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
|
// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.1 (2010/10/01)
#include "Wm5MathematicsPCH.h"
#include "Wm5IntrTriangle3Box3.h"
#include "Wm5IntrSegment3Box3.h"
#include "Wm5IntrUtility3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrTriangle3Box3<Real>::IntrTriangle3Box3 (const Triangle3<Real>& triangle,
const Box3<Real>& box)
:
mTriangle(&triangle),
mBox(&box)
{
mQuantity = 0;
}
//----------------------------------------------------------------------------
template <typename Real>
const Triangle3<Real>& IntrTriangle3Box3<Real>::GetTriangle () const
{
return *mTriangle;
}
//----------------------------------------------------------------------------
template <typename Real>
const Box3<Real>& IntrTriangle3Box3<Real>::GetBox () const
{
return *mBox;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrTriangle3Box3<Real>::Test ()
{
Real min0, max0, min1, max1;
Vector3<Real> D, edge[3];
// Test direction of triangle normal.
edge[0] = mTriangle->V[1] - mTriangle->V[0];
edge[1] = mTriangle->V[2] - mTriangle->V[0];
D = edge[0].Cross(edge[1]);
min0 = D.Dot(mTriangle->V[0]);
max0 = min0;
IntrAxis<Real>::GetProjection(D, *mBox, min1, max1);
if (max1 < min0 || max0 < min1)
{
return false;
}
// Test direction of box faces.
for (int i = 0; i < 3; ++i)
{
D = mBox->Axis[i];
IntrAxis<Real>::GetProjection(D, *mTriangle, min0, max0);
Real DdC = D.Dot(mBox->Center);
min1 = DdC - mBox->Extent[i];
max1 = DdC + mBox->Extent[i];
if (max1 < min0 || max0 < min1)
{
return false;
}
}
// Test direction of triangle-box edge cross products.
edge[2] = edge[1] - edge[0];
for (int i0 = 0; i0 < 3; ++i0)
{
for (int i1 = 0; i1 < 3; ++i1)
{
D = edge[i0].Cross(mBox->Axis[i1]);
IntrAxis<Real>::GetProjection(D, *mTriangle, min0, max0);
IntrAxis<Real>::GetProjection(D, *mBox, min1, max1);
if (max1 < min0 || max0 < min1)
{
return false;
}
}
}
return true;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrTriangle3Box3<Real>::Find ()
{
// Start with the triangle and clip it against each face of the box.
mQuantity = 3;
for (int i = 0; i < 3; ++i)
{
mPoint[i] = mTriangle->V[i];
}
for (int dir = -1; dir <= 1; dir += 2)
{
for (int side = 0; side < 3; ++side)
{
Vector3<Real> innerNormal = ((Real)dir)*mBox->Axis[side];
Real constant = innerNormal.Dot(mBox->Center) -
mBox->Extent[side];
ClipConvexPolygonAgainstPlane(innerNormal, constant,
mQuantity, mPoint);
}
}
return mQuantity > 0;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrTriangle3Box3<Real>::Test (Real tmax,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
// Process as if triangle is stationary, box is moving.
Vector3<Real> relVelocity = velocity1 - velocity0;
mContactTime = (Real)0;
Real tlast = Math<Real>::MAX_REAL;
// Test direction of triangle normal.
Vector3<Real> edge[3] =
{
mTriangle->V[1] - mTriangle->V[0],
mTriangle->V[2] - mTriangle->V[0],
mTriangle->V[2] - mTriangle->V[1]
};
Vector3<Real> D = edge[0].Cross(edge[1]);
if (!IntrAxis<Real>::Test(D, *mTriangle, *mBox, relVelocity, tmax,
mContactTime, tlast))
{
return false;
}
// Test direction of box faces.
for (int i = 0; i < 3; ++i)
{
D = mBox->Axis[i];
if (!IntrAxis<Real>::Test(D, *mTriangle, *mBox, relVelocity, tmax,
mContactTime, tlast))
{
return false;
}
}
// Test direction of triangle-box edge cross products.
for (int i0 = 0; i0 < 3; ++i0)
{
for (int i1 = 0; i1 < 3; ++i1)
{
D = edge[i0].Cross(mBox->Axis[i1]);
if (!IntrAxis<Real>::Test(D, *mTriangle, *mBox, relVelocity,
tmax, mContactTime, tlast))
{
return false;
}
}
}
return true;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrTriangle3Box3<Real>::Find (Real tmax,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
// Process as if triangle is stationary, box is moving.
Vector3<Real> relVelocity = velocity1 - velocity0;
mContactTime = (Real)0;
Real tlast = Math<Real>::MAX_REAL;
int side = IntrConfiguration<Real>::NONE;
IntrConfiguration<Real> triContact, boxContact;
// Test tri-normal.
Vector3<Real> edge[3] =
{
mTriangle->V[1] - mTriangle->V[0],
mTriangle->V[2] - mTriangle->V[1],
mTriangle->V[0] - mTriangle->V[2]
};
Vector3<Real> triNorm = edge[0].Cross(edge[1]);
if (!IntrAxis<Real>::Find(triNorm, *mTriangle, *mBox, relVelocity, tmax,
mContactTime, tlast, side, triContact, boxContact))
{
return false;
}
Vector3<Real> axis;
int coplanar = -1; // triangle coplanar to none of the box normals
int i0;
for (i0 = 0; i0 < 3; ++i0)
{
axis = mBox->Axis[i0];
if (!IntrAxis<Real>::Find(axis, *mTriangle, *mBox, relVelocity,
tmax, mContactTime, tlast, side, triContact, boxContact))
{
return false;
}
// Test if axis is parallel to triangle normal. The test is:
// sin(Angle(normal,axis)) < epsilon
Real NdA = triNorm.Dot(axis);
Real NdN = triNorm.SquaredLength();
Real AdA = axis.SquaredLength();
Real sn = Math<Real>::Sqrt(Math<Real>::FAbs((Real)1 -
NdA*NdA/(NdN*AdA)));
if (sn < Math<Real>::ZERO_TOLERANCE)
{
coplanar = i0;
}
}
if (coplanar == -1)
{
// Test triedges cross boxfaces.
for (i0 = 0; i0 < 3; ++i0)
{
for (int i1 = 0; i1 < 3; ++i1)
{
axis = edge[i0].Cross(mBox->Axis[i1]);
if (!IntrAxis<Real>::Find(axis, *mTriangle, *mBox,
relVelocity, tmax, mContactTime, tlast, side, triContact,
boxContact))
{
return false;
}
}
}
}
else
{
// Test triedges cross coplanar box axis.
for (i0 = 0; i0 < 3; ++i0)
{
axis = edge[i0].Cross(triNorm);
if (!IntrAxis<Real>::Find(axis, *mTriangle, *mBox, relVelocity,
tmax, mContactTime, tlast, side, triContact, boxContact))
{
return false;
}
}
}
// Test velocity cross box faces.
for (i0 = 0; i0 < 3; ++i0)
{
axis = relVelocity.Cross(mBox->Axis[i0]);
if (!IntrAxis<Real>::Find(axis, *mTriangle, *mBox, relVelocity,
tmax, mContactTime, tlast, side, triContact, boxContact))
{
return false;
}
}
if (mContactTime < (Real)0 || side == IntrConfiguration<Real>::NONE)
{
return false;
}
FindContactSet<Real>(*mTriangle, *mBox, side, triContact, boxContact,
velocity0, velocity1, mContactTime, mQuantity, mPoint);
return true;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntrTriangle3Box3<Real>::GetQuantity () const
{
return mQuantity;
}
//----------------------------------------------------------------------------
template <typename Real>
const Vector3<Real>& IntrTriangle3Box3<Real>::GetPoint (int i) const
{
return mPoint[i];
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrTriangle3Box3<float>;
template WM5_MATHEMATICS_ITEM
class IntrTriangle3Box3<double>;
//----------------------------------------------------------------------------
}
|
