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
|
// 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 "Wm5ContSeparatePoints2.h"
#include "Wm5ConvexHull2.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
SeparatePoints2<Real>::SeparatePoints2 (int numPoints0,
const Vector2<Real>* points0, int numPoints1,
const Vector2<Real>* points1, Line2<Real>& separatingLine)
{
// Construct convex hull of point set 0.
ConvexHull2<Real> hull0(numPoints0, (Vector2<Real>*)points0, 0.001f,
false, Query::QT_INT64);
assertion(hull0.GetDimension() == 2,
"Code currently supports only noncollinear points\n");
int numEdges0 = hull0.GetNumSimplices();
const int* edges0 = hull0.GetIndices();
// Construct convex hull of point set 1.
ConvexHull2<Real> hull1(numPoints1,(Vector2<Real>*)points1,0.001f,
false,Query::QT_INT64);
assertion(hull1.GetDimension() == 2,
"Code currently supports only noncollinear points\n");
int numEdges1 = hull1.GetNumSimplices();
const int* edges1 = hull1.GetIndices();
// Test edges of hull 0 for possible separation of points.
int j0, j1, i0, i1, side0, side1;
Vector2<Real> lineNormal;
Real lineConstant;
for (j1 = 0, j0 = numEdges0-1; j1 < numEdges0; j0 = j1++)
{
// Look up edge (assert: i0 != i1 ).
i0 = edges0[j0];
i1 = edges0[j1];
// Compute potential separating line (assert: (xNor,yNor) != (0,0)).
separatingLine.Origin = points0[i0];
separatingLine.Direction = points0[i1] - points0[i0];
separatingLine.Direction.Normalize();
lineNormal = separatingLine.Direction.Perp();
lineConstant = lineNormal.Dot(separatingLine.Origin);
// Determine if hull 1 is on same side of line.
side1 = OnSameSide(lineNormal, lineConstant, numEdges1, edges1,
points1);
if (side1)
{
// Determine which side of line hull 0 lies.
side0 = WhichSide(lineNormal, lineConstant, numEdges0,
edges0, points0);
if (side0*side1 <= 0) // Line separates hulls.
{
mSeparated = true;
return;
}
}
}
// Test edges of hull 1 for possible separation of points.
for (j1 = 0, j0 = numEdges1-1; j1 < numEdges1; j0 = j1++)
{
// Look up edge (assert: i0 != i1 ).
i0 = edges1[j0];
i1 = edges1[j1];
// Compute perpendicular to edge (assert: (xNor,yNor) != (0,0)).
separatingLine.Origin = points1[i0];
separatingLine.Direction = points1[i1] - points1[i0];
separatingLine.Direction.Normalize();
lineNormal = separatingLine.Direction.Perp();
lineConstant = lineNormal.Dot(separatingLine.Origin);
// Determine if hull 0 is on same side of line.
side0 = OnSameSide(lineNormal, lineConstant, numEdges0, edges0,
points0);
if (side0)
{
// Determine which side of line hull 1 lies.
side1 = WhichSide(lineNormal, lineConstant, numEdges1,
edges1, points1);
if (side0*side1 <= 0) // Line separates hulls.
{
mSeparated = true;
return;
}
}
}
mSeparated = false;
}
//----------------------------------------------------------------------------
template <typename Real>
SeparatePoints2<Real>::operator bool ()
{
return mSeparated;
}
//----------------------------------------------------------------------------
template <typename Real>
int SeparatePoints2<Real>::OnSameSide (const Vector2<Real>& lineNormal,
Real lineConstant, int numEdges, const int* edges,
const Vector2<Real>* points)
{
// Test whether all points on same side of line Dot(N,X) = c.
Real c0;
int posSide = 0, negSide = 0;
for (int i1 = 0, i0 = numEdges-1; i1 < numEdges; i0 = i1++)
{
c0 = lineNormal.Dot(points[edges[i0]]);
if (c0 > lineConstant + Math<Real>::ZERO_TOLERANCE)
{
++posSide;
}
else if (c0 < lineConstant - Math<Real>::ZERO_TOLERANCE)
{
++negSide;
}
if (posSide && negSide)
{
// Line splits point set.
return 0;
}
c0 = lineNormal.Dot(points[edges[i1]]);
if (c0 > lineConstant + Math<Real>::ZERO_TOLERANCE)
{
++posSide;
}
else if (c0 < lineConstant - Math<Real>::ZERO_TOLERANCE)
{
++negSide;
}
if (posSide && negSide)
{
// Line splits point set.
return 0;
}
}
return (posSide ? +1 : -1);
}
//----------------------------------------------------------------------------
template <typename Real>
int SeparatePoints2<Real>::WhichSide (const Vector2<Real>& lineNormal,
Real lineConstant, int numEdges, const int* edges,
const Vector2<Real>* points)
{
// Establish which side of line hull is on.
Real c0;
for (int i1 = 0, i0 = numEdges-1; i1 < numEdges; i0 = i1++)
{
c0 = lineNormal.Dot(points[edges[i0]]);
if (c0 > lineConstant + Math<Real>::ZERO_TOLERANCE)
{
// Hull on positive side.
return +1;
}
if (c0 < lineConstant - Math<Real>::ZERO_TOLERANCE)
{
// Hull on negative side.
return -1;
}
c0 = lineNormal.Dot(points[edges[i1]]);
if (c0 > lineConstant + Math<Real>::ZERO_TOLERANCE)
{
// Hull on positive side.
return +1;
}
if (c0 < lineConstant - Math<Real>::ZERO_TOLERANCE)
{
// Hull on negative side.
return -1;
}
}
// Hull is effectively collinear.
return 0;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class SeparatePoints2<float>;
template WM5_MATHEMATICS_ITEM
class SeparatePoints2<double>;
//----------------------------------------------------------------------------
}
|
