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
|
using System;
using System.Collections.Generic;
using System.Text;
using OpenSim.Region.Physics.Manager;
namespace OpenSim.Region.Physics.Meshing
{
// A simplex is a section of a straight line.
// It is defined by its endpoints, i.e. by two vertices
// Operation on vertices are
public class Simplex : IComparable<Simplex>
{
public Vertex v1;
public Vertex v2;
public Simplex(Vertex _v1, Vertex _v2)
{
v1 = _v1;
v2 = _v2;
}
public int CompareTo(Simplex other)
{
Vertex lv1, lv2, ov1, ov2, temp;
lv1 = v1;
lv2 = v2;
ov1 = other.v1;
ov2 = other.v2;
if (lv1 > lv2)
{
temp = lv1;
lv1 = lv2;
lv2 = temp;
}
if (ov1 > ov2)
{
temp = ov1;
ov1 = ov2;
ov2 = temp;
}
if (lv1 > ov1)
{
return 1;
}
if (lv1 < ov1)
{
return -1;
}
if (lv2 > ov2)
{
return 1;
}
if (lv2 < ov2)
{
return -1;
}
return 0;
}
private static void intersectParameter(PhysicsVector p1, PhysicsVector r1, PhysicsVector p2, PhysicsVector r2, ref float lambda, ref float mu)
{
// Intersects two straights
// p1, p2, points on the straight
// r1, r2, directional vectors of the straight. Not necessarily of length 1!
// note, that l, m can be scaled such, that the range 0..1 is mapped to the area between two points,
// thus allowing to decide whether an intersection is between two points
float r1x = r1.X;
float r1y = r1.Y;
float r2x = r2.X;
float r2y = r2.Y;
float denom = r1y*r2x - r1x*r2y;
float p1x = p1.X;
float p1y = p1.Y;
float p2x = p2.X;
float p2y = p2.Y;
float z1=-p2x * r2y + p1x * r2y + (p2y - p1y) * r2x;
float z2=-p2x * r1y + p1x * r1y + (p2y - p1y) * r1x;
if (denom == 0.0f) // Means the straights are parallel. Either no intersection or an infinite number of them
{
if (z1==0.0f) {// Means they are identical -> many, many intersections
lambda = Single.NaN;
mu = Single.NaN;
} else {
lambda = Single.PositiveInfinity;
mu = Single.PositiveInfinity;
}
return;
}
lambda = z1 / denom;
mu = z2 / denom;
}
// Intersects the simplex with another one.
// the borders are used to deal with float inaccuracies
// As a rule of thumb, the borders are
// lowerBorder1 : 0.0
// lowerBorder2 : 0.0
// upperBorder1 : 1.0
// upperBorder2 : 1.0
// Set these to values near the given parameters (e.g. 0.001 instead of 1 to exclude simplex starts safely, or to -0.001 to include them safely)
public static PhysicsVector Intersect(
Simplex s1,
Simplex s2,
float lowerBorder1,
float lowerBorder2,
float upperBorder1,
float upperBorder2)
{
PhysicsVector firstSimplexDirection = s1.v2 - s1.v1;
PhysicsVector secondSimplexDirection = s2.v2 - s2.v1;
float lambda = 0.0f;
float mu = 0.0f;
// Give us the parameters of an intersection. This subroutine does *not* take the constraints
// (intersection must be between v1 and v2 and it must be in the positive direction of the ray)
// into account. We do that afterwards.
intersectParameter(s1.v1, firstSimplexDirection, s2.v1, secondSimplexDirection, ref lambda, ref mu);
if (Single.IsInfinity(lambda)) // Special case. No intersection at all. directions parallel.
return null;
if (Single.IsNaN(lambda)) // Special case. many, many intersections.
return null;
if (lambda > upperBorder1) // We're behind v2
return null;
if (lambda < lowerBorder1)
return null;
if (mu < lowerBorder2) // outside simplex 2
return null;
if (mu > upperBorder2) // outside simplex 2
return null;
return s1.v1 + lambda * firstSimplexDirection;
}
// Intersects the simplex with a ray. The ray is defined as all p=origin + lambda*direction
// where lambda >= 0
public PhysicsVector RayIntersect(Vertex origin, PhysicsVector direction, bool bEndsIncluded)
{
PhysicsVector simplexDirection = v2 - v1;
float lambda = 0.0f;
float mu = 0.0f;
// Give us the parameters of an intersection. This subroutine does *not* take the constraints
// (intersection must be between v1 and v2 and it must be in the positive direction of the ray)
// into account. We do that afterwards.
intersectParameter(v1, simplexDirection, origin, direction, ref lambda, ref mu);
if (Single.IsInfinity(lambda)) // Special case. No intersection at all. directions parallel.
return null;
if (Single.IsNaN(lambda)) // Special case. many, many intersections.
return null;
if (mu < 0.0) // We're on the wrong side of the ray
return null;
if (lambda > 1.0) // We're behind v2
return null;
if (lambda == 1.0 && !bEndsIncluded)
return null; // The end of the simplices are not included
if (lambda < 0.0f) // we're before v1;
return null;
return this.v1 + lambda * simplexDirection;
}
}
}
|
