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
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
|
/**
\file Welder.cpp
\author Morgan McGuire, Kyle Whitson, Corey Taylor
\created 2008-07-30
\edited 2011-07-04
*/
#include "G3D/platform.h"
#include "G3D/Vector2.h"
#include "G3D/Vector3.h"
#include "G3D/Sphere.h"
#include "G3D/PointHashGrid.h"
#include "G3D/Welder.h"
#include "G3D/Stopwatch.h" // for profiling
#include "G3D/AreaMemoryManager.h"
#include "G3D/Any.h"
#include "G3D/stringutils.h"
#include "G3D/BinaryInput.h"
#include "G3D/BinaryOutput.h"
namespace G3D { namespace _internal{
// Uncomment to print information that can help with performance
// profiling.
//#define VERBOSE
/** Used by WeldHelper2::smoothNormals. */
class VN {
public:
Vector3 vertex;
Vector3 normal;
VN() {}
VN(const Vector3& v, const Vector3& n) : vertex(v), normal(n) {}
};
/** Used by WeldHelper::getIndex to maintain a list of vertices by location. */
class VNTi {
public:
Vector3 vertex;
Vector3 normal;
Vector2 texCoord;
int index;
VNTi() : index(0) {}
VNTi(const Vector3& v, const Vector3& n, const Vector2& t, int i) :
vertex(v), normal(n), texCoord(t), index(i) {}
};
}} // G3D
template <> struct HashTrait <G3D::_internal::VN> {
static size_t hashCode(const G3D::_internal::VN& k) { return static_cast<size_t>(k.vertex.hashCode()); }
};
template <> struct HashTrait <G3D::_internal::VNTi> {
static size_t hashCode(const G3D::_internal::VNTi& k) { return static_cast<size_t>(k.vertex.hashCode()); }
};
template<> struct EqualsTrait <G3D::_internal::VN> {
static bool equals(const G3D::_internal::VN& a, const G3D::_internal::VN& b) { return a.vertex == b.vertex; }
};
template<> struct EqualsTrait <G3D::_internal::VNTi> {
static bool equals(const G3D::_internal::VNTi& a, const G3D::_internal::VNTi& b) { return a.vertex == b.vertex; }
};
template<> struct PositionTrait<G3D::_internal::VN> {
static void getPosition(const G3D::_internal::VN& v, G3D::Vector3& p) { p = v.vertex; }
};
template<> struct PositionTrait<G3D::_internal::VNTi> {
static void getPosition(const G3D::_internal::VNTi& v, G3D::Vector3& p) { p = v.vertex; }
};
namespace G3D { namespace _internal {
class WeldHelper {
private:
/** Used by getIndex and updateTriLists. Deallocating this is slow. */
PointHashGrid<VNTi> weldGrid;
Array<Vector3>* outputVertexArray;
Array<Vector3>* outputNormalArray;
Array<Vector2>* outputTexCoordArray;
float vertexWeldRadius;
/** Squared radius allowed for welding similar normals. */
float normalWeldRadius2;
float texCoordWeldRadius2;
float normalSmoothingAngle;
/**
Returns the index of the vertex in
outputVertexArray/outputNormalArray/outputTexCoordArray
that is within the global tolerances of v,n,t. If there
is no such vertex, adds it to the arrays and returns that index.
Called from updateTriLists().
*/
int getIndex(const Vector3& v, const Vector3& n, const Vector2& t) {
PointHashGrid<VNTi>::SphereIterator it =
weldGrid.begin(Sphere(v, vertexWeldRadius));
if (n.isZero()) {
// Don't bother trying to match the surface normal, since this vertex has no surface normal.
while (it.isValid()) {
if ((t - it->texCoord).squaredLength() <= texCoordWeldRadius2) {
// This is the vertex
return it->index;
}
++it;
}
} else {
while (it.isValid()) {
if (((n - it->normal).squaredLength() <= normalWeldRadius2) &&
((t - it->texCoord).squaredLength() <= texCoordWeldRadius2)) {
// This is the vertex
return it->index;
}
++it;
}
}
// Note that a sliver triangle processed before its neighbors may reach here
// with a zero length normal.
// The vertex does not exist. Create it.
const int i = outputVertexArray->size();
outputVertexArray->append(v);
outputNormalArray->append(n);
outputTexCoordArray->append(t);
// Store in the grid so that it will be remembered.
weldGrid.insert(VNTi(v, n, t, i));
return i;
}
/**
Updates each indexArray to refer to vertices in the
outputVertexArray.
Called from process()
*/
void updateTriLists
(Array<Array<int>*>& indexArrayArray,
const Array<Vector3>& vertexArray,
const Array<Vector3>& normalArray,
const Array<Vector2>& texCoordArray) {
# ifdef VERBOSE
debugPrintf("WeldHelper::updateTriLists\n");
# endif
// Compute a hash grid so that we can find neighbors quickly.
// It begins empty and is extended as the tri lists are iterated
// through.
weldGrid.clear();
// Process all triLists
int numTriLists = indexArrayArray.size();
int u = 0;
for (int t = 0; t < numTriLists; ++t) {
if (indexArrayArray[t] != NULL) {
Array<int>& triList = *(indexArrayArray[t]);
// For all vertices in this list
for (int v = 0; v < triList.size(); ++v) {
// This vertex mapped to u in the flatVertexArray
triList[v] = getIndex(vertexArray[u], normalArray[u], texCoordArray[u]);
/*
# ifdef G3D_DEBUG
{
int i = triList[v];
Vector3 N = normalArray[i];
debugAssertM(N.length() > 0.9f, "Produced non-unit normal");
}
# endif
*/
++u;
}
}
}
}
/** Expands the indexed triangle lists into a triangle list.
Called from process() */
void unroll
(const Array<Array<int>*>& indexArrayArray,
const Array<Vector3>& vertexArray,
const Array<Vector2>& texCoordArray,
Array<Vector3>& unrolledVertexArray,
Array<Vector2>& unrolledTexCoordArray) {
# ifdef VERBOSE
debugPrintf("WeldHelper::unroll\n");
# endif
int numTriLists = indexArrayArray.size();
for (int t = 0; t < numTriLists; ++t) {
if (indexArrayArray[t] != NULL) {
const Array<int>& triList = *(indexArrayArray[t]);
for (int v = 0; v < triList.size(); ++v) {
int i = triList[v];
unrolledVertexArray.append(vertexArray[i]);
unrolledTexCoordArray.append(texCoordArray[i]);
}
}
}
}
/** For every three vertices, compute the face normal and store it three times.
Sliver triangles have a zero surface normal, which we will later take to
match *any* surface normal. */
void computeFaceNormals
(const Array<Vector3>& vertexArray,
Array<Vector3>& faceNormalArray) {
# ifdef VERBOSE
debugPrintf("WeldHelper::computeFaceNormals\n");
# endif
debugAssertM(vertexArray.size() % 3 == 0, "Input is not a triangle soup");
debugAssertM(faceNormalArray.size() == 0, "Output must start empty.");
for (int v = 0; v < vertexArray.size(); v += 3) {
const Vector3& e0 = vertexArray[v + 1] - vertexArray[v];
const Vector3& e1 = vertexArray[v + 2] - vertexArray[v];
// Note that the length may be zero in the case of sliver polygons, e.g.,
// those correcting a T-junction. Scale up by 256 to avoid underflow when
// multiplying very small edges
const Vector3& n = (e0.cross(e1 * 256.0f)).directionOrZero();
// Append the normal once per vertex.
faceNormalArray.append(n, n, n);
}
}
/**
Computes @a smoothNormalArray, whose elements are those of normalArray averaged
with neighbors within the angular cutoff.
*/
void smoothNormals
(const Array<Point3>& vertexArray,
const Array<Vector3>& normalArray,
Array<Vector3>& smoothNormalArray) {
if (normalSmoothingAngle <= 0) {
smoothNormalArray = normalArray;
return;
}
# ifdef VERBOSE
debugPrintf("WeldHelper::smoothNormals\n");
# endif
// Create an area memory manager for fast deallocation
MemoryManager::Ref mm = AreaMemoryManager::create(iRound(sizeof(VN) * normalArray.size() * 1.5));
const float cosThresholdAngle = (float)cos(normalSmoothingAngle);
debugAssert(vertexArray.size() == normalArray.size());
smoothNormalArray.resize(normalArray.size());
if (vertexWeldRadius == 0) {
// Look for vertices with the exactly identical normal only
# ifdef VERBOSE
debugPrintf("Taking fast path\n");
# endif
// Maximum expected faces that meet at a vertex
static const int k = 8;
// Maps vertices to the indices of normals at that vertex
Table<Point3, SmallArray<Vector3, k> > normalTable;
for (int v = 0; v < vertexArray.size(); ++v) {
bool ignore = false;
SmallArray<Vector3, k>& list = normalTable.getCreate(vertexArray[v], ignore);
list.append(normalArray[v]);
}
for (int v = 0; v < vertexArray.size(); ++v) {
Vector3 sum;
const Vector3& original = normalArray[v];
const SmallArray<Vector3, k>& list = normalTable[vertexArray[v]];
for (int i = 0; i < list.size(); ++i) {
const Vector3& N = list[i];
const float cosAngle = N.dot(original);
if (cosAngle > cosThresholdAngle) {
// This normal is close enough to consider. Avoid underflow by scaling up
sum += (N * 256.0f);
}
}
const Vector3& average = sum.directionOrZero();
const bool indeterminate = average.isZero();
// Never "smooth" a normal so far that it points backwards
const bool backFacing = original.dot(average) < 0;
if (indeterminate || backFacing) {
// Revert to the face normal
smoothNormalArray[v] = original;
} else {
// Average available normals
smoothNormalArray[v] = average;
}
}
} else {
// Non-zero vertex normal welding
# ifdef VERBOSE
debugPrintf("Taking slower weld path because vertexWeldRadius = %f\n",
vertexWeldRadius);
# endif
// Compute a hash grid so that we can find neighbors quickly.
alwaysAssertM(vertexWeldRadius > 0, "Cannot smooth with zero vertex weld radius");
PointHashGrid<VN> grid(vertexWeldRadius, mm);
for (int v = 0; v < normalArray.size(); ++v) {
grid.insert(VN(vertexArray[v], normalArray[v]));
}
// OPT: this step could be done on multiple threads
for (int v = 0; v < normalArray.size(); ++v) {
// Compute the sum of all nearby normals within the cutoff angle.
// Search within the vertexWeldRadius, since those are the vertices
// that will collapse to the same point.
PointHashGrid<VN>::SphereIterator it =
grid.begin(Sphere(vertexArray[v], vertexWeldRadius));
Vector3 sum;
const Vector3& original = normalArray[v];
while (it.isValid()) {
const Vector3& N = it->normal;
const float cosAngle = N.dot(original);
if (cosAngle > cosThresholdAngle) {
// This normal is close enough to consider. Avoid underflow by scaling up
sum += (N * 256.0f);
}
++it;
}
const Vector3& average = sum.directionOrZero();
const bool indeterminate = average.isZero();
// Never "smooth" a normal so far that it points backwards
const bool backFacing = original.dot(average) < 0;
if (indeterminate || backFacing) {
// Revert to the face normal
smoothNormalArray[v] = original;
} else {
// Average available normals
smoothNormalArray[v] = average;
}
}
}
}
public:
/**
Algorithm:
1. Unroll the indexed triangle list into a triangle list, where
there are duplicated vertices.
2. Compute face normals for all triangles, and expand those into
the triangle vertices.
3. At each vertex, average all normals that are within normalSmoothingAngle.
4. Generate output indexArrayArray. While doing so, merge all vertices where
the distance between position, texCoord, and normal is within the thresholds.
*/
void process
( Array<Vector3>& vertexArray,
Array<Vector2>& texCoordArray,
Array<Vector3>& normalArray,
Array<Array<int>*>& indexArrayArray,
float normAngle,
float texRadius,
float normRadius) {
# ifdef VERBOSE
debugPrintf("WeldHelper::process\n");
# endif
normalSmoothingAngle = normAngle;
normalWeldRadius2 = square(normRadius);
texCoordWeldRadius2 = square(texRadius);
const bool hasTexCoords = (texCoordArray.size() > 0);
if (hasTexCoords) {
debugAssertM(vertexArray.size() == texCoordArray.size(),
"Input arrays are not parallel.");
}
// Create an area memory manager for fast deallocation
Array<Vector3> unrolledVertexArray;
Array<Vector3> unrolledFaceNormalArray;
Array<Vector3> unrolledSmoothNormalArray;
Array<Vector2> unrolledTexCoordArray;
unrolledVertexArray.reserve(vertexArray.size());
unrolledFaceNormalArray.reserve(vertexArray.size());
unrolledSmoothNormalArray.reserve(vertexArray.size());
unrolledTexCoordArray.reserve(vertexArray.size());
if (! hasTexCoords) {
// Generate all zero texture coordinates
texCoordArray.resize(vertexArray.size());
}
// Generate a flat (unrolled) triangle list with texture coordinates.
unroll(indexArrayArray, vertexArray, texCoordArray,
unrolledVertexArray, unrolledTexCoordArray);
// Put the output back into the input slots.
outputVertexArray = &vertexArray;
outputNormalArray = &normalArray;
outputTexCoordArray = &texCoordArray;
outputVertexArray->fastClear();
outputNormalArray->fastClear();
outputTexCoordArray->fastClear();
// For every three vertices, generate their face normal and store it at
// each vertex. The output array has the same length as the input.
computeFaceNormals(unrolledVertexArray, unrolledFaceNormalArray);
// Compute smooth normals at vertices.
if (unrolledFaceNormalArray.size() > 0) {
smoothNormals(unrolledVertexArray, unrolledFaceNormalArray, unrolledSmoothNormalArray);
unrolledFaceNormalArray.clear();
}
// Regenerate the triangle lists
updateTriLists(indexArrayArray, unrolledVertexArray, unrolledSmoothNormalArray, unrolledTexCoordArray);
if (! hasTexCoords) {
// Throw away the generated texCoords
texCoordArray.resize(0);
}
}
WeldHelper(float vertRadius) :
weldGrid(max(vertRadius, 0.1f), AreaMemoryManager::create()),
vertexWeldRadius(vertRadius) {
}
};
} // Internal
void Welder::Settings::serialize(class BinaryOutput& b) const {
b.writeFloat32(normalSmoothingAngle);
b.writeFloat32(vertexWeldRadius);
b.writeFloat32(textureWeldRadius);
b.writeFloat32(normalWeldRadius);
}
void Welder::Settings::deserialize(class BinaryInput& b) {
normalSmoothingAngle = b.readFloat32();
vertexWeldRadius = b.readFloat32();
textureWeldRadius = b.readFloat32();
normalWeldRadius = b.readFloat32();
}
void Welder::weld
(Array<Vector3>& vertexArray,
Array<Vector2>& texCoordArray,
Array<Vector3>& normalArray,
Array<Array<int>*>& indexArrayArray,
const Welder::Settings& settings) {
_internal::WeldHelper(settings.vertexWeldRadius).process
(vertexArray, texCoordArray, normalArray, indexArrayArray,
settings.normalSmoothingAngle, settings.textureWeldRadius, settings.normalWeldRadius);
}
Welder::Settings::Settings(const Any& any) {
*this = Settings();
any.verifyName("Welder::Settings");
for (Any::AnyTable::Iterator it = any.table().begin(); it.isValid(); ++it) {
const std::string& key = toLower(it->key);
if (key == "normalsmoothingangle") {
normalSmoothingAngle = it->value;
} else if (key == "vertexweldradius") {
vertexWeldRadius = it->value;
} else if (key == "textureweldradius") {
textureWeldRadius = it->value;
} else if (key == "normalweldradius") {
normalWeldRadius = it->value;
} else {
any.verify(false, "Illegal key: " + it->key);
}
}
}
Any Welder::Settings::toAny() const {
Any a(Any::TABLE, "Welder::Settings");
a["normalSmoothingAngle"] = normalSmoothingAngle;
a["vertexWeldRadius"] = vertexWeldRadius;
a["textureWeldRadius"] = textureWeldRadius;
a["normalWeldRadius"] = normalWeldRadius;
return a;
}
} // G3D
|