1 /*
2 Copyright (c) 2003-2006 Gino van den Bergen / Erwin Coumans http://continuousphysics.com/Bullet/
3
4 This software is provided 'as-is', without any express or implied warranty.
5 In no event will the authors be held liable for any damages arising from the use of this software.
6 Permission is granted to anyone to use this software for any purpose,
7 including commercial applications, and to alter it and redistribute it freely,
8 subject to the following restrictions:
9
10 1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
11 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
12 3. This notice may not be removed or altered from any source distribution.
13 */
14
15 #include "b3GeometryUtil.h"
16
17 /*
18 Make sure this dummy function never changes so that it
19 can be used by probes that are checking whether the
20 library is actually installed.
21 */
22 extern "C"
23 {
24 void b3BulletMathProbe();
25
b3BulletMathProbe()26 void b3BulletMathProbe() {}
27 }
28
isPointInsidePlanes(const b3AlignedObjectArray<b3Vector3> & planeEquations,const b3Vector3 & point,b3Scalar margin)29 bool b3GeometryUtil::isPointInsidePlanes(const b3AlignedObjectArray<b3Vector3>& planeEquations, const b3Vector3& point, b3Scalar margin)
30 {
31 int numbrushes = planeEquations.size();
32 for (int i = 0; i < numbrushes; i++)
33 {
34 const b3Vector3& N1 = planeEquations[i];
35 b3Scalar dist = b3Scalar(N1.dot(point)) + b3Scalar(N1[3]) - margin;
36 if (dist > b3Scalar(0.))
37 {
38 return false;
39 }
40 }
41 return true;
42 }
43
areVerticesBehindPlane(const b3Vector3 & planeNormal,const b3AlignedObjectArray<b3Vector3> & vertices,b3Scalar margin)44 bool b3GeometryUtil::areVerticesBehindPlane(const b3Vector3& planeNormal, const b3AlignedObjectArray<b3Vector3>& vertices, b3Scalar margin)
45 {
46 int numvertices = vertices.size();
47 for (int i = 0; i < numvertices; i++)
48 {
49 const b3Vector3& N1 = vertices[i];
50 b3Scalar dist = b3Scalar(planeNormal.dot(N1)) + b3Scalar(planeNormal[3]) - margin;
51 if (dist > b3Scalar(0.))
52 {
53 return false;
54 }
55 }
56 return true;
57 }
58
59 bool notExist(const b3Vector3& planeEquation, const b3AlignedObjectArray<b3Vector3>& planeEquations);
60
notExist(const b3Vector3 & planeEquation,const b3AlignedObjectArray<b3Vector3> & planeEquations)61 bool notExist(const b3Vector3& planeEquation, const b3AlignedObjectArray<b3Vector3>& planeEquations)
62 {
63 int numbrushes = planeEquations.size();
64 for (int i = 0; i < numbrushes; i++)
65 {
66 const b3Vector3& N1 = planeEquations[i];
67 if (planeEquation.dot(N1) > b3Scalar(0.999))
68 {
69 return false;
70 }
71 }
72 return true;
73 }
74
getPlaneEquationsFromVertices(b3AlignedObjectArray<b3Vector3> & vertices,b3AlignedObjectArray<b3Vector3> & planeEquationsOut)75 void b3GeometryUtil::getPlaneEquationsFromVertices(b3AlignedObjectArray<b3Vector3>& vertices, b3AlignedObjectArray<b3Vector3>& planeEquationsOut)
76 {
77 const int numvertices = vertices.size();
78 // brute force:
79 for (int i = 0; i < numvertices; i++)
80 {
81 const b3Vector3& N1 = vertices[i];
82
83 for (int j = i + 1; j < numvertices; j++)
84 {
85 const b3Vector3& N2 = vertices[j];
86
87 for (int k = j + 1; k < numvertices; k++)
88 {
89 const b3Vector3& N3 = vertices[k];
90
91 b3Vector3 planeEquation, edge0, edge1;
92 edge0 = N2 - N1;
93 edge1 = N3 - N1;
94 b3Scalar normalSign = b3Scalar(1.);
95 for (int ww = 0; ww < 2; ww++)
96 {
97 planeEquation = normalSign * edge0.cross(edge1);
98 if (planeEquation.length2() > b3Scalar(0.0001))
99 {
100 planeEquation.normalize();
101 if (notExist(planeEquation, planeEquationsOut))
102 {
103 planeEquation[3] = -planeEquation.dot(N1);
104
105 //check if inside, and replace supportingVertexOut if needed
106 if (areVerticesBehindPlane(planeEquation, vertices, b3Scalar(0.01)))
107 {
108 planeEquationsOut.push_back(planeEquation);
109 }
110 }
111 }
112 normalSign = b3Scalar(-1.);
113 }
114 }
115 }
116 }
117 }
118
getVerticesFromPlaneEquations(const b3AlignedObjectArray<b3Vector3> & planeEquations,b3AlignedObjectArray<b3Vector3> & verticesOut)119 void b3GeometryUtil::getVerticesFromPlaneEquations(const b3AlignedObjectArray<b3Vector3>& planeEquations, b3AlignedObjectArray<b3Vector3>& verticesOut)
120 {
121 const int numbrushes = planeEquations.size();
122 // brute force:
123 for (int i = 0; i < numbrushes; i++)
124 {
125 const b3Vector3& N1 = planeEquations[i];
126
127 for (int j = i + 1; j < numbrushes; j++)
128 {
129 const b3Vector3& N2 = planeEquations[j];
130
131 for (int k = j + 1; k < numbrushes; k++)
132 {
133 const b3Vector3& N3 = planeEquations[k];
134
135 b3Vector3 n2n3;
136 n2n3 = N2.cross(N3);
137 b3Vector3 n3n1;
138 n3n1 = N3.cross(N1);
139 b3Vector3 n1n2;
140 n1n2 = N1.cross(N2);
141
142 if ((n2n3.length2() > b3Scalar(0.0001)) &&
143 (n3n1.length2() > b3Scalar(0.0001)) &&
144 (n1n2.length2() > b3Scalar(0.0001)))
145 {
146 //point P out of 3 plane equations:
147
148 // d1 ( N2 * N3 ) + d2 ( N3 * N1 ) + d3 ( N1 * N2 )
149 //P = -------------------------------------------------------------------------
150 // N1 . ( N2 * N3 )
151
152 b3Scalar quotient = (N1.dot(n2n3));
153 if (b3Fabs(quotient) > b3Scalar(0.000001))
154 {
155 quotient = b3Scalar(-1.) / quotient;
156 n2n3 *= N1[3];
157 n3n1 *= N2[3];
158 n1n2 *= N3[3];
159 b3Vector3 potentialVertex = n2n3;
160 potentialVertex += n3n1;
161 potentialVertex += n1n2;
162 potentialVertex *= quotient;
163
164 //check if inside, and replace supportingVertexOut if needed
165 if (isPointInsidePlanes(planeEquations, potentialVertex, b3Scalar(0.01)))
166 {
167 verticesOut.push_back(potentialVertex);
168 }
169 }
170 }
171 }
172 }
173 }
174 }
175