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
|
// 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 "Wm5IntrLine2Triangle2.h"
#include "Wm5Intersector1.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrLine2Triangle2<Real>::IntrLine2Triangle2 (const Line2<Real>& line,
const Triangle2<Real>& triangle)
:
mLine(&line),
mTriangle(&triangle)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Line2<Real>& IntrLine2Triangle2<Real>::GetLine () const
{
return *mLine;
}
//----------------------------------------------------------------------------
template <typename Real>
const Triangle2<Real>& IntrLine2Triangle2<Real>::GetTriangle () const
{
return *mTriangle;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrLine2Triangle2<Real>::Test ()
{
Real dist[3];
int sign[3], positive, negative, zero;
TriangleLineRelations(mLine->Origin, mLine->Direction, *mTriangle,
dist, sign, positive, negative, zero);
if (positive == 3 || negative == 3)
{
mIntersectionType = IT_EMPTY;
}
else
{
Real param[2];
GetInterval(mLine->Origin, mLine->Direction, *mTriangle, dist,
sign, param);
Intersector1<Real> intr(param[0], param[1],
-Math<Real>::MAX_REAL, +Math<Real>::MAX_REAL);
intr.Find();
mQuantity = intr.GetNumIntersections();
if (mQuantity == 2)
{
mIntersectionType = IT_SEGMENT;
}
else if (mQuantity == 1)
{
mIntersectionType = IT_POINT;
}
else
{
mIntersectionType = IT_EMPTY;
}
}
return mIntersectionType != IT_EMPTY;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrLine2Triangle2<Real>::Find ()
{
Real dist[3];
int sign[3], positive, negative, zero;
TriangleLineRelations(mLine->Origin, mLine->Direction, *mTriangle,
dist, sign, positive, negative, zero);
if (positive == 3 || negative == 3)
{
// No intersections.
mQuantity = 0;
mIntersectionType = IT_EMPTY;
}
else
{
Real param[2];
GetInterval(mLine->Origin, mLine->Direction, *mTriangle, dist,
sign, param);
Intersector1<Real> intr(param[0], param[1],
-Math<Real>::MAX_REAL, +Math<Real>::MAX_REAL);
intr.Find();
mQuantity = intr.GetNumIntersections();
if (mQuantity == 2)
{
// Segment intersection.
mIntersectionType = IT_SEGMENT;
mPoint[0] = mLine->Origin +
intr.GetIntersection(0)*mLine->Direction;
mPoint[1] = mLine->Origin +
intr.GetIntersection(1)*mLine->Direction;
}
else if (mQuantity == 1)
{
// Point intersection.
mIntersectionType = IT_POINT;
mPoint[0] = mLine->Origin +
intr.GetIntersection(0)*mLine->Direction;
}
else
{
// No intersections.
mIntersectionType = IT_EMPTY;
}
}
return mIntersectionType != IT_EMPTY;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntrLine2Triangle2<Real>::GetQuantity () const
{
return mQuantity;
}
//----------------------------------------------------------------------------
template <typename Real>
const Vector2<Real>& IntrLine2Triangle2<Real>::GetPoint (int i) const
{
return mPoint[i];
}
//----------------------------------------------------------------------------
template <typename Real>
void IntrLine2Triangle2<Real>::TriangleLineRelations (
const Vector2<Real>& origin, const Vector2<Real>& direction,
const Triangle2<Real>& triangle, Real dist[3], int sign[3],
int& positive, int& negative, int& zero)
{
positive = 0;
negative = 0;
zero = 0;
for (int i = 0; i < 3; ++i)
{
Vector2<Real> diff = triangle.V[i] - origin;
dist[i] = diff.DotPerp(direction);
if (dist[i] > Math<Real>::ZERO_TOLERANCE)
{
sign[i] = 1;
++positive;
}
else if (dist[i] < -Math<Real>::ZERO_TOLERANCE)
{
sign[i] = -1;
++negative;
}
else
{
dist[i] = (Real)0;
sign[i] = 0;
++zero;
}
}
}
//----------------------------------------------------------------------------
template <typename Real>
void IntrLine2Triangle2<Real>::GetInterval (const Vector2<Real>& origin,
const Vector2<Real>& direction, const Triangle2<Real>& triangle,
const Real dist[3], const int sign[3], Real param[2])
{
// Project triangle onto line.
Real proj[3];
int i;
for (i = 0; i < 3; ++i)
{
Vector2<Real> diff = triangle.V[i] - origin;
proj[i] = direction.Dot(diff);
}
// Compute transverse intersections of triangle edges with line.
Real numer, denom;
int i0, i1, i2;
int quantity = 0;
for (i0 = 2, i1 = 0; i1 < 3; i0 = i1++)
{
if (sign[i0]*sign[i1] < 0)
{
assertion(quantity < 2, "Too many intersections\n");
numer = dist[i0]*proj[i1] - dist[i1]*proj[i0];
denom = dist[i0] - dist[i1];
param[quantity++] = numer/denom;
}
}
// Check for grazing contact.
if (quantity < 2)
{
for (i0 = 1, i1 = 2, i2 = 0; i2 < 3; i0 = i1, i1 = i2++)
{
if (sign[i2] == 0)
{
assertion(quantity < 2, "Too many intersections\n");
param[quantity++] = proj[i2];
}
}
}
// Sort.
assertion(quantity >= 1, "Need at least one intersection\n");
if (quantity == 2)
{
if (param[0] > param[1])
{
Real save = param[0];
param[0] = param[1];
param[1] = save;
}
}
else
{
param[1] = param[0];
}
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrLine2Triangle2<float>;
template WM5_MATHEMATICS_ITEM
class IntrLine2Triangle2<double>;
//----------------------------------------------------------------------------
}
|
