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
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
|
/*
* Copyright (c) Contributors, http://opensimulator.org/
* See CONTRIBUTORS.TXT for a full list of copyright holders.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of the OpenSimulator Project nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE DEVELOPERS ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE CONTRIBUTORS BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using OpenMetaverse;
using OpenSim.Region.PhysicsModule.SharedBase;
using OpenSim.Region.PhysicsModule.Meshing;
public class Vertex : IComparable<Vertex>
{
Vector3 vector;
public float X
{
get { return vector.X; }
set { vector.X = value; }
}
public float Y
{
get { return vector.Y; }
set { vector.Y = value; }
}
public float Z
{
get { return vector.Z; }
set { vector.Z = value; }
}
public Vertex(float x, float y, float z)
{
vector.X = x;
vector.Y = y;
vector.Z = z;
}
public Vertex normalize()
{
float tlength = vector.Length();
if (tlength != 0f)
{
float mul = 1.0f / tlength;
return new Vertex(vector.X * mul, vector.Y * mul, vector.Z * mul);
}
else
{
return new Vertex(0f, 0f, 0f);
}
}
public Vertex cross(Vertex v)
{
return new Vertex(vector.Y * v.Z - vector.Z * v.Y, vector.Z * v.X - vector.X * v.Z, vector.X * v.Y - vector.Y * v.X);
}
// disable warning: mono compiler moans about overloading
// operators hiding base operator but should not according to C#
// language spec
#pragma warning disable 0108
public static Vertex operator *(Vertex v, Quaternion q)
{
// From http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/transforms/
Vertex v2 = new Vertex(0f, 0f, 0f);
v2.X = q.W * q.W * v.X +
2f * q.Y * q.W * v.Z -
2f * q.Z * q.W * v.Y +
q.X * q.X * v.X +
2f * q.Y * q.X * v.Y +
2f * q.Z * q.X * v.Z -
q.Z * q.Z * v.X -
q.Y * q.Y * v.X;
v2.Y =
2f * q.X * q.Y * v.X +
q.Y * q.Y * v.Y +
2f * q.Z * q.Y * v.Z +
2f * q.W * q.Z * v.X -
q.Z * q.Z * v.Y +
q.W * q.W * v.Y -
2f * q.X * q.W * v.Z -
q.X * q.X * v.Y;
v2.Z =
2f * q.X * q.Z * v.X +
2f * q.Y * q.Z * v.Y +
q.Z * q.Z * v.Z -
2f * q.W * q.Y * v.X -
q.Y * q.Y * v.Z +
2f * q.W * q.X * v.Y -
q.X * q.X * v.Z +
q.W * q.W * v.Z;
return v2;
}
public static Vertex operator +(Vertex v1, Vertex v2)
{
return new Vertex(v1.X + v2.X, v1.Y + v2.Y, v1.Z + v2.Z);
}
public static Vertex operator -(Vertex v1, Vertex v2)
{
return new Vertex(v1.X - v2.X, v1.Y - v2.Y, v1.Z - v2.Z);
}
public static Vertex operator *(Vertex v1, Vertex v2)
{
return new Vertex(v1.X * v2.X, v1.Y * v2.Y, v1.Z * v2.Z);
}
public static Vertex operator +(Vertex v1, float am)
{
v1.X += am;
v1.Y += am;
v1.Z += am;
return v1;
}
public static Vertex operator -(Vertex v1, float am)
{
v1.X -= am;
v1.Y -= am;
v1.Z -= am;
return v1;
}
public static Vertex operator *(Vertex v1, float am)
{
v1.X *= am;
v1.Y *= am;
v1.Z *= am;
return v1;
}
public static Vertex operator /(Vertex v1, float am)
{
if (am == 0f)
{
return new Vertex(0f,0f,0f);
}
float mul = 1.0f / am;
v1.X *= mul;
v1.Y *= mul;
v1.Z *= mul;
return v1;
}
#pragma warning restore 0108
public float dot(Vertex v)
{
return X * v.X + Y * v.Y + Z * v.Z;
}
public Vertex(Vector3 v)
{
vector = v;
}
public Vertex Clone()
{
return new Vertex(X, Y, Z);
}
public static Vertex FromAngle(double angle)
{
return new Vertex((float) Math.Cos(angle), (float) Math.Sin(angle), 0.0f);
}
public float Length()
{
return vector.Length();
}
public virtual bool Equals(Vertex v, float tolerance)
{
Vertex diff = this - v;
float d = diff.Length();
if (d < tolerance)
return true;
return false;
}
public int CompareTo(Vertex other)
{
if (X < other.X)
return -1;
if (X > other.X)
return 1;
if (Y < other.Y)
return -1;
if (Y > other.Y)
return 1;
if (Z < other.Z)
return -1;
if (Z > other.Z)
return 1;
return 0;
}
public static bool operator >(Vertex me, Vertex other)
{
return me.CompareTo(other) > 0;
}
public static bool operator <(Vertex me, Vertex other)
{
return me.CompareTo(other) < 0;
}
public String ToRaw()
{
// Why this stuff with the number formatter?
// Well, the raw format uses the english/US notation of numbers
// where the "," separates groups of 1000 while the "." marks the border between 1 and 10E-1.
// The german notation uses these characters exactly vice versa!
// The Float.ToString() routine is a localized one, giving different results depending on the country
// settings your machine works with. Unusable for a machine readable file format :-(
NumberFormatInfo nfi = new NumberFormatInfo();
nfi.NumberDecimalSeparator = ".";
nfi.NumberDecimalDigits = 3;
String s1 = X.ToString("N2", nfi) + " " + Y.ToString("N2", nfi) + " " + Z.ToString("N2", nfi);
return s1;
}
}
public class Triangle
{
public Vertex v1;
public Vertex v2;
public Vertex v3;
private float radius_square;
private float cx;
private float cy;
public Triangle(Vertex _v1, Vertex _v2, Vertex _v3)
{
v1 = _v1;
v2 = _v2;
v3 = _v3;
CalcCircle();
}
public bool isInCircle(float x, float y)
{
float dx, dy;
float dd;
dx = x - cx;
dy = y - cy;
dd = dx*dx + dy*dy;
if (dd < radius_square)
return true;
else
return false;
}
public bool isDegraded()
{
// This means, the vertices of this triangle are somewhat strange.
// They either line up or at least two of them are identical
return (radius_square == 0.0);
}
private void CalcCircle()
{
// Calculate the center and the radius of a circle given by three points p1, p2, p3
// It is assumed, that the triangles vertices are already set correctly
double p1x, p2x, p1y, p2y, p3x, p3y;
// Deviation of this routine:
// A circle has the general equation (M-p)^2=r^2, where M and p are vectors
// this gives us three equations f(p)=r^2, each for one point p1, p2, p3
// putting respectively two equations together gives two equations
// f(p1)=f(p2) and f(p1)=f(p3)
// bringing all constant terms to one side brings them to the form
// M*v1=c1 resp.M*v2=c2 where v1=(p1-p2) and v2=(p1-p3) (still vectors)
// and c1, c2 are scalars (Naming conventions like the variables below)
// Now using the equations that are formed by the components of the vectors
// and isolate Mx lets you make one equation that only holds My
// The rest is straight forward and eaasy :-)
//
/* helping variables for temporary results */
double c1, c2;
double v1x, v1y, v2x, v2y;
double z, n;
double rx, ry;
// Readout the three points, the triangle consists of
p1x = v1.X;
p1y = v1.Y;
p2x = v2.X;
p2y = v2.Y;
p3x = v3.X;
p3y = v3.Y;
/* calc helping values first */
c1 = (p1x*p1x + p1y*p1y - p2x*p2x - p2y*p2y)/2;
c2 = (p1x*p1x + p1y*p1y - p3x*p3x - p3y*p3y)/2;
v1x = p1x - p2x;
v1y = p1y - p2y;
v2x = p1x - p3x;
v2y = p1y - p3y;
z = (c1*v2x - c2*v1x);
n = (v1y*v2x - v2y*v1x);
if (n == 0.0) // This is no triangle, i.e there are (at least) two points at the same location
{
radius_square = 0.0f;
return;
}
cy = (float) (z/n);
if (v2x != 0.0)
{
cx = (float) ((c2 - v2y*cy)/v2x);
}
else if (v1x != 0.0)
{
cx = (float) ((c1 - v1y*cy)/v1x);
}
else
{
Debug.Assert(false, "Malformed triangle"); /* Both terms zero means nothing good */
}
rx = (p1x - cx);
ry = (p1y - cy);
radius_square = (float) (rx*rx + ry*ry);
}
public override String ToString()
{
NumberFormatInfo nfi = new NumberFormatInfo();
nfi.CurrencyDecimalDigits = 2;
nfi.CurrencyDecimalSeparator = ".";
String s1 = "<" + v1.X.ToString(nfi) + "," + v1.Y.ToString(nfi) + "," + v1.Z.ToString(nfi) + ">";
String s2 = "<" + v2.X.ToString(nfi) + "," + v2.Y.ToString(nfi) + "," + v2.Z.ToString(nfi) + ">";
String s3 = "<" + v3.X.ToString(nfi) + "," + v3.Y.ToString(nfi) + "," + v3.Z.ToString(nfi) + ">";
return s1 + ";" + s2 + ";" + s3;
}
public Vector3 getNormal()
{
// Vertices
// Vectors for edges
Vector3 e1;
Vector3 e2;
e1 = new Vector3(v1.X - v2.X, v1.Y - v2.Y, v1.Z - v2.Z);
e2 = new Vector3(v1.X - v3.X, v1.Y - v3.Y, v1.Z - v3.Z);
// Cross product for normal
Vector3 n = Vector3.Cross(e1, e2);
// Length
float l = n.Length();
// Normalized "normal"
n = n/l;
return n;
}
public void invertNormal()
{
Vertex vt;
vt = v1;
v1 = v2;
v2 = vt;
}
// Dumps a triangle in the "raw faces" format, blender can import. This is for visualisation and
// debugging purposes
public String ToStringRaw()
{
String output = v1.ToRaw() + " " + v2.ToRaw() + " " + v3.ToRaw();
return output;
}
}
|