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
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
|
C
C The following code was excerpted from: angle.f
C
DOUBLE PRECISION FUNCTION ANGLE(XA,YA,XB,YB,XC,YC)
IMPLICIT LOGICAL (A-Z)
DOUBLE PRECISION XA,XB,XC,YA,YB,YC
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Compute the interior angle (in radians) at vertex
C (XB,YB) of the chain formed by the directed edges from
C (XA,YA) to (XB,YB) to (XC,YC) - the interior is to the
C left of the two directed edges.
C
C Input parameters:
C XA,YA, XB,YB, XC,YC - vertex coordinates
C
C Returned function value:
C ANGLE - angle between 0 and 2*PI (PI/2 in degenerate case)
C
DOUBLE PRECISION PI,TOL
COMMON /GCONST/ PI,TOL
SAVE /GCONST/
C
DOUBLE PRECISION T,X1,X2,Y1,Y2
DOUBLE PRECISION SIGNUS
C
X1 = XA - XB
Y1 = YA - YB
X2 = XC - XB
Y2 = YC - YB
T = SQRT((X1**2 + Y1**2)*(X2**2 + Y2**2))
IF (T .EQ. 0.0D0) T = 1.0D0
T = (X1*X2 + Y1*Y2)/T
C
C Eliminate the call to sign to avoid using the fortran math library
C IF (ABS(T) .GT. 1.0D0 - TOL) T = SIGN(1.0D0,T)
C
SIGNUS = -1.0D0
IF (T .GT. 0.0D0) SIGNUS = 1.0D0
C
IF (ABS(T) .GT. 1.0D0 - TOL) T = SIGNUS
ANGLE = ACOS(T)
IF (X2*Y1 - Y2*X1 .LT. 0.0D0) ANGLE = 2.0D0*PI - ANGLE
END
C
C The following code was excerpted from: areapg.f
C
DOUBLE PRECISION FUNCTION AREAPG(NVRT,XC,YC)
IMPLICIT LOGICAL (A-Z)
INTEGER NVRT
DOUBLE PRECISION XC(NVRT),YC(NVRT)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Compute twice the signed area of a simple polygon with
C vertices given in circular (CCW or CW) order.
C
C Input parameters:
C NVRT - number of vertices on the boundary of polygon (>= 3)
C XC(1:NVRT),YC(1:NVRT) - vertex coordinates in CCW or CW order
C
C Returned function value:
C AREAPG - twice the signed area of polygon, positive if CCW
C
INTEGER I
DOUBLE PRECISION SUM
C
SUM = XC(1)*(YC(2) - YC(NVRT)) + XC(NVRT)*(YC(1) - YC(NVRT-1))
DO 10 I = 2,NVRT-1
SUM = SUM + XC(I)*(YC(I+1) - YC(I-1))
10 CONTINUE
AREAPG = SUM
END
C
C The following code was excerpted from: areatr.f
C
DOUBLE PRECISION FUNCTION AREATR(XA,YA,XB,YB,XC,YC)
IMPLICIT LOGICAL (A-Z)
DOUBLE PRECISION XA,XB,XC,YA,YB,YC
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Compute twice the signed area of the triangle with
C vertices (XA,YA), (XB,YB), and (XC,YC) in CCW or CW order.
C
C Input parameters:
C XA,YA, XB,YB, XC,YC - vertex coordinates
C
C Returned function value:
C AREATR - twice the signed area of triangle, positive if CCW
C
AREATR = (XB - XA)*(YC - YA) - (XC - XA)*(YB - YA)
END
C
C The following code was excerpted from: diaedg.f
C
INTEGER FUNCTION DIAEDG(X0,Y0,X1,Y1,X2,Y2,X3,Y3)
IMPLICIT LOGICAL (A-Z)
DOUBLE PRECISION X0,X1,X2,X3,Y0,Y1,Y2,Y3
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Determine whether 02 or 13 is the diagonal edge chosen
C based on the circumcircle criterion, where (X0,Y0), (X1,Y1),
C (X2,Y2), (X3,Y3) are the vertices of a simple quadrilateral
C in counterclockwise order.
C
C Input parameters:
C X0,Y0, X1,Y1, X2,Y2, X3,Y3 - vertex coordinates
C
C Returned function value:
C DIAEDG - 1 if diagonal edge 02 is chosen, i.e. 02 is inside
C quadrilateral + vertex 3 is outside circumcircle 012
C -1 if diagonal edge 13 is chosen, i.e. 13 is inside
C quadrilateral + vertex 0 is outside circumcircle 123
C 0 if four vertices are cocircular
C
DOUBLE PRECISION PI,TOL
COMMON /GCONST/ PI,TOL
SAVE /GCONST/
C
DOUBLE PRECISION CA,CB,DX10,DX12,DX30,DX32,DY10,DY12,DY30,DY32
DOUBLE PRECISION S,TOLA,TOLB
C
DX10 = X1 - X0
DY10 = Y1 - Y0
DX12 = X1 - X2
DY12 = Y1 - Y2
DX30 = X3 - X0
DY30 = Y3 - Y0
DX32 = X3 - X2
DY32 = Y3 - Y2
TOLA = TOL*MAX(ABS(DX10),ABS(DY10),ABS(DX30),ABS(DY30))
TOLB = TOL*MAX(ABS(DX12),ABS(DY12),ABS(DX32),ABS(DY32))
CA = DX10*DX30 + DY10*DY30
CB = DX12*DX32 + DY12*DY32
IF (CA .GT. TOLA .AND. CB .GT. TOLB) THEN
DIAEDG = -1
ELSE IF (CA .LT. -TOLA .AND. CB .LT. -TOLB) THEN
DIAEDG = 1
ELSE
TOLA = MAX(TOLA,TOLB)
S = (DX10*DY30 - DX30*DY10)*CB + (DX32*DY12 - DX12*DY32)*CA
IF (S .GT. TOLA) THEN
DIAEDG = -1
ELSE IF (S .LT. -TOLA) THEN
DIAEDG = 1
ELSE
DIAEDG = 0
ENDIF
ENDIF
END
C
C The following code was excerpted from: diam2.f
C
SUBROUTINE DIAM2(NVRT,XC,YC,I1,I2,DIAMSQ)
IMPLICIT LOGICAL (A-Z)
INTEGER I1,I2,NVRT
DOUBLE PRECISION DIAMSQ,XC(NVRT),YC(NVRT)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Find the diameter of a convex polygon with vertices
C given in CCW order and with all interior angles < PI.
C
C Input parameters:
C NVRT - number of vertices on the boundary of convex polygon
C XC(1:NVRT),YC(1:NVRT) - vertex coordinates in CCW order
C
C Output parameters:
C I1,I2 - indices in XC,YC of diameter edge; diameter is from
C (XC(I1),YC(I1)) to (XC(I2),YC(I2))
C DIAMSQ - square of diameter
C
C Abnormal return:
C IERR is set to 200
C
C Routines called:
C AREATR
C
INTEGER IERR
DOUBLE PRECISION PI,TOL
COMMON /GERROR/ IERR
COMMON /GCONST/ PI,TOL
SAVE /GERROR/,/GCONST/
C
INTEGER J,JP1,K,KP1,M
DOUBLE PRECISION AREATR
DOUBLE PRECISION AREA1,AREA2,C1MTOL,C1PTOL,DIST
C
C Find first vertex which is farthest from edge connecting
C vertices with indices NVRT, 1.
C
C1MTOL = 1.0D0 - TOL
C1PTOL = 1.0D0 + TOL
J = NVRT
JP1 = 1
K = 2
AREA1 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(K),YC(K))
10 CONTINUE
AREA2 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(K+1),YC(K+1))
IF (AREA2 .GT. AREA1*C1PTOL) THEN
AREA1 = AREA2
K = K + 1
GO TO 10
ENDIF
M = K
DIAMSQ = 0.0D0
C
C Find diameter = maximum distance of antipodal pairs.
C
AREA1 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(K),YC(K))
20 CONTINUE
KP1 = K + 1
IF (KP1 .GT. NVRT) KP1 = 1
AREA2 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(KP1),YC(KP1))
IF (AREA2 .GT. AREA1*C1PTOL) THEN
K = K + 1
AREA1 = AREA2
ELSE IF (AREA2 .LT. AREA1*C1MTOL) THEN
J = JP1
JP1 = J + 1
AREA1 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(K),YC(K))
ELSE
K = K + 1
J = JP1
JP1 = J + 1
AREA1 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(K),YC(K))
ENDIF
IF (J .GT. M .OR. K .GT. NVRT) THEN
IERR = 200
RETURN
ENDIF
DIST = (XC(J) - XC(K))**2 + (YC(J) - YC(K))**2
IF (DIST .GT. DIAMSQ) THEN
DIAMSQ = DIST
I1 = J
I2 = K
ENDIF
IF (J .NE. M .OR. K .NE. NVRT) GO TO 20
END
C
C The following code was excerpted from: lrline.f
C
INTEGER FUNCTION LRLINE(XU,YU,XV1,YV1,XV2,YV2,DV)
IMPLICIT LOGICAL (A-Z)
DOUBLE PRECISION DV,XU,XV1,XV2,YU,YV1,YV2
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Determine whether a point is to the left of, right of,
C or on a directed line parallel to a line through given points.
C
C Input parameters:
C XU,YU, XV1,YV1, XV2,YV2 - vertex coordinates; the directed
C line is parallel to and at signed distance DV to the
C left of the directed line from (XV1,YV1) to (XV2,YV2);
C (XU,YU) is the vertex for which the position
C relative to the directed line is to be determined
C DV - signed distance (positive for left)
C
C Returned function value:
C LRLINE - +1, 0, or -1 depending on whether (XU,YU) is
C to the right of, on, or left of the directed line
C (0 if line degenerates to a point)
C
DOUBLE PRECISION PI,TOL
COMMON /GCONST/ PI,TOL
SAVE /GCONST/
C
DOUBLE PRECISION DX,DXU,DY,DYU,T,TOLABS
DOUBLE PRECISION SIGNUS
C
DX = XV2 - XV1
DY = YV2 - YV1
DXU = XU - XV1
DYU = YU - YV1
TOLABS = TOL*MAX(ABS(DX),ABS(DY),ABS(DXU),ABS(DYU),ABS(DV))
T = DY*DXU - DX*DYU
IF (DV .NE. 0.0D0) T = T + DV*SQRT(DX**2 + DY**2)
C
C Eliminate the call to sign to avoid using the fortran math library
C LRLINE = INT(SIGN(1.0D0,T))
C
SIGNUS = -1.0D0
IF (T .GT. 0.0D0) SIGNUS = 1.0D0
C
LRLINE = INT(SIGNUS)
IF (ABS(T) .LE. TOLABS) LRLINE = 0
END
C
C The following code was excerpted from: shrnk2.f
C
SUBROUTINE SHRNK2(NVRT,XC,YC,SDIST,NSHR,XS,YS,IEDGE)
IMPLICIT LOGICAL (A-Z)
INTEGER NSHR,NVRT
INTEGER IEDGE(0:NVRT)
DOUBLE PRECISION SDIST(0:NVRT-1)
DOUBLE PRECISION XC(0:NVRT),YC(0:NVRT),XS(0:NVRT),YS(0:NVRT)
C
C Purpose: Shrink a convex polygon, with vertices given in CCW
C order and with all interior angles < PI, by distance SDIST(I)
C for Ith edge, I = 0,...,NVRT-1.
C
C Input parameters:
C NVRT - number of vertices on the boundary of convex polygon
C XC(0:NVRT),YC(0:NVRT) - vertex coordinates in CCW order;
C (XC(0),YC(0)) = (XC(NVRT),YC(NVRT))
C SDIST(0:NVRT-1) - nonnegative shrink distances for edges
C
C Output parameters:
C NSHR - number of vertices on boundary of shrunken polygon;
C 0 if shrunken polygon is empty else 3 <= NSHR <= NVRT
C XS(0:NSHR),YS(0:NSHR) - coordinates of shrunken polygon in CCW
C order if NSHR > 0; (XS(0),YS(0)) = (XS(NSHR),YS(NSHR))
C IEDGE(0:NVRT) - indices of edges of shrunken polygon in
C range from 0 to NVRT-1
C
C Abnormal return:
C IERR is set to 202
C
C Routines called:
C LRLINE, XLINE
C
INTEGER IERR
DOUBLE PRECISION PI,TOL
COMMON /GERROR/ IERR
COMMON /GCONST/ PI,TOL
SAVE /GERROR/,/GCONST/
C
INTEGER LRLINE
INTEGER I,J,K,LR
DOUBLE PRECISION ALPHA,PI2,THETA
LOGICAL FIRST,PARALL
C
PI2 = 2.0D0*PI
ALPHA = ATAN2(YC(1)-YC(0),XC(1)-XC(0))
CALL XLINE(XC(0),YC(0),XC(1),YC(1),XC(1),YC(1),XC(2),YC(2),
$ SDIST(0),SDIST(1),XS(1),YS(1),PARALL)
IF (PARALL) THEN
IERR = 202
GO TO 90
ENDIF
IEDGE(0) = 0
IEDGE(1) = 1
I = 2
J = 0
NSHR = 1
FIRST = .TRUE.
C
C First while loop processes edges subtending angle <= PI
C with respect to first edge.
C
10 CONTINUE
THETA = ATAN2(YC(I+1)-YC(I),XC(I+1)-XC(I)) - ALPHA
IF (THETA .LT. 0.0D0) THETA = THETA + PI2
IF (THETA .GT. PI + TOL) GO TO 40
20 CONTINUE
LR = LRLINE(XS(NSHR),YS(NSHR),XC(I),YC(I),XC(I+1),YC(I+1),
$ SDIST(I))
IF (LR .LT. 0) GO TO 30
NSHR = NSHR - 1
IF (NSHR .GE. 1) GO TO 20
30 CONTINUE
IF (NSHR .LT. 1 .AND. ABS(THETA - PI) .LE. TOL) GO TO 90
K = IEDGE(NSHR)
NSHR = NSHR + 1
CALL XLINE(XC(K),YC(K),XC(K+1),YC(K+1),XC(I),YC(I),XC(I+1),
$ YC(I+1),SDIST(K),SDIST(I),XS(NSHR),YS(NSHR),PARALL)
IF (PARALL) THEN
IERR = 202
GO TO 90
ENDIF
IEDGE(NSHR) = I
I = I + 1
GO TO 10
C
C Second while loop processes remaining edges.
C
40 CONTINUE
IF (FIRST) THEN
FIRST = .FALSE.
GO TO 50
ENDIF
LR = LRLINE(XS(J),YS(J),XC(I),YC(I),XC(I+1),YC(I+1),SDIST(I))
IF (LR .LE. 0) GO TO 70
50 CONTINUE
IF (NSHR .LE. J) GO TO 90
LR = LRLINE(XS(NSHR),YS(NSHR),XC(I),YC(I),XC(I+1),
$ YC(I+1),SDIST(I))
IF (LR .GE. 0) THEN
NSHR = NSHR - 1
GO TO 50
ENDIF
K = IEDGE(NSHR)
NSHR = NSHR + 1
CALL XLINE(XC(K),YC(K),XC(K+1),YC(K+1),XC(I),YC(I),XC(I+1),
$ YC(I+1),SDIST(K),SDIST(I),XS(NSHR),YS(NSHR),PARALL)
IF (PARALL) THEN
IERR = 202
GO TO 90
ENDIF
IEDGE(NSHR) = I
60 CONTINUE
LR = LRLINE(XS(J+1),YS(J+1),XC(I),YC(I),XC(I+1),YC(I+1),
$ SDIST(I))
IF (LR .GE. 0) THEN
J = J + 1
GO TO 60
ENDIF
K = IEDGE(J)
CALL XLINE(XC(K),YC(K),XC(K+1),YC(K+1),XC(I),YC(I),XC(I+1),
$ YC(I+1),SDIST(K),SDIST(I),XS(J),YS(J),PARALL)
IF (PARALL) THEN
IERR = 202
GO TO 90
ENDIF
XS(NSHR+1) = XS(J)
YS(NSHR+1) = YS(J)
IEDGE(NSHR+1) = IEDGE(J)
70 CONTINUE
I = I + 1
IF (I .LT. NVRT) GO TO 40
C
IF (J .GT. 0) THEN
DO 80 I = 0,NSHR+1-J
XS(I) = XS(I+J)
YS(I) = YS(I+J)
IEDGE(I) = IEDGE(I+J)
80 CONTINUE
ENDIF
NSHR = NSHR + 1 - J
RETURN
C
90 CONTINUE
NSHR = 0
RETURN
END
C
C The following code was excerpted from: width2.f
C
SUBROUTINE WIDTH2(NVRT,XC,YC,I1,I2,WIDSQ)
IMPLICIT LOGICAL (A-Z)
INTEGER I1,I2,NVRT
DOUBLE PRECISION WIDSQ,XC(NVRT),YC(NVRT)
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Find the width (minimum breadth) of a convex polygon with
C vertices given in CCW order and with all interior angles < PI.
C
C Input parameters:
C NVRT - number of vertices on the boundary of convex polygon
C XC(1:NVRT),YC(1:NVRT) - vertex coordinates in CCW order
C
C Output parameters:
C I1,I2 - indices in XC,YC such that width is from vertex
C (XC(I1),YC(I1)) to line joining (XC(I2),YC(I2)) and
C (XC(I2+1),YC(I2+1)), where index NVRT+1 is same as 1
C WIDSQ - square of width
C
C Abnormal return:
C IERR is set to 201
C
C Routines called:
C AREATR
C
INTEGER IERR
DOUBLE PRECISION PI,TOL
COMMON /GERROR/ IERR
COMMON /GCONST/ PI,TOL
SAVE /GERROR/,/GCONST/
C
INTEGER A,B,C,J,JP1,K,KP1,M
DOUBLE PRECISION AREATR
DOUBLE PRECISION AREA1,AREA2,C1MTOL,C1PTOL,DIST,DX,DY
C
C Find first vertex which is farthest from edge connecting
C vertices with indices NVRT, 1.
C
C1MTOL = 1.0D0 - TOL
C1PTOL = 1.0D0 + TOL
J = NVRT
JP1 = 1
K = 2
AREA1 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(K),YC(K))
10 CONTINUE
AREA2 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(K+1),YC(K+1))
IF (AREA2 .GT. AREA1*C1PTOL) THEN
AREA1 = AREA2
K = K + 1
GO TO 10
ENDIF
M = K
WIDSQ = 0.0D0
C
C Find width = min distance of antipodal edge-vertex pairs.
C
AREA1 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(K),YC(K))
20 CONTINUE
KP1 = K + 1
IF (KP1 .GT. NVRT) KP1 = 1
AREA2 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(KP1),YC(KP1))
IF (AREA2 .GT. AREA1*C1PTOL) THEN
A = J
B = K
K = K + 1
C = K
IF (C .GT. NVRT) C = 1
AREA1 = AREA2
ELSE IF (AREA2 .LT. AREA1*C1MTOL) THEN
A = K
B = J
C = JP1
J = JP1
JP1 = J + 1
AREA1 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(K),YC(K))
ELSE
A = K
B = J
C = JP1
K = K + 1
J = JP1
JP1 = J + 1
AREA1 = AREATR(XC(J),YC(J),XC(JP1),YC(JP1),XC(K),YC(K))
ENDIF
IF (J .GT. M .OR. K .GT. NVRT) THEN
IERR = 201
RETURN
ENDIF
DX = XC(C) - XC(B)
DY = YC(C) - YC(B)
DIST = ((YC(A) - YC(B))*DX - (XC(A) - XC(B))*DY)**2/
$ (DX**2 + DY**2)
IF (DIST .LT. WIDSQ .OR. WIDSQ .LE. 0.0D0) THEN
WIDSQ = DIST
I1 = A
I2 = B
ENDIF
IF (J .NE. M .OR. K .NE. NVRT) GO TO 20
END
C
C The following code was excerpted from: xedge.f
C
SUBROUTINE XEDGE(MODE,XV1,YV1,XV2,YV2,XW1,YW1,XW2,YW2,XU,YU,
$ INTSCT)
IMPLICIT LOGICAL (A-Z)
INTEGER MODE
DOUBLE PRECISION XU,XV1,XV2,XW1,XW2,YU,YV1,YV2,YW1,YW2
LOGICAL INTSCT
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Determine whether two edges or a ray and an edge
C intersect and return the intersection point if they do.
C
C Input parameters:
C MODE - 0 for two edges, 1 (or nonzero) for a ray and an edge
C XV1,YV1, XV2,YV2, XW1,YW1, XW2,YW2 - vertex coordinates;
C an edge (ray) is from (XV1,YV1) to (thru) (XV2,YV2);
C an edge joins vertices (XW1,YW1) and (XW2,YW2)
C
C Output parameters:
C XU,YU - coordinates of the point of intersection iff INTSCT
C is .TRUE.
C INTSCT - .TRUE. if the edges/ray are nondegenerate, not
C parallel, and intersect, .FALSE. otherwise
C
DOUBLE PRECISION PI,TOL
COMMON /GCONST/ PI,TOL
SAVE /GCONST/
C
DOUBLE PRECISION DENOM,DXV,DXW,DYV,DYW,T,TOLABS
C
INTSCT = .FALSE.
DXV = XV2 - XV1
DYV = YV2 - YV1
DXW = XW2 - XW1
DYW = YW2 - YW1
TOLABS = TOL*MAX(ABS(DXV),ABS(DYV),ABS(DXW),ABS(DYW))
DENOM = DYV*DXW - DXV*DYW
IF (ABS(DENOM) .LE. TOLABS) RETURN
T = (DYV*(XV1 - XW1) - DXV*(YV1 - YW1))/DENOM
IF (T .LT. -TOL .OR. T .GT. 1.0D0 + TOL) RETURN
XU = XW1 + T*DXW
YU = YW1 + T*DYW
IF (ABS(DXV) .GE. ABS(DYV)) THEN
T = (XU - XV1)/DXV
ELSE
T = (YU - YV1)/DYV
ENDIF
IF (MODE .EQ. 0) THEN
IF (T .GE. -TOL .AND. T .LE. 1.0D0 + TOL) INTSCT = .TRUE.
ELSE
IF (T .GE. -TOL) INTSCT = .TRUE.
ENDIF
END
C
C The following code was excerpted from: xline.f
C
SUBROUTINE XLINE(XV1,YV1,XV2,YV2,XW1,YW1,XW2,YW2,DV,DW,
$ XU,YU,PARALL)
IMPLICIT LOGICAL (A-Z)
DOUBLE PRECISION DV,DW,XU,XV1,XV2,XW1,XW2,YU,YV1,YV2,YW1,YW2
LOGICAL PARALL
C
C Written and copyright by:
C Barry Joe, Dept. of Computing Science, Univ. of Alberta
C Edmonton, Alberta, Canada T6G 2H1
C Phone: (403) 492-5757 Email: barry@cs.ualberta.ca
C
C Purpose: Determine the intersection point of two lines parallel
C to lines through given points.
C
C Input parameters:
C XV1,YV1, XV2,YV2, XW1,YW1, XW2,YW2 - vertex coordinates;
C first line is parallel to and at signed distance DV to
C left of directed line from (XV1,YV1) to (XV2,YV2);
C second line is parallel to and at signed distance DW to
C left of directed line from (XW1,YW1) to (XW2,YW2)
C DV,DW - signed distances (positive for left)
C
C Output parameters:
C XU,YU - coordinates of the point of intersection iff PARALL
C is .FALSE.
C PARALL - .TRUE. if the lines are parallel or two points for a
C line are identical, .FALSE. otherwise
C
DOUBLE PRECISION PI,TOL
COMMON /GCONST/ PI,TOL
SAVE /GCONST/
C
DOUBLE PRECISION A11,A12,A21,A22,B1,B2,DET,TOLABS
C
PARALL = .TRUE.
A11 = YV2 - YV1
A12 = XV1 - XV2
A21 = YW2 - YW1
A22 = XW1 - XW2
TOLABS = TOL*MAX(ABS(A11),ABS(A12),ABS(A21),ABS(A22))
DET = A11*A22 - A21*A12
IF (ABS(DET) .LE. TOLABS) RETURN
B1 = XV1*A11 + YV1*A12
IF (DV .NE. 0.0D0) B1 = B1 - DV*SQRT(A11**2 + A12**2)
B2 = XW1*A21 + YW1*A22
IF (DW .NE. 0.0D0) B2 = B2 - DW*SQRT(A21**2 + A22**2)
XU = (B1*A22 - B2*A12)/DET
YU = (B2*A11 - B1*A21)/DET
PARALL = .FALSE.
END
|
