-
Notifications
You must be signed in to change notification settings - Fork 13
/
PGS_Triangulation.java
481 lines (429 loc) · 19.4 KB
/
PGS_Triangulation.java
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
package micycle.pgs;
import static micycle.pgs.PGS_Conversion.fromPShape;
import java.util.ArrayList;
import java.util.Collection;
import java.util.List;
import java.util.function.Consumer;
import org.locationtech.jts.algorithm.Orientation;
import org.locationtech.jts.algorithm.locate.IndexedPointInAreaLocator;
import org.locationtech.jts.geom.Coordinate;
import org.locationtech.jts.geom.Envelope;
import org.locationtech.jts.geom.Geometry;
import org.locationtech.jts.geom.LinearRing;
import org.locationtech.jts.geom.Location;
import org.tinfour.common.IConstraint;
import org.tinfour.common.PolygonConstraint;
import org.tinfour.common.SimpleTriangle;
import org.tinfour.common.Vertex;
import org.tinfour.standard.IncrementalTin;
import org.tinfour.utils.TriangleCollector;
import earcut4j.Earcut;
import micycle.pgs.PGS.LinearRingIterator;
import micycle.pgs.color.RGB;
import micycle.pgs.commons.Nullable;
import processing.core.PConstants;
import processing.core.PShape;
import processing.core.PVector;
/**
* Delaunay and earcut triangulation of shapes and point sets.
*
* @author Michael Carleton
*
*/
public final class PGS_Triangulation {
private PGS_Triangulation() {
}
/**
* Generates a constrained Delaunay Triangulation from the given shape.
*
* @param shape the shape whose vertices to generate a triangulation from
* @return a GROUP PShape, where each child shape is one triangle
* @see #delaunayTriangulation(PShape, Collection, boolean, int, boolean)
*/
public static PShape delaunayTriangulation(PShape shape) {
return delaunayTriangulation(shape, null, true, 0, true);
}
/**
* Generates a Delaunay Triangulation from the given shape. The triangulation
* can be both constrained (meaning the triangulation is masked by the original
* shape) and refined (meaning additional points are inserted, usually leading
* to more uniform triangle shapes and sizes).
*
* @param shape the shape whose vertices to generate a triangulation
* from
* @param steinerPoints A list of additional points to insert into the
* triangulation in addition to the vertices of the input
* shape. <b>Can be null</b>.
* @param constrain Constrain the triangulation output using the shape
* boundary (from point set). With shapes, you'll probably
* want to this to be true.
* @param refinements The number of triangulation refinement passes to
* perform. Each pass inserts the centroids of every
* existing triangle into the triangulation. Should be 0 or
* greater (probably no more than 5).
* @param pretty Whether to maintain the Delaunay nature when
* constraining the triangulation, and whether to check
* that centroid locations lie within the shape during
* refinement. When pretty=true, triangles in the
* triangulation may be slightly more regular in
* shape/size. There is a small performance overhead which
* becomes more considerable at higher refinement levels.
* When constrain=false and refinements=0, this argument
* has no effect.
* @return a GROUP PShape, where each child shape is one triangle
* @see #delaunayTriangulationPoints(PShape, List, boolean, int, boolean)
* @see #delaunayTriangulationMesh(PShape, List, boolean, int, boolean)
*/
public static PShape delaunayTriangulation(PShape shape, @Nullable Collection<PVector> steinerPoints, boolean constrain,
int refinements, boolean pretty) {
final IncrementalTin tin = delaunayTriangulationMesh(shape, steinerPoints, constrain, refinements, pretty);
final PShape triangulation = new PShape(PConstants.GROUP);
final Consumer<Vertex[]> triangleVertexConsumer = t -> {
final PShape triangle = new PShape(PShape.PATH);
triangle.beginShape();
triangle.vertex((float) t[0].x, (float) t[0].y);
triangle.vertex((float) t[1].x, (float) t[1].y);
triangle.vertex((float) t[2].x, (float) t[2].y);
triangle.endShape(PConstants.CLOSE);
triangulation.addChild(triangle);
};
if (constrain) {
TriangleCollector.visitTrianglesConstrained(tin, triangleVertexConsumer);
} else {
TriangleCollector.visitTriangles(tin, triangleVertexConsumer);
}
PGS_Conversion.setAllFillColor(triangulation, RGB.WHITE);
PGS_Conversion.setAllStrokeColor(triangulation, RGB.PINK, 2);
return triangulation;
}
/**
* Generates a Delaunay Triangulation from a collection of points.
*
* @param points the point collection to triangulate
* @return a TRIANGLES PShape
* @see #delaunayTriangulation(PShape, Collection, boolean, int, boolean)
* @since 1.1.0
*/
public static PShape delaunayTriangulation(Collection<PVector> points) {
return delaunayTriangulation(null, points, false, 0, false);
}
/**
* Generates a constrained Delaunay Triangulation from a collection of points.
* <p>
* This method returns the triangulation as a list of points, rather than a
* PShape.
*
* @param shape the shape whose vertices to generate a triangulation from
* @return List of PVector coordinates, where each consecutive triplet of
* coordinates are the 3 vertices belonging to one triangle
*/
public static List<PVector> delaunayTriangulationPoints(PShape shape) {
return delaunayTriangulationPoints(shape, null, true, 0, true);
}
/**
* Generates a Delaunay Triangulation from the given shape. The triangulation
* can be both constrained (meaning the triangulation is masked by the original
* shape) and refined (meaning additional points are inserted, usually leading
* to more uniform triangle shapes and sizes).
* <p>
* This method returns the triangulation as a list of points, rather than a
* PShape.
*
* @param shape the shape whose vertices to generate a triangulation of
* @param steinerPoints A list of additional points to insert into the
* triangulation in addition to the vertices of the input
* shape. <b>Can be null</b>.
* @param constrain Constrain the triangulation output using the shape
* boundary (from point set). With shapes, you'll probably
* want to this to be true.
* @param refinements The number of triangulation refinement passes to
* perform. Each pass inserts the centroids of every
* existing triangle into the triangulation. Should be 0 or
* greater (probably no more than 5).
* @param pretty Whether to maintain the Delaunay nature when
* constraining the triangulation, and whether to check
* that centroid locations lie within the shape during
* refinement. When pretty=true, triangles in the
* triangulation may be slightly more regular in
* shape/size. There is a small performance overhead which
* becomes more considerable at higher refinement levels.
* When constrain=false and refinements=0, this argument
* has no effect.
* @return List of PVector coordinates, where each consecutive triplet of
* coordinates are the 3 vertices belonging to one triangle
* @see #delaunayTriangulationPoints(PShape, List, boolean, int, boolean)
* @see #delaunayTriangulationMesh(PShape, List, boolean, int, boolean)
*/
public static List<PVector> delaunayTriangulationPoints(PShape shape, @Nullable Collection<PVector> steinerPoints, boolean constrain,
int refinements, boolean pretty) {
final IncrementalTin tin = delaunayTriangulationMesh(shape, steinerPoints, constrain, refinements, pretty);
final ArrayList<PVector> triangles = new ArrayList<>();
final Consumer<Vertex[]> triangleVertexConsumer = t -> {
triangles.add(toPVector(t[0]));
triangles.add(toPVector(t[1]));
triangles.add(toPVector(t[2]));
};
if (constrain) {
TriangleCollector.visitTrianglesConstrained(tin, triangleVertexConsumer);
} else {
TriangleCollector.visitTriangles(tin, triangleVertexConsumer);
}
return triangles;
}
/**
* Generates a Delaunay Triangulation from a collection of points.
* <p>
* This method returns the triangulation as a list of points, rather than a
* PShape.
*
* @param points the point collection to triangulate
* @return List of PVector coordinates, where each consecutive triplet of
* coordinates are the 3 vertices belonging to one triangle
* @see #delaunayTriangulationPoints(PShape, Collection, boolean, int, boolean)
* @since 1.1.0
*/
public static List<PVector> delaunayTriangulationPoints(Collection<PVector> points) {
return delaunayTriangulationPoints(null, points, false, 0, false);
}
/**
* Generates a constrained Delaunay Triangulation from the given shape.
* <p>
* This method returns the triangulation in its raw form: a Triangulated
* Irregular Network (mesh).
*
* @param shape the shape whose vertices to generate a triangulation from
* @return Triangulated Irregular Network object (mesh)
* @see #delaunayTriangulationMesh(PShape, Collection, boolean, int, boolean)
*/
public static IncrementalTin delaunayTriangulationMesh(PShape shape) {
return delaunayTriangulationMesh(shape, null, true, 0, true);
}
/**
* Generates a Delaunay Triangulation from the given shape. The triangulation
* can be both constrained (meaning the triangulation is masked by the original
* shape) and refined (meaning additional points are inserted, usually leading
* to more uniform triangle shapes and sizes).
* <p>
* This method returns the triangulation in its raw form: a Triangulated
* Irregular Network (mesh).
*
* @param shape the shape whose vertices to generate a triangulation
* from. <b>Can be null</b>.
* @param steinerPoints A list of additional points to insert into the
* triangulation in addition to the vertices of the input
* shape. <b>Can be null</b>.
* @param constrain Constrain the triangulation output using the shape
* boundary (from point set). With shapes, you'll probably
* want to this to be true.
* @param refinements The number of triangulation refinement/subdivision
* passes to perform. Each pass inserts the centroids of
* every existing triangle into the triangulation. Should
* be 0 or greater (probably no more than 5).
* @param pretty Whether to maintain the Delaunay nature when
* constraining the triangulation, and whether to check
* that centroid locations lie within the shape during
* refinement. When pretty=true, triangles in the
* triangulation may be slightly more regular in
* shape/size. There is a small performance overhead which
* becomes more considerable at higher refinement levels.
* When constrain=false and refinements=0, this argument
* has no effect.
* @return Triangulated Irregular Network object (mesh)
* @see #delaunayTriangulation(PShape, List, boolean, int, boolean)
* @see #delaunayTriangulationPoints(PShape, List, boolean, int, boolean)
*/
public static IncrementalTin delaunayTriangulationMesh(@Nullable PShape shape, @Nullable Collection<PVector> steinerPoints, boolean constrain,
int refinements, boolean pretty) {
Geometry g = shape == null ? PGS.GEOM_FACTORY.createEmpty(2) : fromPShape(shape);
final IncrementalTin tin = new IncrementalTin(10);
final ArrayList<Vertex> vertices = new ArrayList<>();
final Coordinate[] coords = g.getCoordinates();
for (int i = 0; i < coords.length; i++) {
vertices.add(new Vertex(coords[i].x, coords[i].y, 0));
}
tin.add(vertices, null); // initial triangulation
if (steinerPoints != null) {
steinerPoints.forEach(v -> tin.add(new Vertex(v.x, v.y, 0))); // add steiner points
}
if (refinements > 0) {
final IndexedPointInAreaLocator pointLocator = new IndexedPointInAreaLocator(g);
final ArrayList<Vertex> refinementVertices = new ArrayList<>();
/*
* A possible optimisation is to recursely split within each triangle upto the
* refinement depth (in one pass), so perform many less location checks. Another
* is to rasterise the PShape and check pixel[] array. TODO See 'sqrt(3)
* Subdivision' by Leif Kobbelt
*/
for (int i = 0; i < refinements; i++) {
refinementVertices.clear();
TriangleCollector.visitSimpleTriangles(tin, t -> {
if (t.getArea() > 50) { // don't refine small triangles
final Coordinate center = centroid(t); // use centroid rather than circumcircle center
if (pretty || pointLocator.locate(center) != Location.EXTERIOR) {
refinementVertices.add(new Vertex(center.x, center.y, 0));
}
}
});
tin.add(refinementVertices, null); // add refinement (steiner) points
}
}
if (constrain) {
// If geom is a point set, constrain tin using its concave hull.
if (g.getGeometryType().equals(Geometry.TYPENAME_MULTIPOINT)) {
g = fromPShape(PGS_Processing.concaveHull2(PGS_Conversion.toPVector(shape), 0.3));
}
List<IConstraint> constraints = new ArrayList<>();
for (int n = 0; n < g.getNumGeometries(); n++) {
boolean hole = false;
LinearRingIterator lri = new LinearRingIterator(g.getGeometryN(n));
for (LinearRing ring : lri) {
ArrayList<Vertex> points = new ArrayList<>();
Coordinate[] c = ring.getCoordinates();
if (c.length == 0) {
continue;
}
if (Orientation.isCCW(c) && !hole) {
for (int i = 0; i < c.length; i++) {
points.add(new Vertex(c[i].x, c[i].y, 0));
}
} else {
// holes are CW; region to keep lies to left the of constraints
for (int i = c.length - 1; i >= 0; i--) {
points.add(new Vertex(c[i].x, c[i].y, 0));
}
}
constraints.add(new PolygonConstraint(points));
hole = true; // all rings except the first are holes
}
}
if (!constraints.isEmpty()) {
tin.addConstraints(constraints, pretty); // true/false is negligible?
}
}
return tin;
}
/**
* Generates a Delaunay Triangulation from a collection of points.
* <p>
* This method returns the triangulation in its raw form: a Triangulated
* Irregular Network (mesh).
*
* @param points the point collection to triangulate
* @return Triangulated Irregular Network object (mesh)
* @see #delaunayTriangulationMesh(PShape, Collection, boolean, int, boolean)
* @since 1.1.0
*/
public static IncrementalTin delaunayTriangulationMesh(Collection<PVector> points) {
return delaunayTriangulationMesh(null, points, false, 0, false);
}
/**
* Creates a Delaunay triangulation of the shape where additional steiner
* points, populated by poisson sampling, are included.
*
* @param shape
* @param spacing (Minimum) spacing between poisson points
* @return a GROUP PShape, where each child shape is one triangle
* @see #poissonTriangulationPoints(PShape, double)
*/
public static PShape poissonTriangulation(PShape shape, double spacing) {
final Envelope e = fromPShape(shape).getEnvelopeInternal();
final List<PVector> poissonPoints = PGS_PointSet.poisson(e.getMinX(), e.getMinY(), e.getMinX() + e.getWidth(),
e.getMinY() + e.getHeight(), spacing, 0);
final IncrementalTin tin = delaunayTriangulationMesh(shape, poissonPoints, true, 0, false);
final PShape triangulation = new PShape(PConstants.GROUP);
TriangleCollector.visitTrianglesConstrained(tin, t -> {
final PShape triangle = new PShape(PShape.PATH);
triangle.beginShape();
triangle.vertex((float) t[0].x, (float) t[0].y);
triangle.vertex((float) t[1].x, (float) t[1].y);
triangle.vertex((float) t[2].x, (float) t[2].y);
triangle.endShape(PConstants.CLOSE);
triangulation.addChild(triangle);
});
PGS_Conversion.setAllFillColor(triangulation, RGB.WHITE);
PGS_Conversion.setAllStrokeColor(triangulation, RGB.PINK, 2);
return triangulation;
}
/**
* Creates a Delaunay triangulation of the shape where additional steiner
* points, populated by poisson sampling, are included.
*
* @param shape
* @param spacing (Minimum) spacing between poisson points
* @return list of PVectors, where each successive triplet of PVectors
* correspond to the 3 vertices of one triangle
* @see #poissonTriangulation(PShape, double)
*/
public static List<PVector> poissonTriangulationPoints(PShape shape, double spacing) {
final Envelope e = fromPShape(shape).getEnvelopeInternal();
final List<PVector> poissonPoints = PGS_PointSet.poisson(e.getMinX(), e.getMinY(), e.getMinX() + e.getWidth(),
e.getMinY() + e.getHeight(), spacing, 0);
final IncrementalTin tin = delaunayTriangulationMesh(shape, poissonPoints, true, 0, false);
final ArrayList<PVector> triangles = new ArrayList<>();
TriangleCollector.visitTrianglesConstrained(tin, t -> {
triangles.add(toPVector(t[0]));
triangles.add(toPVector(t[1]));
triangles.add(toPVector(t[2]));
});
return triangles;
}
/**
* Computes a triangulation of the shape according to the ear clipping
* ("earcut") method. The triangulation is constrained to the shape by default.
* Does not support holes (for now...).
*
* @param shape shape whose vertices to triangulate
* @return a GROUP PShape, where each child shape is one triangle
* @since 1.1.0
*/
public static PShape earCutTriangulation(PShape shape) {
return earCutTriangulation(PGS_Conversion.toPVector(shape));
}
/**
* Computes a triangulation of the given points according to the ear clipping
* ("earcut") method.
*
* @param points
* @return a GROUP PShape, where each child shape is one triangle
*/
public static PShape earCutTriangulation(List<PVector> points) {
final double[] arrCoords = new double[points.size() * 2];
for (int i = 0; i < points.size(); i++) {
arrCoords[2 * i] = points.get(i).x;
arrCoords[2 * i + 1] = points.get(i).y;
}
final List<Integer> triangles = Earcut.earcut(arrCoords, null, 2);
final PShape triangulation = new PShape(PConstants.GROUP);
for (int i = 0; i < triangles.size(); i += 3) {
final int v1 = 2 * triangles.get(i);
final int v2 = 2 * triangles.get(i + 1);
final int v3 = 2 * triangles.get(i + 2);
final PShape triangle = new PShape(PShape.PATH);
triangle.beginShape();
triangle.vertex((float) arrCoords[v1], (float) arrCoords[v1 + 1]);
triangle.vertex((float) arrCoords[v2], (float) arrCoords[v2 + 1]);
triangle.vertex((float) arrCoords[v3], (float) arrCoords[v3 + 1]);
triangle.endShape(PConstants.CLOSE);
triangulation.addChild(triangle);
}
PGS_Conversion.setAllFillColor(triangulation, RGB.WHITE);
PGS_Conversion.setAllStrokeColor(triangulation, RGB.PINK, 2);
return triangulation;
}
static PVector toPVector(final Vertex v) {
return new PVector((float) v.getX(), (float) v.getY());
}
/**
* Computes the centroid/barycentre of a triangle.
*/
private static Coordinate centroid(final SimpleTriangle t) {
final Vertex a = t.getVertexA();
final Vertex b = t.getVertexB();
final Vertex c = t.getVertexC();
double x = a.x + b.x + c.x;
x /= 3;
double y = a.y + b.y + c.y;
y /= 3;
return new Coordinate(x, y);
}
}