orthonormalize();
72 Transform orthonormalized() const;
73 bool is_equal_approx(const Transform &p_transform) const;
74
75 bool operator==(const Transform &p_transform) const;
76 bool operator!=(const Transform &p_transform) const;
77
78 _FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const;
79 _FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const;
80
81 _FORCE_INLINE_ Plane xform(const Plane &p_plane) const;
82 _FORCE_INLINE_ Plane xform_inv(const Plane &p_plane) const;
83
84 _FORCE_INLINE_ AABB xform(const AABB &p_aabb) const;
85 _FORCE_INLINE_ AABB xform_inv(const AABB &p_aabb) const;
86
87 _FORCE_INLINE_ PoolVector<Vector3> xform(const PoolVector<Vector3> &p_array) const;
88 _FORCE_INLINE_ PoolVector<Vector3> xform_inv(const PoolVector<Vector3> &p_array) const;
89
90 void operator*=(const Transform &p_transform);
91 Transform operator*(const Transform &p_transform) const;
92
93 Transform interpolate_with(const Transform &p_transform, real_t p_c) const;
94
inverse_xform(const Transform & t)95 _FORCE_INLINE_ Transform inverse_xform(const Transform &t) const {
96
97 Vector3 v = t.origin - origin;
98 return Transform(basis.transpose_xform(t.basis),
99 basis.xform(v));
100 }
101
set(real_t xx,real_t xy,real_t xz,real_t yx,real_t yy,real_t yz,real_t zx,real_t zy,real_t zz,real_t tx,real_t ty,real_t tz)102 void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t tx, real_t ty, real_t tz) {
103
104 basis.set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
105 origin.x = tx;
106 origin.y = ty;
107 origin.z = tz;
108 }
109
110 operator String() const;
111
112 Transform(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t ox, real_t oy, real_t oz);
113 Transform(const Basis &p_basis, const Vector3 &p_origin = Vector3());
Transform()114 Transform() {}
115 };
116
xform(const Vector3 & p_vector)117 _FORCE_INLINE_ Vector3 Transform::xform(const Vector3 &p_vector) const {
118
119 return Vector3(
120 basis[0].dot(p_vector) + origin.x,
121 basis[1].dot(p_vector) + origin.y,
122 basis[2].dot(p_vector) + origin.z);
123 }
xform_inv(const Vector3 & p_vector)124 _FORCE_INLINE_ Vector3 Transform::xform_inv(const Vector3 &p_vector) const {
125
126 Vector3 v = p_vector - origin;
127
128 return Vector3(
129 (basis.elements[0][0] * v.x) + (basis.elements[1][0] * v.y) + (basis.elements[2][0] * v.z),
130 (basis.elements[0][1] * v.x) + (basis.elements[1][1] * v.y) + (basis.elements[2][1] * v.z),
131 (basis.elements[0][2] * v.x) + (basis.elements[1][2] * v.y) + (basis.elements[2][2] * v.z));
132 }
133
xform(const Plane & p_plane)134 _FORCE_INLINE_ Plane Transform::xform(const Plane &p_plane) const {
135
136 Vector3 point = p_plane.normal * p_plane.d;
137 Vector3 point_dir = point + p_plane.normal;
138 point = xform(point);
139 point_dir = xform(point_dir);
140
141 Vector3 normal = point_dir - point;
142 normal.normalize();
143 real_t d = normal.dot(point);
144
145 return Plane(normal, d);
146 }
xform_inv(const Plane & p_plane)147 _FORCE_INLINE_ Plane Transform::xform_inv(const Plane &p_plane) const {
148
149 Vector3 point = p_plane.normal * p_plane.d;
150 Vector3 point_dir = point + p_plane.normal;
151 xform_inv(point);
152 xform_inv(point_dir);
153
154 Vector3 normal = point_dir - point;
155 normal.normalize();
156 real_t d = normal.dot(point);
157
158 return Plane(normal, d);
159 }
160
xform(const AABB & p_aabb)161 _FORCE_INLINE_ AABB Transform::xform(const AABB &p_aabb) const {
162
163 /* http://dev.theomader.com/transform-bounding-boxes/ */
164 Vector3 min = p_aabb.position;
165 Vector3 max = p_aabb.position + p_aabb.size;
166 Vector3 tmin, tmax;
167 for (int i = 0; i < 3; i++) {
168 tmin[i] = tmax[i] = origin[i];
169 for (int j = 0; j < 3; j++) {
170 real_t e = basis[i][j] * min[j];
171 real_t f = basis[i][j] * max[j];
172 if (e < f) {
173 tmin[i] += e;
174 tmax[i] += f;
175 } else {
176 tmin[i] += f;
177 tmax[i] += e;
178 }
179 }
180 }
181 AABB r_aabb;
182 r_aabb.position = tmin;
183 r_aabb.size = tmax - tmin;
184 return r_aabb;
185 }
186
xform_inv(const AABB & p_aabb)187 _FORCE_INLINE_ AABB Transform::xform_inv(const AABB &p_aabb) const {
188
189 /* define vertices */
190 Vector3 vertices[8] = {
191 Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z),
192 Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z),
193 Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z),
194 Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z),
195 Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z),
196 Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z),
197 Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z),
198 Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z)
199 };
200
201 AABB ret;
202
203 ret.position = xform_inv(vertices[0]);
204
205 for (int i = 1; i < 8; i++) {
206
207 ret.expand_to(xform_inv(vertices[i]));
208 }
209
210 return ret;
211 }
212
xform(const PoolVector<Vector3> & p_array)213 PoolVector<Vector3> Transform::xform(const PoolVector<Vector3> &p_array) const {
214
215 PoolVector<Vector3> array;
216 array.resize(p_array.size());
217
218 PoolVector<Vector3>::Read r = p_array.read();
219 PoolVector<Vector3>::Write w = array.write();
220
221 for (int i = 0; i < p_array.size(); ++i) {
222 w[i] = xform(r[i]);
223 }
224 return array;
225 }
226
xform_inv(const PoolVector<Vector3> & p_array)227 PoolVector<Vector3> Transform::xform_inv(const PoolVector<Vector3> &p_array) const {
228
229 PoolVector<Vector3> array;
230 array.resize(p_array.size());
231
232 PoolVector<Vector3>::Read r = p_array.read();
233 PoolVector<Vector3>::Write w = array.write();
234
235 for (int i = 0; i < p_array.size(); ++i) {
236 w[i] = xform_inv(r[i]);
237 }
238 return array;
239 }
240
241 #endif // TRANSFORM_H
242