-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathPenrose.cs
375 lines (342 loc) · 27.7 KB
/
Penrose.cs
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
using System;
using System.Collections.Generic;
using System.Linq;
namespace RT.Coordinates
{
/// <summary>
/// <para>
/// Describes a cell in a Penrose tiling (P2, consisting of kites and darts; or P3, consisting of thick and thin
/// rhombuses).</para></summary>
/// <image type="raw">
/// <svg xmlns='http://www.w3.org/2000/svg' viewBox='-3.5 -3.5 7 7'><path d='M3.07768353717525
/// -4.23606797749979L2.48989828488278 -3.42705098312484L2.48989828488278 -4.42705098312484M0.951056516295154
/// -2.92705098312484L0 -2.61803398874989L0.587785252292473 -3.42705098312484M-0.951056516295154 -2.92705098312484L0
/// -2.61803398874989L-0.587785252292473 -3.42705098312484M4.02874005347041 -2.92705098312484L3.07768353717525
/// -2.61803398874989L2.48989828488278 -3.42705098312484L3.44095480117793 -3.73606797749979M-2.48989828488278
/// -4.42705098312484L-2.48989828488278 -3.42705098312484L-3.07768353717525 -4.23606797749979M-1.53884176858763
/// -3.73606797749979L-0.951056516295154 -2.92705098312484L-1.90211303259031 -2.61803398874989L-2.48989828488278
/// -3.42705098312484L-1.53884176858763 -3.73606797749979L-0.587785252292473 -3.42705098312484L0
/// -4.23606797749979L0.587785252292473 -3.42705098312484L1.53884176858763 -3.73606797749979L2.48989828488278
/// -3.42705098312484L1.90211303259031 -2.61803398874989L0.951056516295154 -2.92705098312484L1.53884176858763
/// -3.73606797749979M-3.44095480117793 -3.73606797749979L-2.48989828488278 -3.42705098312484L-3.07768353717525
/// -2.61803398874989L-4.02874005347041 -2.92705098312484M1.90211303259031 -2.61803398874989L1.90211303259031
/// -1.61803398874989L0.951056516295154 -1.30901699437495L0.951056516295154 -2.30901699437495zM3.07768353717525
/// -1.61803398874989L3.07768353717525 -2.61803398874989L2.48989828488278 -1.80901699437495L1.90211303259031
/// -2.61803398874989M2.48989828488278 -1.80901699437495L2.48989828488278 -0.809016994374947L1.90211303259031
/// -1.61803398874989M1.53884176858763 -0.5L1.53884176858763 0.5L2.48989828488278 0.190983005625053L2.48989828488278
/// -0.809016994374947L1.53884176858763 -0.5L0.951056516295154 -1.30901699437495L0 -1.61803398874989L0
/// -2.61803398874989L0.951056516295154 -2.30901699437495M1.53884176858763 -0.5L0.951056516295154 0.309016994374947L0
/// 0L0.587785252292473 -0.809016994374947zM0.951056516295154 1.30901699437495L0 1.61803398874989L0.587785252292473
/// 2.42705098312484L1.53884176858763 2.11803398874989L0.951056516295154 1.30901699437495L0 1L0 0L-0.587785252292473
/// -0.809016994374947L0 -1.61803398874989L0.587785252292473 -0.809016994374947M0 -1.61803398874989L-0.951056516295154
/// -1.30901699437495L-0.951056516295154 -2.30901699437495L0 -2.61803398874989M-0.587785252292473
/// -0.809016994374947L-1.53884176858763 -0.5L-0.951056516295154 -1.30901699437495L-1.90211303259031
/// -1.61803398874989L-1.90211303259031 -2.61803398874989L-0.951056516295154 -2.30901699437495M2.48989828488278
/// -0.809016994374947L3.07768353717525 -1.61803398874989L4.02874005347041 -1.30901699437495L3.44095480117793
/// -0.5zM3.07768353717525 -2.61803398874989L4.02874005347041 -2.30901699437495M3.07768353717525 1L2.48989828488278
/// 1.80901699437495L3.44095480117793 2.11803398874989L4.02874005347041 1.30901699437495L3.07768353717525
/// 1L3.07768353717525 0L4.02874005347041 0.309016994374947L3.44095480117793 -0.5M3.07768353717525 0L2.48989828488278
/// -0.809016994374947M2.48989828488278 0.190983005625053L3.07768353717525 1L2.1266270208801
/// 1.30901699437495L1.53884176858763 0.5L0.951056516295154 1.30901699437495L0.951056516295154
/// 0.309016994374947M2.48989828488278 1.80901699437495L1.53884176858763 2.11803398874989L2.1266270208801
/// 1.30901699437495M0 1L-0.951056516295154 1.30901699437495L0 1.61803398874989L-0.587785252292473
/// 2.42705098312484L-1.53884176858763 2.11803398874989L-0.951056516295154 1.30901699437495M-0.951056516295154
/// 0.309016994374947L-0.951056516295154 1.30901699437495L-1.53884176858763 0.5L-2.1266270208801
/// 1.30901699437495L-3.07768353717525 1L-2.48989828488278 0.190983005625053M1.53884176858763
/// 2.11803398874989L2.48989828488278 2.42705098312484L2.48989828488278 3.42705098312484L1.53884176858763
/// 3.11803398874989zM3.07768353717525 4.23606797749979L2.48989828488278 3.42705098312484L3.44095480117793
/// 3.11803398874989L3.44095480117793 2.11803398874989L2.48989828488278 2.42705098312484M4.02874005347041
/// 2.92705098312484L3.44095480117793 2.11803398874989M4.02874005347041 3.92705098312484L3.44095480117793
/// 3.11803398874989M-1.90211303259031 -2.61803398874989L-2.48989828488278 -1.80901699437495L-3.07768353717525
/// -2.61803398874989L-3.07768353717525 -1.61803398874989M-1.90211303259031 -1.61803398874989L-2.48989828488278
/// -0.809016994374947L-2.48989828488278 -1.80901699437495M-1.53884176858763 -0.5L-1.53884176858763
/// 0.5L-2.48989828488278 0.190983005625053L-2.48989828488278 -0.809016994374947L-1.53884176858763
/// -0.5L-0.951056516295154 0.309016994374947L0 0M-2.48989828488278 -0.809016994374947L-3.44095480117793
/// -0.5L-4.02874005347041 -1.30901699437495L-3.07768353717525 -1.61803398874989zM-4.02874005347041
/// -2.30901699437495L-3.07768353717525 -2.61803398874989M-2.48989828488278 -0.809016994374947L-3.07768353717525
/// 0M-3.07768353717525 1L-2.48989828488278 1.80901699437495L-3.44095480117793 2.11803398874989L-4.02874005347041
/// 1.30901699437495L-3.07768353717525 1L-3.07768353717525 0L-4.02874005347041 0.309016994374947L-3.44095480117793
/// -0.5M-2.1266270208801 1.30901699437495L-1.53884176858763 2.11803398874989L-2.48989828488278
/// 1.80901699437495M-1.53884176858763 2.11803398874989L-1.53884176858763 3.11803398874989L-2.48989828488278
/// 3.42705098312484L-2.48989828488278 2.42705098312484zM-3.07768353717525 4.23606797749979L-2.48989828488278
/// 3.42705098312484L-3.44095480117793 3.11803398874989L-3.44095480117793 2.11803398874989L-2.48989828488278
/// 2.42705098312484M-3.44095480117793 2.11803398874989L-4.02874005347041 2.92705098312484M-3.44095480117793
/// 3.11803398874989L-4.02874005347041 3.92705098312484M1.90211303259031 4.23606797749979L2.48989828488278
/// 3.42705098312484M0 4.23606797749979L0 3.23606797749979L0.951056516295154 2.92705098312484L0.951056516295154
/// 3.92705098312484L1.53884176858763 3.11803398874989M0.951056516295154 2.92705098312484L1.53884176858763
/// 2.11803398874989M-0.587785252292473 2.42705098312484L0 3.23606797749979L0.587785252292473
/// 2.42705098312484M-1.53884176858763 3.11803398874989L-0.951056516295154 3.92705098312484L-0.951056516295154
/// 2.92705098312484L0 3.23606797749979M-0.951056516295154 2.92705098312484L-1.53884176858763
/// 2.11803398874989M-1.90211303259031 4.23606797749979L-2.48989828488278 3.42705098312484' fill='none'
/// stroke-width='.05' stroke='black' /></svg></image>
/// <image type="raw">
/// <svg xmlns='http://www.w3.org/2000/svg' viewBox='-3.5 -3.5 7 7'><path d='M-1.53884176858763
/// -4.73606797749979L-2.48989828488278 -3.42705098312484L-3.44095480117793 -4.73606797749979M3.44095480117793
/// -4.73606797749979L2.48989828488278 -3.42705098312484L1.53884176858763 -4.73606797749979M2.48989828488278
/// -1.80901699437495L2.48989828488278 -3.42705098312484L4.02874005347041 -2.92705098312484L3.44095480117793
/// -2.11803398874989L3.44095480117793 -1.11803398874989L4.02874005347041 -0.309016994374947L4.97979656976556
/// 0M-2.48989828488278 -1.80901699437495L-1.53884176858763 -2.11803398874989L-2.48989828488278
/// -0.809016994374947L-3.44095480117793 -2.11803398874989zM-0.951056516295154 -2.92705098312484L-0.951056516295154
/// -3.92705098312484L0 -2.61803398874989L-1.53884176858763 -2.11803398874989zM-2.48989828488278
/// -1.80901699437495L-2.48989828488278 -3.42705098312484M-2.48989828488278 1.80901699437495L-2.48989828488278
/// 0.809016994374947L-1.53884176858763 2.11803398874989L-3.07768353717525 2.61803398874989zM-3.07768353717525
/// 0L-4.02874005347041 -0.309016994374947L-2.48989828488278 -0.809016994374947L-2.48989828488278
/// 0.809016994374947zM-2.48989828488278 1.80901699437495L-4.02874005347041 1.30901699437495L-3.07768353717525
/// 0M-4.97979656976556 0L-4.02874005347041 -0.309016994374947L-3.44095480117793 -1.11803398874989L-3.44095480117793
/// -2.11803398874989L-4.02874005347041 -2.92705098312484L-2.48989828488278 -3.42705098312484L-0.951056516295154
/// -2.92705098312484M-0.951056516295154 0.309016994374947L-1.53884176858763 -0.5L0 0L-0.951056516295154
/// 1.30901699437495zM-0.951056516295154 0.309016994374947L-2.48989828488278 0.809016994374947M-1.53884176858763
/// -2.11803398874989L-0.587785252292473 -0.809016994374947M-2.48989828488278 -0.809016994374947L-1.53884176858763
/// -0.5L-0.587785252292473 -0.809016994374947L0 -1.61803398874989L0 0L1.53884176858763 -0.5L0.587785252292473
/// -0.809016994374947L0 -1.61803398874989L0 -2.61803398874989L1.53884176858763 -2.11803398874989L0.587785252292473
/// -0.809016994374947M0 0L0.951056516295154 1.30901699437495L0 1L-0.951056516295154
/// 1.30901699437495L-1.53884176858763 2.11803398874989L0 2.61803398874989L0 1M1.53884176858763
/// -2.11803398874989L2.48989828488278 -1.80901699437495L3.44095480117793 -2.11803398874989L2.48989828488278
/// -0.809016994374947L2.48989828488278 0.809016994374947L0.951056516295154 0.309016994374947M0.951056516295154
/// -2.92705098312484L2.48989828488278 -3.42705098312484M-3.44095480117793 -1.11803398874989L-4.97979656976556
/// -1.61803398874989M2.48989828488278 0.809016994374947L2.48989828488278 1.80901699437495L3.07768353717525
/// 2.61803398874989L1.53884176858763 2.11803398874989L2.48989828488278 0.809016994374947L3.07768353717525
/// 0L4.02874005347041 -0.309016994374947L2.48989828488278 -0.809016994374947M3.07768353717525 0L4.02874005347041
/// 1.30901699437495L2.48989828488278 1.80901699437495M4.02874005347041 2.92705098312484L3.07768353717525
/// 2.61803398874989L2.1266270208801 2.92705098312484L1.53884176858763 3.73606797749979L1.53884176858763
/// 4.73606797749979M4.97979656976556 -1.61803398874989L3.44095480117793 -1.11803398874989M1.53884176858763
/// 2.11803398874989L1.53884176858763 3.73606797749979L0.951056516295154 2.92705098312484L0
/// 2.61803398874989L1.53884176858763 2.11803398874989L0.951056516295154 1.30901699437495L0.951056516295154
/// 0.309016994374947L1.53884176858763 -0.5L2.48989828488278 -0.809016994374947L1.53884176858763
/// -2.11803398874989L0.951056516295154 -2.92705098312484L0.951056516295154 -3.92705098312484L0 -2.61803398874989M0
/// 2.61803398874989L-0.951056516295154 2.92705098312484L-1.53884176858763 3.73606797749979L-1.53884176858763
/// 2.11803398874989M0.951056516295154 2.92705098312484L0 4.23606797749979L-0.951056516295154
/// 2.92705098312484M-1.53884176858763 4.73606797749979L-1.53884176858763 3.73606797749979L-2.1266270208801
/// 2.92705098312484L-3.07768353717525 2.61803398874989L-4.02874005347041 2.92705098312484M-2.1266270208801
/// 2.92705098312484L-3.07768353717525 4.23606797749979M3.07768353717525 4.23606797749979L2.1266270208801
/// 2.92705098312484' fill='none' stroke-width='.05' stroke='black' /></svg></image>
public struct Penrose : IEquatable<Penrose>, INeighbor<Penrose>, INeighbor<object>, IHasSvgGeometry
{
/// <summary>
/// Constructor.</summary>
/// <param name="kind">
/// The kind of shape.</param>
/// <param name="corner">
/// The “main” corner of the shape.</param>
/// <param name="angle">
/// The rotation angle of the shape.</param>
public Penrose(Kind kind, Pentavector corner, int angle)
{
TileKind = kind;
Corner = corner;
Angle = (angle % 10 + 10) % 10;
}
/// <summary>Indicates which kind of shape this is.</summary>
public Kind TileKind { get; private set; }
/// <summary>Indicates the “main” corner of this shape.</summary>
public Pentavector Corner { get; private set; }
/// <summary>Indicates the rotation angle of this shape.</summary>
public int Angle { get; private set; }
/// <inheritdoc/>
public readonly bool Equals(Penrose other) => other.TileKind == TileKind && other.Corner == Corner && other.Angle == Angle;
/// <inheritdoc/>
public override readonly bool Equals(object obj) => obj is Penrose other && other.TileKind == TileKind && other.Corner == Corner && other.Angle == Angle;
/// <inheritdoc/>
public override readonly int GetHashCode() => unchecked((Corner.GetHashCode() * 10 + Angle) * 4 + (int) TileKind);
/// <inheritdoc/>
public readonly IEnumerable<Link<Vertex>> Edges => Vertices.MakeEdges();
/// <inheritdoc/>
public readonly PointD Center => TileKind switch
{
Kind.Dart => (3 * Corner.MultiplyByPhi + Pentavector.Base(Angle)).Point / 3,
Kind.Kite => (Corner.MultiplyByPhi + Pentavector.Base(Angle)).Point,
Kind.ThinRhomb => (2 * (Corner + Pentavector.Base(Angle)) + Pentavector.Base(Angle + 3).DivideByPhi).Point / 2,
Kind.ThickRhomb => (2 * Corner + Pentavector.Base(Angle).MultiplyByPhi).Point / 2,
_ => throw new InvalidOperationException($"Invalid TileKind value ‘{TileKind}’.")
};
/// <summary>
/// Returns the vertices along the perimeter of this <see cref="Penrose"/>, going clockwise from the “main” vertex
/// (<see cref="Corner"/> in P2; <see cref="Corner"/> times φ in P3).</summary>
public readonly Vertex[] Vertices => TileKind switch
{
Kind.Dart => new Vertex[] { Corner.MultiplyByPhi, Corner.MultiplyByPhi + Pentavector.Base(Angle + 7), Corner.MultiplyByPhi + Pentavector.Base(Angle), Corner.MultiplyByPhi + Pentavector.Base(Angle + 3) },
Kind.Kite => new Vertex[] { Corner.MultiplyByPhi, (Corner + Pentavector.Base(Angle + 9)).MultiplyByPhi, (Corner + Pentavector.Base(Angle)).MultiplyByPhi, (Corner + Pentavector.Base(Angle + 1)).MultiplyByPhi },
Kind.ThickRhomb => new Vertex[] { Corner, Corner + Pentavector.Base(Angle + 9), Corner + Pentavector.Base(Angle + 9) + Pentavector.Base(Angle + 1), Corner + Pentavector.Base(Angle + 1) },
Kind.ThinRhomb => new Vertex[] { Corner, Corner + Pentavector.Base(Angle), Corner + Pentavector.Base(Angle) + Pentavector.Base(Angle + 1), Corner + Pentavector.Base(Angle + 1) },
_ => throw new InvalidOperationException($"Invalid TileKind value ‘{TileKind}’."),
};
/// <summary>
/// Returns a collection of tiles obtained from one iteration of deflating (expanding) this tile.</summary>
/// <remarks>
/// Note that deflating several adjacent tiles will generate some duplicated tiles.</remarks>
public readonly IEnumerable<Penrose> DeflatedTiles
{
get
{
switch (TileKind)
{
case Kind.Kite:
yield return new Penrose(Kind.Dart, Corner.MultiplyByPhi + Pentavector.Base(Angle + 9).DivideByPhi, Angle + 4);
yield return new Penrose(Kind.Dart, Corner.MultiplyByPhi + Pentavector.Base(Angle + 1).DivideByPhi, Angle + 6);
yield return new Penrose(Kind.Kite, (Corner + Pentavector.Base(Angle + 9)).MultiplyByPhi, Angle + 3);
yield return new Penrose(Kind.Kite, (Corner + Pentavector.Base(Angle + 1)).MultiplyByPhi, Angle + 7);
// Extra
yield return new Penrose(Kind.Kite, (Corner + Pentavector.Base(Angle + 1)).MultiplyByPhi, Angle + 5);
yield return new Penrose(Kind.Kite, (Corner + Pentavector.Base(Angle + 9)).MultiplyByPhi, Angle + 5);
yield break;
case Kind.Dart:
yield return new Penrose(Kind.Dart, Corner.MultiplyByPhi + new Pentavector(0, -1, 1, -1).Rotate(Angle), Angle + 6);
yield return new Penrose(Kind.Dart, Corner.MultiplyByPhi + new Pentavector(1, -1, 1, 0).Rotate(Angle), Angle + 4);
yield return new Penrose(Kind.Kite, Corner.MultiplyByPhi + Pentavector.Base(Angle), Angle + 5);
// Extra
yield return new Penrose(Kind.Kite, Corner.MultiplyByPhi + Pentavector.Base(Angle), Angle + 7);
yield return new Penrose(Kind.Kite, Corner.MultiplyByPhi + Pentavector.Base(Angle), Angle + 3);
yield break;
case Kind.ThickRhomb:
yield return new Penrose(Kind.ThickRhomb, (Corner + Pentavector.Base(Angle)).MultiplyByPhi, Angle + 5);
yield return new Penrose(Kind.ThickRhomb, (Corner + Pentavector.Base(Angle).MultiplyByPhi).MultiplyByPhi, Angle + 6);
yield return new Penrose(Kind.ThickRhomb, (Corner + Pentavector.Base(Angle).MultiplyByPhi).MultiplyByPhi, Angle + 4);
yield return new Penrose(Kind.ThinRhomb, (Corner + Pentavector.Base(Angle)).MultiplyByPhi, Angle + 6);
yield return new Penrose(Kind.ThinRhomb, Corner.MultiplyByPhi + new Pentavector(1, 0, 1, 0).Rotate(Angle), Angle + 8);
// Extra
yield return new Penrose(Kind.ThickRhomb, Corner.MultiplyByPhi + new Pentavector(1, 0, 1, 0).Rotate(Angle), Angle + 7);
yield return new Penrose(Kind.ThickRhomb, Corner.MultiplyByPhi + new Pentavector(0, -1, 0, -1).Rotate(Angle), Angle + 3);
yield break;
case Kind.ThinRhomb:
var cb = (Corner + Pentavector.Base(Angle + 1)).MultiplyByPhi;
yield return new Penrose(Kind.ThickRhomb, cb, Angle + 6);
yield return new Penrose(Kind.ThickRhomb, cb, Angle);
yield return new Penrose(Kind.ThinRhomb, cb, Angle + 7);
yield return new Penrose(Kind.ThinRhomb, (Corner + Pentavector.Base(Angle)).MultiplyByPhi + Pentavector.Base(Angle + 9), Angle + 3);
yield break;
default: throw new InvalidOperationException($"Invalid Penrose.TileKind value ‘{TileKind}’.");
}
}
}
/// <inheritdoc/>
public readonly IEnumerable<Penrose> Neighbors
{
get
{
if (TileKind == Kind.Kite)
{
// Neighbors left/right of the Corner vertex
yield return new Penrose(Kind.Kite, Corner, Angle + 8);
yield return new Penrose(Kind.Kite, Corner, Angle + 2);
yield return new Penrose(Kind.Dart, Corner + new Pentavector(0, -1, 1, -1).Rotate(Angle), Angle);
yield return new Penrose(Kind.Dart, Corner + new Pentavector(1, -1, 1, 0).Rotate(Angle), Angle);
// Neighbors left/right of the opposite vertex
yield return new Penrose(Kind.Dart, Corner + new Pentavector(0, 0, 0, -1).Rotate(Angle), Angle + 9);
yield return new Penrose(Kind.Dart, Corner + new Pentavector(1, 0, 0, 0).Rotate(Angle), Angle + 1);
yield return new Penrose(Kind.Kite, Corner + new Pentavector(1, -1, 1, -2).Rotate(Angle), Angle + 4);
yield return new Penrose(Kind.Kite, Corner + new Pentavector(2, -1, 1, -1).Rotate(Angle), Angle + 6);
}
else if (TileKind == Kind.Dart)
{
// Neighbors left/right of the Corner vertex
yield return new Penrose(Kind.Kite, Corner + new Pentavector(-1, 1, -1, 1).Rotate(Angle), Angle + 9);
yield return new Penrose(Kind.Kite, Corner + new Pentavector(-1, 1, -1, 1).Rotate(Angle), Angle + 1);
// Neighbors of the left/right edge
yield return new Penrose(Kind.Kite, Corner + new Pentavector(-1, 1, -1, 0).Rotate(Angle), Angle);
yield return new Penrose(Kind.Kite, Corner + new Pentavector(0, 1, -1, 1).Rotate(Angle), Angle);
// Neighbors left/right of the opposite vertex
yield return new Penrose(Kind.Dart, Corner + new Pentavector(0, 2, -2, 1).Rotate(Angle), Angle + 8);
yield return new Penrose(Kind.Dart, Corner + new Pentavector(-1, 2, -2, 0).Rotate(Angle), Angle + 2);
}
else if (TileKind == Kind.ThickRhomb)
{
// Neighbors left/right of the Corner vertex
yield return new Penrose(Kind.ThickRhomb, Corner, Angle + 2);
yield return new Penrose(Kind.ThickRhomb, Corner, Angle + 8);
yield return new Penrose(Kind.ThinRhomb, Corner, Angle + 1);
yield return new Penrose(Kind.ThinRhomb, Corner + new Pentavector(0, 0, -1, -1).Rotate(Angle), Angle + 3);
// Neighbors left/right of the opposite vertex
yield return new Penrose(Kind.ThickRhomb, Corner + new Pentavector(0, 0, -1, -1).Rotate(Angle), Angle + 2);
yield return new Penrose(Kind.ThinRhomb, Corner + new Pentavector(0, 0, 0, -1).Rotate(Angle), Angle);
yield return new Penrose(Kind.ThickRhomb, Corner + new Pentavector(1, 1, 0, 0).Rotate(Angle), Angle + 8);
yield return new Penrose(Kind.ThinRhomb, Corner + new Pentavector(2, -1, 1, -2).Rotate(Angle), Angle + 4);
}
else if (TileKind == Kind.ThinRhomb)
{
// Neighbors left/right of the Corner vertex
yield return new Penrose(Kind.ThickRhomb, Corner, Angle + 9);
yield return new Penrose(Kind.ThickRhomb, Corner + new Pentavector(0, 0, 0, 1).Rotate(Angle), Angle);
yield return new Penrose(Kind.ThinRhomb, Corner + new Pentavector(1, 1, 0, 0).Rotate(Angle), Angle + 6);
// Neighbors left/right of the opposite vertex
yield return new Penrose(Kind.ThickRhomb, Corner + new Pentavector(2, -1, 1, -1).Rotate(Angle), Angle + 7);
yield return new Penrose(Kind.ThickRhomb, Corner + new Pentavector(2, 0, 1, -1).Rotate(Angle), Angle + 6);
yield return new Penrose(Kind.ThinRhomb, Corner + new Pentavector(2, -1, 1, -1).Rotate(Angle), Angle + 4);
}
else
throw new InvalidOperationException($"Invalid Penrose.TileKind value ‘{TileKind}’.");
}
}
readonly IEnumerable<object> INeighbor<object>.Neighbors => Neighbors.Cast<object>();
/// <inheritdoc/>
public override readonly string ToString() => $"P{Corner}/{(int) TileKind}/{Angle}";
/// <summary>Describes the kind of shape of a <see cref="Penrose"/> tile.</summary>
public enum Kind
{
/// <summary>A kite shape, which is part of the P2 tiling.</summary>
Kite,
/// <summary>A dart shape, which is part of the P2 tiling.</summary>
Dart,
/// <summary>
/// A thick rhombus shape, which is part of the P3 tiling. The side lengths are 1 and the internal angles are
/// 72° and 108°.</summary>
ThickRhomb,
/// <summary>
/// A thin rhombus shape, which is part of the P3 tiling. The side lengths are 1 and the internal angles are
/// 36° and 144°.</summary>
ThinRhomb
}
/// <summary>Represents a grid of <see cref="Penrose"/> cells. The grid conforms to Penrose tiling P2 or P3.</summary>
public class Grid : Structure<Penrose>
{
/// <summary>
/// See <see cref="Structure{TCell}.Structure(IEnumerable{TCell}, IEnumerable{Link{TCell}}, Func{TCell,
/// IEnumerable{TCell}})"/>.</summary>
public Grid(IEnumerable<Penrose> cells, IEnumerable<Link<Penrose>> links = null, Func<Penrose, IEnumerable<Penrose>> getNeighbors = null)
: base(cells, links, getNeighbors)
{
}
/// <summary>
/// Constructs a grid consisting of <see cref="Penrose"/> tiles obtained by deflating (subdividing) a star
/// consisting of five initial shapes.</summary>
/// <param name="useRhombs">
/// If <c>true</c>, the initial shapes are <see cref="Kind.ThickRhomb"/> tiles and the final grid will consist
/// of those and <see cref="Kind.ThinRhomb"/> tiles. If <c>false</c>, the initial shapes are <see
/// cref="Kind.Kite"/> tiles and the final grid will consist of those and <see cref="Kind.Dart"/> tiles.</param>
/// <param name="numIterations">
/// Number of deflation iterations to perform.</param>
public Grid(bool useRhombs, int numIterations) : base(GenerateGrid(useRhombs, numIterations))
{
}
/// <summary>
/// Rotates the entire grid by the specified <paramref name="angle"/>.</summary>
/// <param name="angle">
/// The angle, specified as a multiple of 36° going clockwise (SVG) or counter-clockwise (geometry).</param>
/// <returns>
/// The new grid.</returns>
public Grid Rotate(int angle) => new Grid(_cells.Select(c => c.Rotate(angle)), _links.Select(l => new Link<Penrose>(l.Apart(out var other).Rotate(angle), other.Rotate(angle))));
/// <inheritdoc/>
protected override Structure<Penrose> makeModifiedStructure(IEnumerable<Penrose> cells, IEnumerable<Link<Penrose>> traversible) => new Grid(cells, traversible);
/// <summary>See <see cref="Structure{TCell}.GenerateMaze(Random, MazeBias)"/>.</summary>
public new Grid GenerateMaze(Random rnd = null, MazeBias bias = MazeBias.Default) => (Grid) base.GenerateMaze(rnd, bias);
/// <summary>See <see cref="Structure{TCell}.GenerateMaze(Func{int, int, int}, MazeBias)"/>.</summary>
public new Grid GenerateMaze(Func<int, int, int> rndNext, MazeBias bias = MazeBias.Default) => (Grid) base.GenerateMaze(rndNext, bias);
private static IEnumerable<Penrose> GenerateGrid(bool useRhombs, int numIterations)
{
var origTiles = Enumerable.Range(0, 5).Select(angle => new Penrose(useRhombs ? Kind.ThickRhomb : Kind.Kite, default, 2 * angle));
var tiles = origTiles;
IEnumerable<Penrose> prev = null;
for (var i = 0; i < numIterations; i++)
{
prev = tiles;
tiles = tiles.SelectMany(t => t.DeflatedTiles).Distinct();
}
return tiles;
}
}
/// <summary>
/// Rotates this cell by the specified <paramref name="angle"/> about the origin.</summary>
/// <param name="angle">
/// The angle, specified as a multiple of 36° going clockwise (SVG) or counter-clockwise (geometry).</param>
public readonly Penrose Rotate(int angle) => new Penrose(TileKind, Corner.Rotate(angle), Angle + angle);
}
}