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
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
|
/*************************************************************************/
/* test_basis.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2022 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 TEST_BASIS_H
#define TEST_BASIS_H
#include "core/math/basis.h"
#include "core/math/random_number_generator.h"
#include "tests/test_macros.h"
namespace TestBasis {
enum RotOrder {
EulerXYZ,
EulerXZY,
EulerYZX,
EulerYXZ,
EulerZXY,
EulerZYX
};
Vector3 deg_to_rad(const Vector3 &p_rotation) {
return p_rotation / 180.0 * Math_PI;
}
Vector3 rad2deg(const Vector3 &p_rotation) {
return p_rotation / Math_PI * 180.0;
}
Basis EulerToBasis(RotOrder mode, const Vector3 &p_rotation) {
Basis ret;
switch (mode) {
case EulerXYZ:
ret.set_euler(p_rotation, Basis::EULER_ORDER_XYZ);
break;
case EulerXZY:
ret.set_euler(p_rotation, Basis::EULER_ORDER_XZY);
break;
case EulerYZX:
ret.set_euler(p_rotation, Basis::EULER_ORDER_YZX);
break;
case EulerYXZ:
ret.set_euler(p_rotation, Basis::EULER_ORDER_YXZ);
break;
case EulerZXY:
ret.set_euler(p_rotation, Basis::EULER_ORDER_ZXY);
break;
case EulerZYX:
ret.set_euler(p_rotation, Basis::EULER_ORDER_ZYX);
break;
default:
// If you land here, Please integrate all rotation orders.
FAIL("This is not unreachable.");
}
return ret;
}
Vector3 BasisToEuler(RotOrder mode, const Basis &p_rotation) {
switch (mode) {
case EulerXYZ:
return p_rotation.get_euler(Basis::EULER_ORDER_XYZ);
case EulerXZY:
return p_rotation.get_euler(Basis::EULER_ORDER_XZY);
case EulerYZX:
return p_rotation.get_euler(Basis::EULER_ORDER_YZX);
case EulerYXZ:
return p_rotation.get_euler(Basis::EULER_ORDER_YXZ);
case EulerZXY:
return p_rotation.get_euler(Basis::EULER_ORDER_ZXY);
case EulerZYX:
return p_rotation.get_euler(Basis::EULER_ORDER_ZYX);
default:
// If you land here, Please integrate all rotation orders.
FAIL("This is not unreachable.");
return Vector3();
}
}
String get_rot_order_name(RotOrder ro) {
switch (ro) {
case EulerXYZ:
return "XYZ";
case EulerXZY:
return "XZY";
case EulerYZX:
return "YZX";
case EulerYXZ:
return "YXZ";
case EulerZXY:
return "ZXY";
case EulerZYX:
return "ZYX";
default:
return "[Not supported]";
}
}
void test_rotation(Vector3 deg_original_euler, RotOrder rot_order) {
// This test:
// 1. Converts the rotation vector from deg to rad.
// 2. Converts euler to basis.
// 3. Converts the above basis back into euler.
// 4. Converts the above euler into basis again.
// 5. Compares the basis obtained in step 2 with the basis of step 4
//
// The conversion "basis to euler", done in the step 3, may be different from
// the original euler, even if the final rotation are the same.
// This happens because there are more ways to represents the same rotation,
// both valid, using eulers.
// For this reason is necessary to convert that euler back to basis and finally
// compares it.
//
// In this way we can assert that both functions: basis to euler / euler to basis
// are correct.
// Euler to rotation
const Vector3 original_euler = deg_to_rad(deg_original_euler);
const Basis to_rotation = EulerToBasis(rot_order, original_euler);
// Euler from rotation
const Vector3 euler_from_rotation = BasisToEuler(rot_order, to_rotation);
const Basis rotation_from_computed_euler = EulerToBasis(rot_order, euler_from_rotation);
Basis res = to_rotation.inverse() * rotation_from_computed_euler;
CHECK_MESSAGE((res.get_column(0) - Vector3(1.0, 0.0, 0.0)).length() <= 0.1, vformat("Fail due to X %s\n", String(res.get_column(0))).utf8().ptr());
CHECK_MESSAGE((res.get_column(1) - Vector3(0.0, 1.0, 0.0)).length() <= 0.1, vformat("Fail due to Y %s\n", String(res.get_column(1))).utf8().ptr());
CHECK_MESSAGE((res.get_column(2) - Vector3(0.0, 0.0, 1.0)).length() <= 0.1, vformat("Fail due to Z %s\n", String(res.get_column(2))).utf8().ptr());
// Double check `to_rotation` decomposing with XYZ rotation order.
const Vector3 euler_xyz_from_rotation = to_rotation.get_euler(Basis::EULER_ORDER_XYZ);
Basis rotation_from_xyz_computed_euler = Basis::from_euler(euler_xyz_from_rotation, Basis::EULER_ORDER_XYZ);
res = to_rotation.inverse() * rotation_from_xyz_computed_euler;
CHECK_MESSAGE((res.get_column(0) - Vector3(1.0, 0.0, 0.0)).length() <= 0.1, vformat("Double check with XYZ rot order failed, due to X %s\n", String(res.get_column(0))).utf8().ptr());
CHECK_MESSAGE((res.get_column(1) - Vector3(0.0, 1.0, 0.0)).length() <= 0.1, vformat("Double check with XYZ rot order failed, due to Y %s\n", String(res.get_column(1))).utf8().ptr());
CHECK_MESSAGE((res.get_column(2) - Vector3(0.0, 0.0, 1.0)).length() <= 0.1, vformat("Double check with XYZ rot order failed, due to Z %s\n", String(res.get_column(2))).utf8().ptr());
INFO(vformat("Rotation order: %s\n.", get_rot_order_name(rot_order)).utf8().ptr());
INFO(vformat("Original Rotation: %s\n", String(deg_original_euler)).utf8().ptr());
INFO(vformat("Quaternion to rotation order: %s\n", String(rad2deg(euler_from_rotation))).utf8().ptr());
}
TEST_CASE("[Basis] Euler conversions") {
Vector<RotOrder> rotorder_to_test;
rotorder_to_test.push_back(EulerXYZ);
rotorder_to_test.push_back(EulerXZY);
rotorder_to_test.push_back(EulerYZX);
rotorder_to_test.push_back(EulerYXZ);
rotorder_to_test.push_back(EulerZXY);
rotorder_to_test.push_back(EulerZYX);
Vector<Vector3> vectors_to_test;
// Test the special cases.
vectors_to_test.push_back(Vector3(0.0, 0.0, 0.0));
vectors_to_test.push_back(Vector3(0.5, 0.5, 0.5));
vectors_to_test.push_back(Vector3(-0.5, -0.5, -0.5));
vectors_to_test.push_back(Vector3(40.0, 40.0, 40.0));
vectors_to_test.push_back(Vector3(-40.0, -40.0, -40.0));
vectors_to_test.push_back(Vector3(0.0, 0.0, -90.0));
vectors_to_test.push_back(Vector3(0.0, -90.0, 0.0));
vectors_to_test.push_back(Vector3(-90.0, 0.0, 0.0));
vectors_to_test.push_back(Vector3(0.0, 0.0, 90.0));
vectors_to_test.push_back(Vector3(0.0, 90.0, 0.0));
vectors_to_test.push_back(Vector3(90.0, 0.0, 0.0));
vectors_to_test.push_back(Vector3(0.0, 0.0, -30.0));
vectors_to_test.push_back(Vector3(0.0, -30.0, 0.0));
vectors_to_test.push_back(Vector3(-30.0, 0.0, 0.0));
vectors_to_test.push_back(Vector3(0.0, 0.0, 30.0));
vectors_to_test.push_back(Vector3(0.0, 30.0, 0.0));
vectors_to_test.push_back(Vector3(30.0, 0.0, 0.0));
vectors_to_test.push_back(Vector3(0.5, 50.0, 20.0));
vectors_to_test.push_back(Vector3(-0.5, -50.0, -20.0));
vectors_to_test.push_back(Vector3(0.5, 0.0, 90.0));
vectors_to_test.push_back(Vector3(0.5, 0.0, -90.0));
vectors_to_test.push_back(Vector3(360.0, 360.0, 360.0));
vectors_to_test.push_back(Vector3(-360.0, -360.0, -360.0));
vectors_to_test.push_back(Vector3(-90.0, 60.0, -90.0));
vectors_to_test.push_back(Vector3(90.0, 60.0, -90.0));
vectors_to_test.push_back(Vector3(90.0, -60.0, -90.0));
vectors_to_test.push_back(Vector3(-90.0, -60.0, -90.0));
vectors_to_test.push_back(Vector3(-90.0, 60.0, 90.0));
vectors_to_test.push_back(Vector3(90.0, 60.0, 90.0));
vectors_to_test.push_back(Vector3(90.0, -60.0, 90.0));
vectors_to_test.push_back(Vector3(-90.0, -60.0, 90.0));
vectors_to_test.push_back(Vector3(60.0, 90.0, -40.0));
vectors_to_test.push_back(Vector3(60.0, -90.0, -40.0));
vectors_to_test.push_back(Vector3(-60.0, -90.0, -40.0));
vectors_to_test.push_back(Vector3(-60.0, 90.0, 40.0));
vectors_to_test.push_back(Vector3(60.0, 90.0, 40.0));
vectors_to_test.push_back(Vector3(60.0, -90.0, 40.0));
vectors_to_test.push_back(Vector3(-60.0, -90.0, 40.0));
vectors_to_test.push_back(Vector3(-90.0, 90.0, -90.0));
vectors_to_test.push_back(Vector3(90.0, 90.0, -90.0));
vectors_to_test.push_back(Vector3(90.0, -90.0, -90.0));
vectors_to_test.push_back(Vector3(-90.0, -90.0, -90.0));
vectors_to_test.push_back(Vector3(-90.0, 90.0, 90.0));
vectors_to_test.push_back(Vector3(90.0, 90.0, 90.0));
vectors_to_test.push_back(Vector3(90.0, -90.0, 90.0));
vectors_to_test.push_back(Vector3(20.0, 150.0, 30.0));
vectors_to_test.push_back(Vector3(20.0, -150.0, 30.0));
vectors_to_test.push_back(Vector3(-120.0, -150.0, 30.0));
vectors_to_test.push_back(Vector3(-120.0, -150.0, -130.0));
vectors_to_test.push_back(Vector3(120.0, -150.0, -130.0));
vectors_to_test.push_back(Vector3(120.0, 150.0, -130.0));
vectors_to_test.push_back(Vector3(120.0, 150.0, 130.0));
for (int h = 0; h < rotorder_to_test.size(); h += 1) {
for (int i = 0; i < vectors_to_test.size(); i += 1) {
test_rotation(vectors_to_test[i], rotorder_to_test[h]);
}
}
}
TEST_CASE("[Stress][Basis] Euler conversions") {
Vector<RotOrder> rotorder_to_test;
rotorder_to_test.push_back(EulerXYZ);
rotorder_to_test.push_back(EulerXZY);
rotorder_to_test.push_back(EulerYZX);
rotorder_to_test.push_back(EulerYXZ);
rotorder_to_test.push_back(EulerZXY);
rotorder_to_test.push_back(EulerZYX);
Vector<Vector3> vectors_to_test;
// Add 1000 random vectors with weirds numbers.
RandomNumberGenerator rng;
for (int _ = 0; _ < 1000; _ += 1) {
vectors_to_test.push_back(Vector3(
rng.randf_range(-1800, 1800),
rng.randf_range(-1800, 1800),
rng.randf_range(-1800, 1800)));
}
for (int h = 0; h < rotorder_to_test.size(); h += 1) {
for (int i = 0; i < vectors_to_test.size(); i += 1) {
test_rotation(vectors_to_test[i], rotorder_to_test[h]);
}
}
}
TEST_CASE("[Basis] Set axis angle") {
Vector3 axis;
real_t angle;
real_t pi = (real_t)Math_PI;
// Testing the singularity when the angle is 0°.
Basis identity(1, 0, 0, 0, 1, 0, 0, 0, 1);
identity.get_axis_angle(axis, angle);
CHECK(angle == 0);
// Testing the singularity when the angle is 180°.
Basis singularityPi(-1, 0, 0, 0, 1, 0, 0, 0, -1);
singularityPi.get_axis_angle(axis, angle);
CHECK(Math::is_equal_approx(angle, pi));
// Testing reversing the an axis (of an 30° angle).
float cos30deg = Math::cos(Math::deg_to_rad((real_t)30.0));
Basis z_positive(cos30deg, -0.5, 0, 0.5, cos30deg, 0, 0, 0, 1);
Basis z_negative(cos30deg, 0.5, 0, -0.5, cos30deg, 0, 0, 0, 1);
z_positive.get_axis_angle(axis, angle);
CHECK(Math::is_equal_approx(angle, Math::deg_to_rad((real_t)30.0)));
CHECK(axis == Vector3(0, 0, 1));
z_negative.get_axis_angle(axis, angle);
CHECK(Math::is_equal_approx(angle, Math::deg_to_rad((real_t)30.0)));
CHECK(axis == Vector3(0, 0, -1));
// Testing a rotation of 90° on x-y-z.
Basis x90deg(1, 0, 0, 0, 0, -1, 0, 1, 0);
x90deg.get_axis_angle(axis, angle);
CHECK(Math::is_equal_approx(angle, pi / (real_t)2));
CHECK(axis == Vector3(1, 0, 0));
Basis y90deg(0, 0, 1, 0, 1, 0, -1, 0, 0);
y90deg.get_axis_angle(axis, angle);
CHECK(axis == Vector3(0, 1, 0));
Basis z90deg(0, -1, 0, 1, 0, 0, 0, 0, 1);
z90deg.get_axis_angle(axis, angle);
CHECK(axis == Vector3(0, 0, 1));
// Regression test: checks that the method returns a small angle (not 0).
Basis tiny(1, 0, 0, 0, 0.9999995, -0.001, 0, 001, 0.9999995); // The min angle possible with float is 0.001rad.
tiny.get_axis_angle(axis, angle);
CHECK(Math::is_equal_approx(angle, (real_t)0.001, (real_t)0.0001));
// Regression test: checks that the method returns an angle which is a number (not NaN)
Basis bugNan(1.00000024, 0, 0.000100001693, 0, 1, 0, -0.000100009143, 0, 1.00000024);
bugNan.get_axis_angle(axis, angle);
CHECK(!Math::is_nan(angle));
}
TEST_CASE("[Basis] Finite number checks") {
const Vector3 x(0, 1, 2);
const Vector3 infinite(NAN, NAN, NAN);
CHECK_MESSAGE(
Basis(x, x, x).is_finite(),
"Basis with all components finite should be finite");
CHECK_FALSE_MESSAGE(
Basis(infinite, x, x).is_finite(),
"Basis with one component infinite should not be finite.");
CHECK_FALSE_MESSAGE(
Basis(x, infinite, x).is_finite(),
"Basis with one component infinite should not be finite.");
CHECK_FALSE_MESSAGE(
Basis(x, x, infinite).is_finite(),
"Basis with one component infinite should not be finite.");
CHECK_FALSE_MESSAGE(
Basis(infinite, infinite, x).is_finite(),
"Basis with two components infinite should not be finite.");
CHECK_FALSE_MESSAGE(
Basis(infinite, x, infinite).is_finite(),
"Basis with two components infinite should not be finite.");
CHECK_FALSE_MESSAGE(
Basis(x, infinite, infinite).is_finite(),
"Basis with two components infinite should not be finite.");
CHECK_FALSE_MESSAGE(
Basis(infinite, infinite, infinite).is_finite(),
"Basis with three components infinite should not be finite.");
}
} // namespace TestBasis
#endif // TEST_BASIS_H
|