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
|
/* -------------------------------------------------------------------------- *
* Simbody(tm) *
* -------------------------------------------------------------------------- *
* This is part of the SimTK biosimulation toolkit originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody. *
* *
* Portions copyright (c) 2008-12 Stanford University and the Authors. *
* Authors: Peter Eastman *
* Contributors: *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); you may *
* not use this file except in compliance with the License. You may obtain a *
* copy of the License at http://www.apache.org/licenses/LICENSE-2.0. *
* *
* Unless required by applicable law or agreed to in writing, software *
* distributed under the License is distributed on an "AS IS" BASIS, *
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
* See the License for the specific language governing permissions and *
* limitations under the License. *
* -------------------------------------------------------------------------- */
#include "SimTKsimbody.h"
using namespace SimTK;
using namespace std;
const Real TOL = 1e-10;
#define ASSERT(cond) {SimTK_ASSERT_ALWAYS(cond, "Assertion failed");}
template <class T>
void assertEqual(T val1, T val2) {
ASSERT(abs(val1-val2) < TOL);
}
template <int N>
void assertEqual(Vec<N> val1, Vec<N> val2) {
for (int i = 0; i < N; ++i)
ASSERT(abs(val1[i]-val2[i]) < TOL);
}
void testContainsPoint() {
OrientedBoundingBox box(Vec3(0), Vec3(1, 2, 3));
ASSERT(box.containsPoint(Vec3(0)));
ASSERT(box.containsPoint(Vec3(1, 2, 3)));
ASSERT(box.containsPoint(Vec3(0.5, 1.0, 1.5)));
ASSERT(!box.containsPoint(Vec3(-0.5, 1.0, 1.5)));
ASSERT(!box.containsPoint(Vec3(0.5, -1.0, 1.5)));
ASSERT(!box.containsPoint(Vec3(0.5, 1.0, -1.5)));
ASSERT(!box.containsPoint(Vec3(1.01, 1.0, 1.5)));
ASSERT(!box.containsPoint(Vec3(0.5, 2.01, 1.5)));
ASSERT(!box.containsPoint(Vec3(0.5, 1.0, 3.01)));
box = OrientedBoundingBox(Vec3(3, 2, 1), Vec3(1, 2, 3));
ASSERT(box.containsPoint(Vec3(3, 2, 1)));
ASSERT(box.containsPoint(Vec3(4, 4, 4)));
ASSERT(box.containsPoint(Vec3(3.5, 3.0, 2.5)));
ASSERT(!box.containsPoint(Vec3(2.5, 3.0, 2.5)));
ASSERT(!box.containsPoint(Vec3(4.5, 1.0, 2.5)));
ASSERT(!box.containsPoint(Vec3(4.5, 3.0, -0.5)));
ASSERT(!box.containsPoint(Vec3(5.01, 3.0, 2.5)));
ASSERT(!box.containsPoint(Vec3(3.5, 4.01, 2.5)));
ASSERT(!box.containsPoint(Vec3(3.5, 3.0, 4.01)));
box = OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1));
ASSERT(box.containsPoint(Vec3(0)));
ASSERT(box.containsPoint(Vec3(0, Sqrt2-1e-10, 0)));
ASSERT(!box.containsPoint(Vec3(0, Sqrt2+1e-10, 0)));
ASSERT(box.containsPoint(Vec3(0, Sqrt2-1e-10, 1e-10)));
ASSERT(!box.containsPoint(Vec3(0, Sqrt2-1e-10, -1e-10)));
}
void verifyCorners(Vec3 expected[8], Vec3 found[8]) {
for (int i = 0; i < 8; i++) {
bool match = false;
for (int j = 0; j < 8 && !match; j++) {
if (abs(expected[i][0]-found[j][0]) < TOL && abs(expected[i][1]-found[j][1]) < TOL && abs(expected[i][2]-found[j][2]) < TOL) {
match = true;
break;
}
}
ASSERT(match);
}
}
void testGetCorners() {
Vec3 corners[8];
OrientedBoundingBox(Vec3(0), Vec3(1, 2, 3)).getCorners(corners);
{
Vec3 expected[] = {Vec3(0), Vec3(1, 0, 0), Vec3(0, 2, 0), Vec3(1, 2, 0), Vec3(0, 0, 3), Vec3(1, 0, 3), Vec3(0, 2, 3), Vec3(1, 2, 3)};
verifyCorners(expected, corners);
}
OrientedBoundingBox(Vec3(3, 2, 1), Vec3(1, 2, 3)).getCorners(corners);
{
Vec3 expected[] = {Vec3(3, 2, 1), Vec3(4, 2, 1), Vec3(3, 4, 1), Vec3(4, 4, 1), Vec3(3, 2, 4), Vec3(4, 2, 4), Vec3(3, 4, 4), Vec3(4, 4, 4)};
verifyCorners(expected, corners);
}
OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1)).getCorners(corners);
{
Real d = 0.5*Sqrt2;
Vec3 expected[] = {Vec3(0), Vec3(-d, d, 0), Vec3(d, d, 0), Vec3(0, Sqrt2, 0), Vec3(0, 0, 1), Vec3(-d, d, 1), Vec3(d, d, 1), Vec3(0, Sqrt2, 1)};
verifyCorners(expected, corners);
}
}
void verifyBoxIntersection(bool shouldIntersect, OrientedBoundingBox box1, OrientedBoundingBox box2) {
ASSERT(box1.intersectsBox(box2) == shouldIntersect);
ASSERT(box2.intersectsBox(box1) == shouldIntersect);
}
void testIntersectsBox() {
// Try boxes with identical orientations.
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(0), Vec3(1, 2, 3)), OrientedBoundingBox(Vec3(0), Vec3(3, 2, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(0), Vec3(1, 2, 3)), OrientedBoundingBox(Vec3(1-1e-10, 2-1e-10, 3-1e-10), Vec3(3, 2, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(0), Vec3(1, 2, 3)), OrientedBoundingBox(Vec3(1+1e-10, 2-1e-10, 3-1e-10), Vec3(3, 2, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(0), Vec3(1, 2, 3)), OrientedBoundingBox(Vec3(1-1e-10, 2+1e-10, 3-1e-10), Vec3(3, 2, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(0), Vec3(1, 2, 3)), OrientedBoundingBox(Vec3(1-1e-10, 2-1e-10, 3+1e-10), Vec3(3, 2, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(0), Vec3(1, 2, 3)), OrientedBoundingBox(Vec3(-3+1e-10, -2+1e-10, -1+1e-10), Vec3(3, 2, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(0), Vec3(1, 2, 3)), OrientedBoundingBox(Vec3(-3-1e-10, -2+1e-10, -1+1e-10), Vec3(3, 2, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(0), Vec3(1, 2, 3)), OrientedBoundingBox(Vec3(-3+1e-10, -2-1e-10, -1+1e-10), Vec3(3, 2, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(0), Vec3(1, 2, 3)), OrientedBoundingBox(Vec3(-3+1e-10, -2+1e-10, -1-1e-10), Vec3(3, 2, 1)));
// Try some rotations by 90 degrees.
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(-0.5, 0, 0), Vec3(1, 2, 3)), OrientedBoundingBox(Rotation(0.5*Pi, ZAxis), Vec3(3, 2, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(-0.5, -2+1e-10, 0), Vec3(1, 2, 3)), OrientedBoundingBox(Rotation(0.5*Pi, ZAxis), Vec3(3, 2, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(-0.5, -2-1e-10, 0), Vec3(1, 2, 3)), OrientedBoundingBox(Rotation(0.5*Pi, ZAxis), Vec3(3, 2, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(-0.5, 3-1e-10, 0), Vec3(1, 2, 3)), OrientedBoundingBox(Rotation(0.5*Pi, ZAxis), Vec3(3, 2, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(-0.5, 3+1e-10, 0), Vec3(1, 2, 3)), OrientedBoundingBox(Rotation(0.5*Pi, ZAxis), Vec3(3, 2, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Rotation(0.5*Pi, ZAxis), Vec3(1, 2, 3)), OrientedBoundingBox(Rotation(0.5*Pi, ZAxis), Vec3(3, 2, 1)));
// Try rotations by 45 degrees.
const Real d = 0.5*Sqrt2;
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(-0.5, 0, 0), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(-0.5, -1+1e-10, 0), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(-0.5, -1-1e-10, 0), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(-0.5, Sqrt2-1e-10, 0), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(-0.5, Sqrt2+1e-10, 0), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(d-1e-10, 0, 0), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(d+1e-10, 0, 0), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(-1-d+1e-10, 0, 0), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(-1-d-1e-10, 0, 0), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(0.25*Pi, ZAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(0, 0, d-1e-10), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(-0.25*Pi, XAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(0, 0, d+1e-10), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(-0.25*Pi, XAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(true, OrientedBoundingBox(Vec3(0, 0, -1-d+1e-10), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(-0.25*Pi, XAxis), Vec3(1, 1, 1)));
verifyBoxIntersection(false, OrientedBoundingBox(Vec3(0, 0, -1-d-1e-10), Vec3(1, 1, 1)), OrientedBoundingBox(Rotation(-0.25*Pi, XAxis), Vec3(1, 1, 1)));
// The following case detects a bug that came up in a different test case.
Rotation r;
r.setRotationToBodyFixedXYZ(Vec3(Pi/2, 0, -1.1));;
verifyBoxIntersection(true, OrientedBoundingBox(Transform(r, Vec3(-0.95, 1.1, 2.5)), Vec3(2e-10, 1.118, 1)), OrientedBoundingBox(Vec3(0, -50, -50), Vec3(100, 100, 100)));
}
void verifyRayIntersection(const OrientedBoundingBox& box, const Vec3& origin, const UnitVec3& direction, bool shouldIntersect, Real expectedDistance) {
Real distance;
ASSERT(shouldIntersect == box.intersectsRay(origin, direction, distance));
assertEqual(expectedDistance, distance);
}
void testIntersectsRay() {
// Try rays starting inside the box.
verifyRayIntersection(OrientedBoundingBox(Transform(), Vec3(1, 2, 3)), Vec3(0.5, 0.5, 0.5), UnitVec3(1, 0, 0), true, 0);
verifyRayIntersection(OrientedBoundingBox(Transform(), Vec3(1, 2, 3)), Vec3(0.5, 0.5, 0.5), UnitVec3(0, 1, 0), true, 0);
verifyRayIntersection(OrientedBoundingBox(Transform(), Vec3(1, 2, 3)), Vec3(0.5, 0.5, 0.5), UnitVec3(0, 0, 1), true, 0);
// Try rays that hit it on various sides.
verifyRayIntersection(OrientedBoundingBox(Transform(), Vec3(1, 2, 3)), Vec3(-1.5, 0.5, 0.5), UnitVec3(1, 0, 0), true, 1.5);
verifyRayIntersection(OrientedBoundingBox(Transform(), Vec3(1, 2, 3)), Vec3(2.5, 0.5, 0.5), UnitVec3(-1, 0, 0), true, 1.5);
verifyRayIntersection(OrientedBoundingBox(Transform(), Vec3(1, 2, 3)), Vec3(0.5, -0.5, 0.5), UnitVec3(0, 1, 0), true, 0.5);
verifyRayIntersection(OrientedBoundingBox(Transform(), Vec3(1, 2, 3)), Vec3(0.5, 2.5, 0.5), UnitVec3(0, -1, 0), true, 0.5);
verifyRayIntersection(OrientedBoundingBox(Transform(), Vec3(1, 2, 3)), Vec3(0.5, 0.5, -1.0), UnitVec3(0, 0, 1), true, 1.0);
verifyRayIntersection(OrientedBoundingBox(Transform(), Vec3(1, 2, 3)), Vec3(0.5, 0.5, 4.0), UnitVec3(0, 0, -1), true, 1.0);
// Try a box at an angle.
verifyRayIntersection(OrientedBoundingBox(Rotation(-0.25*Pi, ZAxis), Vec3(2, 2, 2)), Vec3(0, 0, 0.5), UnitVec3(1, 0, 0), true, 0);
verifyRayIntersection(OrientedBoundingBox(Rotation(-0.25*Pi, ZAxis), Vec3(2, 2, 2)), Vec3(-1, 0, 0.5), UnitVec3(1, 0, 0), true, 1.0);
}
void testCreateFromPoints() {
Random::Uniform random(0, 1);
for (int trial = 0; trial < 100; trial++) {
// Select a volume in which to generate points.
Vec3 size(10*random.getValue(), 10*random.getValue(), 10*random.getValue());
Rotation rotation;
rotation.setRotationToBodyFixedXYZ(Vec3(random.getValue(), random.getValue(), random.getValue()));
Transform transform(rotation, Vec3(10*random.getValue(), 10*random.getValue(), 10*random.getValue()));
// Create a set of points inside it.
int numPoints = (int)(50*random.getValue()+1);
Vector_<Vec3> points(numPoints);
for (int i = 0; i < numPoints; i++)
points[i] = transform*Vec3(size[0]*random.getValue(), size[1]*random.getValue(), size[2]*random.getValue());
// Create a bounding box from them.
OrientedBoundingBox box(points);
// Verify that it contains all the points.
for (int i = 0; i < numPoints; i++) {
ASSERT(box.containsPoint(points[i]));
}
// Verify that it gives a reasonably tight fit to them.
Real expectedVolume = size[0]*size[1]*size[2];
Real volume = box.getSize()[0]*box.getSize()[1]*box.getSize()[2];
ASSERT(volume < 1.5*expectedVolume);
}
}
void testFindNearestPoint() {
Vec3 size(1, 1.5, 3);
Transform trans(Rotation(0.3, XAxis), Vec3(1, 2, 0.5));
OrientedBoundingBox box(trans, size);
// First test some points inside the box.
Random::Uniform random(0, 1);
for (int i = 0; i < 100; i++) {
Vec3 p(random.getValue()*size[0], random.getValue()*size[1], random.getValue()*size[2]);
p = trans*p;
assertEqual(p, box.findNearestPoint(p));
}
// Try some points outside the box.
assertEqual(size, ~trans*box.findNearestPoint(trans*(size+Vec3(1, 2, 3))));
assertEqual(Vec3(1, 1.5, 0.25), ~trans*box.findNearestPoint(trans*Vec3(2, 3, 0.25)));
assertEqual(Vec3(0, 0, 0), ~trans*box.findNearestPoint(trans*Vec3(-1, -1, -2)));
assertEqual(Vec3(0, 0, 0.5), ~trans*box.findNearestPoint(trans*Vec3(-1, -1, 0.5)));
}
int main() {
try {
testContainsPoint();
testGetCorners();
testIntersectsBox();
testIntersectsRay();
testCreateFromPoints();
testFindNearestPoint();
}
catch(const std::exception& e) {
cout << "exception: " << e.what() << endl;
return 1;
}
cout << "Done" << endl;
return 0;
}
|
