-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathCRESC50.SIF
818 lines (680 loc) · 18.8 KB
/
CRESC50.SIF
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
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
***************************
* SET UP THE INITIAL DATA *
***************************
NAME CRESC50
* Problem :
* *********
* This problem consists in finding the crescent of smallest area containing
* a set of points given in the plane. This problem arises as a subproblem
* in pattern recognition and has been suggested by J.P. Rasson. It
* originates in the detection of "salt domes" (with the potential presence of
* oil pockets!) from geological data.
* The problem is not convex.
* A crescent is defined as follows. Assume one has two circles of center
* C1 and C2 and of radii r1 and r2 respectively. Assume furthermore that
* r1 >= r2 and that C2 is within C1. Assume finally that the distance from
* C1 to C2 is >= r1 - r2. Then the crescent is the part of the plane
* contained in circle 2 but not in circle 1.
* In order to preserve feasibility at all stages (ensuring that the
* crescent exists and that its area can be computed), the following
* parametrization is used:
* ( C2x, C2y ) = ( C1x, C1y ) + a * d * ( cos(t), sin(t) )
* r1 = a * d + r
* r2 = ( a + 1 ) * d + r
* with the bounds
* a >= 1, 0 <= t <= 2 * pi, r2 >= 0 , 0 <= d <= 1.
* SIF input: Ph. Toint, June 1993.
* classification OOR2-MY-6-100
* number of points to be included in the crescent.
* the number of constraints is 2*NP
IE NP 50
* data points
RE X1 0.514
RE Y1 0.176
RE X2 0.948
RE Y2 0.172
RE X3 0.702
RE Y3 0.226
RE X4 0.495
RE Y4 0.125
RE X5 0.823
RE Y5 0.152
RE X6 0.625
RE Y6 0.315
RE X7 0.347
RE Y7 0.917
RE X8 0.520
RE Y8 0.401
RE X9 0.607
RE Y9 0.785
RE X10 0.758
RE Y10 0.582
RE X11 0.200
RE Y11 0.827
RE X12 0.416
RE Y12 0.464
RE X13 0.979
RE Y13 0.126
RE X14 0.213
RE Y14 0.958
RE X15 0.737
RE Y15 0.409
RE X16 0.957
RE Y16 0.028
RE X17 0.319
RE Y17 0.757
RE X18 0.572
RE Y18 0.119
RE X19 0.570
RE Y19 0.252
RE X20 0.496
RE Y20 0.237
RE X21 0.477
RE Y21 0.406
RE X22 0.873
RE Y22 0.427
RE X23 0.522
RE Y23 0.697
RE X24 0.773
RE Y24 0.245
RE X25 0.887
RE Y25 0.037
RE X26 0.651
RE Y26 0.399
RE X27 0.676
RE Y27 0.733
RE X28 0.938
RE Y28 0.233
RE X29 0.779
RE Y29 0.431
RE X30 0.750
RE Y30 0.208
RE X31 0.803
RE Y31 0.219
RE X32 0.563
RE Y32 0.716
RE X33 0.653
RE Y33 0.604
RE X34 0.790
RE Y34 0.079
RE X35 0.246
RE Y35 0.945
RE X36 0.477
RE Y36 0.800
RE X37 0.744
RE Y37 0.381
RE X38 0.480
RE Y38 0.527
RE X39 0.446
RE Y39 0.705
RE X40 0.095
RE Y40 0.963
RE X41 0.551
RE Y41 0.740
RE X42 0.579
RE Y42 0.638
RE X43 0.782
RE Y43 0.188
RE X44 0.684
RE Y44 0.293
RE X45 0.565
RE Y45 0.418
RE X46 0.566
RE Y46 0.488
RE X47 0.607
RE Y47 0.416
RE X48 0.036
RE Y48 0.977
RE X49 0.647
RE Y49 0.350
RE X50 0.553
RE Y50 0.358
* useful constants
IE 1 1
VARIABLES
X V1
X W1
X D
X A
X T
X R
GROUPS
XN OBJ
DO I 1 NP
XL IS2(I)
XG OS1(I)
ND
BOUNDS
XR CRESC50 V1
XR CRESC50 W1
XL CRESC50 R 0.39
XL CRESC50 A 1.0
XL CRESC50 T 0.0
XU CRESC50 T 6.2831852
XL CRESC50 D 1.0D-8
START POINT
XV CRESC50 V1 -40.0
XV CRESC50 W1 5.0
XV CRESC50 R 0.75
XV CRESC50 A 2.0
XV CRESC50 T 1.5
XV CRESC50 D 1.0
* Global solution
*XV CRESC50 V1 -0.75
*XV CRESC50 W1 0.0
*XV CRESC50 R 0.5
*XV CRESC50 A 1.5
*XV CRESC50 T 0.0
*XV CRESC50 D 0.5
ELEMENT TYPE
EV SQR1 A R
EV SQR1 D
EV SQR2 D R
IV SQR2 RAD
EV SC AZ BZ
EV SC DZ
EV DIST X
EP DIST P
EV DISTX X T
EV DISTX A D
EP DISTX P
EV DISTY X T
EV DISTY A D
EP DISTY P
ELEMENT USES
XT OB SC
ZV OB AZ A
ZV OB BZ R
ZV OB DZ D
XT R2SQ SQR2
ZV R2SQ D D
ZV R2SQ R R
XT R1SQ SQR1
ZV R1SQ D D
ZV R1SQ A A
ZV R1SQ R R
DO I 1 NP
XT XV1(I) DIST
ZV XV1(I) X V1
ZP XV1(I) P X(I)
XT XV2(I) DISTX
ZV XV2(I) X V1
ZV XV2(I) A A
ZV XV2(I) D D
ZV XV2(I) T T
ZP XV2(I) P X(I)
XT YW1(I) DIST
ZV YW1(I) X W1
ZP YW1(I) P Y(I)
XT YW2(I) DISTY
ZV YW2(I) X W1
ZV YW2(I) A A
ZV YW2(I) D D
ZV YW2(I) T T
ZP YW2(I) P Y(I)
ND
GROUP USES
XE OBJ OB
DO I 1 NP
XE IS2(I) XV2(I) YW2(I)
XE IS2(I) R2SQ -1.0
XE OS1(I) XV1(I) YW1(I)
XE OS1(I) R1SQ -1.0
ND
OBJECT BOUND
* Solution 0.87189692
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS CRESC50
TEMPORARIES
R A
R AB
R AD
R B
R BT
R BA
R BB
R BD
R BAD
R C
R CQ
R CT
R CA
R CB
R CD
R CH
R CHH
R CAA
R CAB
R CAD
R CBB
R CBD
R CDD
R D
R D2
R DA
R DD
R DAD
R E
R EA
R EB
R ED
R EAB
R EAD
R EBD
R EDD
R F
R FA
R FB
R FD
R FAA
R FAB
R FAD
R FBB
R FBD
R FDD
R G
R SG
R CG
R GF
R GA
R GB
R GD
R GFF
R GAA
R GAB
R GAD
R GBB
R GBD
R GDD
R H
R HA
R HB
R HD
R HAA
R HAB
R HAD
R HBB
R HBD
R HDD
R I
R IA
R IB
R ID
R IAA
R IAB
R IAD
R IBB
R IBD
R IDD
R J
R JA
R JB
R JD
R JAA
R JAB
R JAD
R JBB
R JBD
R JDD
R K
R KX
R KY
R KA
R KB
R KD
R L
R LA
R LB
R LD
R LAA
R LAB
R LAD
R LBB
R LBD
R LDD
R M
R MA
R MB
R MD
R N
R NB
R ND
R O
R OD
R P
R PA
R PB
R PD
R PAA
R PAB
R PAD
R PBD
R PDD
R Q
R QL
R QLL
R QA
R QB
R QD
R QAA
R QAB
R QAD
R QBB
R QBD
R QDD
R R
R RA
R RB
R RD
R RAA
R RAB
R RAD
R RBB
R RBD
R RDD
R S
R SQ
R ST
R SA
R SB
R SD
R SAA
R SAB
R SAD
R SBB
R SBD
R SDD
R U
R UA
R UB
R UD
R UAA
R UAB
R UAD
R UBB
R UBD
R UDD
R V
R VA
R VB
R VD
R VAA
R VAB
R VAD
R VBB
R VBD
R VDD
R W
R WA
R WB
R WD
R WAA
R WAB
R WAD
R WBB
R WBD
R WDD
M SQRT
M SIN
M COS
M ACOS
M ACOS
INDIVIDUALS
T SQR1
A Q A * D + R
F Q * Q
G A 2.0 * Q * D
G D 2.0 * Q * A
G R 2.0 * Q
H A A 2.0 * D * D
H A D 2.0 * ( A * D + Q )
H A R 2.0 * D
H D D 2.0 * A * A
H D R 2.0 * A
H R R 2.0
T SQR2
R RAD D 1.0 R 1.0
F RAD * RAD
G RAD RAD + RAD
H RAD RAD 2.0
T SC
A A DZ + BZ
A AB 1.0
A AD 1.0
A B AZ * DZ + BZ
A BA DZ
A BB 1.0
A BD AZ
A BAD 1.0
A D AZ * DZ
A DA DZ
A DD AZ
A DAD 1.0
A E 2.0 * A * D
A EA 2.0 * A * DA
A EB 2.0 * AB * D
A ED 2.0 * ( A * DD + AD * D )
A EAB 2.0 * AB * DA
A EAD 2.0 * ( AD * DA + A * DAD )
A EBD 2.0 * AB * DD
A EDD 2.0 * ( AD * DD + AD * DD )
A P 2.0 * B * D
A PA 2.0 * ( B * DA + BA * D )
A PB 2.0 * BB * D
A PD 2.0 * ( B * DD + BD * D )
A PAA 2.0 * ( BA * DA + BA * DA )
A PAB 2.0 * BB * DA
A PAD 2.0 * ( BD * DA + B * DAD + BAD * D
A+ + BA * DD )
A PBD 2.0 * BB * DD
A PDD 2.0 * ( BD * DD + BD * DD )
A F D * D + B * B - A * A
A FA 2.0 * ( D * DA + B * BA )
A FB 2.0 * ( B * BB - A * AB )
A FD 2.0 * ( D * DD + B * BD - A * AD )
A FAA 2.0 * ( DA * DA + BA * BA )
A FAB 2.0 * BB * BA
A FAD 2.0 * ( DD * DA + D * DAD + BD * BA
A+ + B * BAD )
A FBB 2.0 * ( BB * BB - AB * AB )
A FBD 2.0 * ( BD * BB - AD * AB )
A FDD 2.0 * ( DD * DD + BD * BD - AD * AD )
A G D * D - B * B + A * A
A GA 2.0 * ( D * DA - B * BA )
A GB 2.0 * ( - B * BB + A * AB )
A GD 2.0 * ( D * DD - B * BD + A * AD )
A GAA 2.0 * ( DA * DA - BA * BA )
A GAB - 2.0 * BB * BA
A GAD 2.0 * ( DD * DA + D * DAD - BD * BA
A+ - B * BAD )
A GBB 2.0 * ( - BB * BB + AB * AB )
A GBD 2.0 * ( - BD * BB + AD * AB )
A GDD 2.0 * ( DD * DD - BD * BD + AD * AD )
A H F / P
A I FA - H * PA
A J FB - H * PB
A K FD - H * PD
A HA I / P
A HB J / P
A HD K / P
A IA FAA - HA * PA - H * PAA
A IB FAB - HB * PA - H * PAB
A ID FAD - HD * PA - H * PAD
A JB FBB - HB * PB
A JD FBD - HD * PB - H * PBD
A KD FDD - HD * PD - H * PDD
A HAA ( IA - HA * PA ) / P
A HAB ( IB - HA * PB ) / P
A HAD ( ID - HA * PD ) / P
A HBB ( JB - HB * PB ) / P
A HBD ( JD - HB * PD ) / P
A HDD ( KD - HD * PD ) / P
A L - G / E
A M - GA - L * EA
A N - GB - L * EB
A O - GD - L * ED
A LA M / E
A LB N / E
A LD O / E
A MA - GAA - LA * EA
A MB - GAB - LB * EA - L * EAB
A MD - GAD - LD * EA - L * EAD
A NB - GBB - LB * EB
A ND - GBD - LD * EB - L * EBD
A OD - GDD - LD * ED - L * EDD
A LAA ( MA - LA * EA ) / E
A LAB ( MB - LA * EB ) / E
A LAD ( MD - LA * ED ) / E
A LBB ( NB - LB * EB ) / E
A LBD ( ND - LB * ED ) / E
A LDD ( OD - LD * ED ) / E
A C ACOS( H )
A CH - 1.0 / SQRT( 1.0 - H * H )
A CHH CH * H / ( 1.0 - H * H )
A CA CH * HA
A CB CH * HB
A CD CH * HD
A CAA CHH * HA * HA + CH * HAA
A CAB CHH * HA * HB + CH * HAB
A CAD CHH * HA * HD + CH * HAD
A CBB CHH * HB * HB + CH * HBB
A CBD CHH * HB * HD + CH * HBD
A CDD CHH * HD * HD + CH * HDD
A Q ACOS( L )
A QL - 1.0 / SQRT( 1.0 - L * L )
A QLL QL * L / ( 1.0 - L * L )
A QA QL * LA
A QB QL * LB
A QD QL * LD
A QAA QLL * LA * LA + QL * LAA
A QAB QLL * LA * LB + QL * LAB
A QAD QLL * LA * LD + QL * LAD
A QBB QLL * LB * LB + QL * LBB
A QBD QLL * LB * LD + QL * LBD
A QDD QLL * LD * LD + QL * LDD
A R B * B * C
A RA 2.0 * B * BA * C + B * B * CA
A RB 2.0 * B * BB * C + B * B * CB
A RD 2.0 * B * BD * C + B * B * CD
A RAA 2.0 * ( BA * BA * C + B * BA * CA
A+ + B * BA * CA ) + B * B * CAA
A RAB 2.0 * ( BB * BA * C + B * BA * CB
A+ + B * BB * CA ) + B * B * CAB
A RAD 2.0 * ( BD * BA * C + B * BAD * C
A+ + B * BA * CD + B * BD * CA )
A+ + B * B * CAD
A RBB 2.0 * ( BB * BB * C + B * BB * CB
A+ + B * BB * CB ) + B * B * CBB
A RBD 2.0 * ( BD * BB * C + B * BB * CD
A+ + B * BD * CB ) + B * B * CBD
A RDD 2.0 * ( BD * BD * C + B * BD * CD
A+ + B * BD * CD ) + B * B * CDD
A S A * A * Q
A SA A * A * QA
A SB 2.0 * A * AB * Q + A * A * QB
A SD 2.0 * A * AD * Q + A * A * QD
A SAA A * A * QAA
A SAB 2.0 * A * AB * QA + A * A * QAB
A SAD 2.0 * A * AD * QA + A * A * QAD
A SBB 2.0 * ( AB * AB * Q + A * AB * QB
A+ + A * AB * QB ) + A * A * QBB
A SBD 2.0 * ( AD * AB * Q + A * AB * QD
A+ + A * AD * QB ) + A * A * QBD
A SDD 2.0 * ( AD * AD * Q + A * AD * QD
A+ + A * AD * QD ) + A * A * QDD
A SQ SIN( Q )
A CQ L
A W 0.5 * E * SQ
A WA 0.5 * ( EA * SQ + E * CQ * QA )
A WB 0.5 * ( EB * SQ + E * CQ * QB )
A WD 0.5 * ( ED * SQ + E * CQ * QD )
A WAA 0.5 * ( EA * CQ * QA + EA * CQ * QA
A+ - E * SQ * QA * QA + E * CQ * QAA )
A WAB 0.5 * ( EAB * SQ + EA * CQ * QB
A+ + EB * CQ * QA - E * SQ * QB * QA
A+ + E * CQ * QAB )
A WAD 0.5 * ( EAD * SQ + EA * CQ * QD
A+ + ED * CQ * QA - E * SQ * QD * QA
A+ + E * CQ * QAD )
A WBB 0.5 * ( EB * CQ * QB
A+ + EB * CQ * QB - E * SQ * QB * QB
A+ + E * CQ * QBB )
A WBD 0.5 * ( EBD * SQ + EB * CQ * QD
A+ + ED * CQ * QB - E * SQ * QD * QB
A+ + E * CQ * QBD )
A WDD 0.5 * ( EDD * SQ + ED * CQ * QD
A+ + ED * CQ * QD - E * SQ * QD * QD
A+ + E * CQ * QDD )
A V S - R + W
A VA SA - RA + WA
A VB SB - RB + WB
A VD SD - RD + WD
A VAA SAA - RAA + WAA
A VAB SAB - RAB + WAB
A VAD SAD - RAD + WAD
A VBB SBB - RBB + WBB
A VBD SBD - RBD + WBD
A VDD SDD - RDD + WDD
F V
G AZ VA
G BZ VB
G DZ VD
H AZ AZ VAA
H AZ BZ VAB
H AZ DZ VAD
H BZ BZ VBB
H BZ DZ VBD
H DZ DZ VDD
T DIST
F ( X - P )**2
G X 2.0 * ( X - P )
H X X 2.0
T DISTY
A ST SIN( T )
A CT COS( T )
A B X + A * D * ST - P
A BA D * ST
A BD A * ST
A BT A * D * CT
F B * B
G X 2.0 * B
G A 2.0 * B * BA
G D 2.0 * B * BD
G T 2.0 * B * BT
H X X 2.0
H X A 2.0 * BA
H X D 2.0 * BD
H X T 2.0 * BT
H A A 2.0 * BA * BA
H A D 2.0 * ( BD * BA + B * ST )
H A T 2.0 * ( BT * BA + B * D * CT )
H D D 2.0 * BD * BD
H D T 2.0 * ( BT * BD + B * A * CT )
H T T 2.0 * ( BT * BT - B * A * D * ST )
T DISTX
A ST SIN( T )
A CT COS( T )
A B X + A * D * CT - P
A BA D * CT
A BD A * CT
A BT - A * D * ST
F B * B
G X 2.0 * B
G A 2.0 * B * BA
G D 2.0 * B * BD
G T 2.0 * B * BT
H X X 2.0
H X A 2.0 * BA
H X D 2.0 * BD
H X T 2.0 * BT
H A A 2.0 * BA * BA
H A D 2.0 * ( BD * BA + B * CT )
H A T 2.0 * ( BT * BA - B * D * ST )
H D D 2.0 * BD * BD
H D T 2.0 * ( BT * BD - B * A * ST )
H T T 2.0 * ( BT * BT - B * A * D * CT )
ENDATA