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1/*
2 * Copyright (c) Contributors, http://opensimulator.org/
3 * See CONTRIBUTORS.TXT for a full list of copyright holders.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions are met:
7 * * Redistributions of source code must retain the above copyright
8 * notice, this list of conditions and the following disclaimer.
9 * * Redistributions in binary form must reproduce the above copyright
10 * notice, this list of conditions and the following disclaimer in the
11 * documentation and/or other materials provided with the distribution.
12 * * Neither the name of the OpenSim Project nor the
13 * names of its contributors may be used to endorse or promote products
14 * derived from this software without specific prior written permission.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE DEVELOPERS ``AS IS'' AND ANY
17 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
18 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
19 * DISCLAIMED. IN NO EVENT SHALL THE CONTRIBUTORS BE LIABLE FOR ANY
20 * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
21 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
22 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
23 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
25 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 */
27
28using System;
29using OpenSim.Region.Physics.Manager;
30
31namespace OpenSim.Region.Physics.Meshing
32{
33 // A simplex is a section of a straight line.
34 // It is defined by its endpoints, i.e. by two vertices
35 // Operation on vertices are
36 public class Simplex : IComparable<Simplex>
37 {
38 public Vertex v1;
39 public Vertex v2;
40
41 public Simplex(Vertex _v1, Vertex _v2)
42 {
43 v1 = _v1;
44 v2 = _v2;
45 }
46
47 public int CompareTo(Simplex other)
48 {
49 Vertex lv1, lv2, ov1, ov2, temp;
50
51 lv1 = v1;
52 lv2 = v2;
53 ov1 = other.v1;
54 ov2 = other.v2;
55
56 if (lv1 > lv2)
57 {
58 temp = lv1;
59 lv1 = lv2;
60 lv2 = temp;
61 }
62
63 if (ov1 > ov2)
64 {
65 temp = ov1;
66 ov1 = ov2;
67 ov2 = temp;
68 }
69
70 if (lv1 > ov1)
71 {
72 return 1;
73 }
74 if (lv1 < ov1)
75 {
76 return -1;
77 }
78
79 if (lv2 > ov2)
80 {
81 return 1;
82 }
83 if (lv2 < ov2)
84 {
85 return -1;
86 }
87
88 return 0;
89 }
90
91 private static void intersectParameter(PhysicsVector p1, PhysicsVector r1, PhysicsVector p2, PhysicsVector r2,
92 ref float lambda, ref float mu)
93 {
94 // Intersects two straights
95 // p1, p2, points on the straight
96 // r1, r2, directional vectors of the straight. Not necessarily of length 1!
97 // note, that l, m can be scaled such, that the range 0..1 is mapped to the area between two points,
98 // thus allowing to decide whether an intersection is between two points
99
100 float r1x = r1.X;
101 float r1y = r1.Y;
102 float r2x = r2.X;
103 float r2y = r2.Y;
104
105 float denom = r1y*r2x - r1x*r2y;
106
107 float p1x = p1.X;
108 float p1y = p1.Y;
109 float p2x = p2.X;
110 float p2y = p2.Y;
111
112 float z1 = -p2x*r2y + p1x*r2y + (p2y - p1y)*r2x;
113 float z2 = -p2x*r1y + p1x*r1y + (p2y - p1y)*r1x;
114
115 if (denom == 0.0f) // Means the straights are parallel. Either no intersection or an infinite number of them
116 {
117 if (z1 == 0.0f)
118 {
119// Means they are identical -> many, many intersections
120 lambda = Single.NaN;
121 mu = Single.NaN;
122 }
123 else
124 {
125 lambda = Single.PositiveInfinity;
126 mu = Single.PositiveInfinity;
127 }
128 return;
129 }
130
131
132 lambda = z1/denom;
133 mu = z2/denom;
134 }
135
136
137 // Intersects the simplex with another one.
138 // the borders are used to deal with float inaccuracies
139 // As a rule of thumb, the borders are
140 // lowerBorder1 : 0.0
141 // lowerBorder2 : 0.0
142 // upperBorder1 : 1.0
143 // upperBorder2 : 1.0
144 // 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)
145 public static PhysicsVector Intersect(
146 Simplex s1,
147 Simplex s2,
148 float lowerBorder1,
149 float lowerBorder2,
150 float upperBorder1,
151 float upperBorder2)
152 {
153 PhysicsVector firstSimplexDirection = s1.v2 - s1.v1;
154 PhysicsVector secondSimplexDirection = s2.v2 - s2.v1;
155
156 float lambda = 0.0f;
157 float mu = 0.0f;
158
159 // Give us the parameters of an intersection. This subroutine does *not* take the constraints
160 // (intersection must be between v1 and v2 and it must be in the positive direction of the ray)
161 // into account. We do that afterwards.
162 intersectParameter(s1.v1, firstSimplexDirection, s2.v1, secondSimplexDirection, ref lambda, ref mu);
163
164 if (Single.IsInfinity(lambda)) // Special case. No intersection at all. directions parallel.
165 return null;
166
167 if (Single.IsNaN(lambda)) // Special case. many, many intersections.
168 return null;
169
170 if (lambda > upperBorder1) // We're behind v2
171 return null;
172
173 if (lambda < lowerBorder1)
174 return null;
175
176 if (mu < lowerBorder2) // outside simplex 2
177 return null;
178
179 if (mu > upperBorder2) // outside simplex 2
180 return null;
181
182 return s1.v1 + lambda*firstSimplexDirection;
183 }
184
185 // Intersects the simplex with a ray. The ray is defined as all p=origin + lambda*direction
186 // where lambda >= 0
187 public PhysicsVector RayIntersect(Vertex origin, PhysicsVector direction, bool bEndsIncluded)
188 {
189 PhysicsVector simplexDirection = v2 - v1;
190
191 float lambda = 0.0f;
192 float mu = 0.0f;
193
194 // Give us the parameters of an intersection. This subroutine does *not* take the constraints
195 // (intersection must be between v1 and v2 and it must be in the positive direction of the ray)
196 // into account. We do that afterwards.
197 intersectParameter(v1, simplexDirection, origin, direction, ref lambda, ref mu);
198
199 if (Single.IsInfinity(lambda)) // Special case. No intersection at all. directions parallel.
200 return null;
201
202 if (Single.IsNaN(lambda)) // Special case. many, many intersections.
203 return null;
204
205 if (mu < 0.0) // We're on the wrong side of the ray
206 return null;
207
208 if (lambda > 1.0) // We're behind v2
209 return null;
210
211 if (lambda == 1.0 && !bEndsIncluded)
212 return null; // The end of the simplices are not included
213
214 if (lambda < 0.0f) // we're before v1;
215 return null;
216
217 return v1 + lambda*simplexDirection;
218 }
219 }
220}
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