-
Notifications
You must be signed in to change notification settings - Fork 6
/
mo_poly.f90
559 lines (444 loc) · 16.4 KB
/
mo_poly.f90
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
MODULE mo_poly
! This module determines wether a 2D point lies inside, outside, or
! on the vertice/edge of a 2D polygon
! and is part of the JAMS Fortran library.
!
! Written Juliane Mai, July 2012
! Modified Maren Goehler, July 2012 - area & center of mass
! License
! -------
! This file is part of the JAMS Fortran package, distributed under the MIT License.
!
! Copyright (c) 2012 Juliane Mai
!
! Permission is hereby granted, free of charge, to any person obtaining a copy
! of this software and associated documentation files (the "Software"), to deal
! in the Software without restriction, including without limitation the rights
! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
! copies of the Software, and to permit persons to whom the Software is
! furnished to do so, subject to the following conditions:
!
! The above copyright notice and this permission notice shall be included in all
! copies or substantial portions of the Software.
!
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
! SOFTWARE.
USE mo_kind, ONLY: i4, sp, dp
USE mo_utils, only: eq, ge, le
IMPLICIT NONE
PUBLIC :: areapoly ! compute the area of a polygon
PUBLIC :: center_of_mass ! compute the center of mass of a polygon
PUBLIC :: inpoly ! Test if 2D point is inside, outside or&
! on vertice/edge of a 2D polygon
! ------------------------------------------------------------------
! NAME
! areapoly
! PURPOSE
! Function for computing the area of a polygon
! The polygon can be convex or not.
!
! The method is only applicable for 2D polygons and points.
!
! http://de.wikipedia.org/wiki/Geometrischer_Schwerpunkt
!
! CALLING SEQUENCE
! area = areapoly(coord)
! INTENT(IN)
! real(sp/dp) :: coord(:,2) (x,y) coordinates of edges of the polygon
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
! INTENT(IN), OPTIONAL
! None
! INTENT(INOUT), OPTIONAL
! None
! INTENT(OUT), OPTIONAL
! None
! RESTRICTIONS
! Only available in 2D version
! EXAMPLE
! polygon(:,1) = (/ 1.0_dp,2.0_dp,2.0_dp,1.0_dp /)
! polygon(:,2) = (/ 1.0_dp,1.0_dp,2.0_dp,2.0_dp /)
!
! area = areapoly(polygon )
!
! --> area = 1
!
! -> see also example in test directory
! LITERATURE
! http://de.wikipedia.org/wiki/Geometrischer_Schwerpunkt
! HISTORY
! Written, Maren Goehler, July 2012
INTERFACE areapoly
MODULE PROCEDURE areapoly_sp, areapoly_dp
END INTERFACE areapoly
! ------------------------------------------------------------------
! NAME
! center_of_mass
! PURPOSE
! Function for computing the center of mass of a polygon
! Computation of polygon area needed for center of mass.
! The polygon can be convex or not.
!
! The method is only applicable for 2D polygons and points.
!
! http://de.wikipedia.org/wiki/Geometrischer_Schwerpunkt
!
! A = sum(xiyi+1-xi+1yi)
! xs = 1/(6*A) * sum(xi+xi+1)(xiyi+1-xi+1yi)
! ys = 1/(6*A) * sum(yi+yi+1)(xiyi+1-xi+1yi)
! CALLING SEQUENCE
! com = center_of_mass(coord)
! INTENT(IN)
! real(sp/dp) :: coord(:,2) (x,y) coordinates of edges of the polygon
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
! INTENT(IN), OPTIONAL
! None
! INTENT(INOUT), OPTIONAL
! None
! INTENT(OUT), OPTIONAL
! None
! RESTRICTIONS
! Only available in 2D version
! EXAMPLE
! polygon(:,1) = (/ 1.0_dp,2.0_dp,2.0_dp,1.0_dp /)
! polygon(:,2) = (/ 1.0_dp,1.0_dp,2.0_dp,2.0_dp /)
!
! com = center_of_mass(polygon)
!
! --> com = (/1.5_dp, 1.5_dp/)
!
! -> see also example in test directory
! LITERATURE
! http://de.wikipedia.org/wiki/Geometrischer_Schwerpunkt
! HISTORY
! Written, Maren Goehler, July 2012
INTERFACE center_of_mass
MODULE PROCEDURE center_of_mass_sp,center_of_mass_dp
END INTERFACE center_of_mass
! ------------------------------------------------------------------
! NAME
! inpoly
! PURPOSE
! Determines whether a 2D point falls in a polygon or is located outside or
! lies on a vertex or an edge of the polygon.
! The polygon can be convex or not.
!
! The method is only applicable for 2D polygons and points.
!
! The original version of the source code (pnpoly) was implemented by
! W. Randolph Franklin. It was insufficiently assigning vertex/edge points.
! CALLING SEQUENCE
! call inpoly( p, coord, inside )
! INTENT(IN)
! real(sp/dp) :: p(2) coordinates of the point in question
! real(sp/dp) :: coord(:,2) (x,y) coordinates of edges of the polygon
! INTENT(INOUT)
! None
! INTENT(OUT)
! integer(i4) :: inside whether point is inside (=1), outside (=-1) or
! on a vertex/edge of the polygon
! INTENT(IN), OPTIONAL
! None
! INTENT(INOUT), OPTIONAL
! None
! INTENT(OUT), OPTIONAL
! None
! RESTRICTIONS
! Only available in 2D version
! EXAMPLE
! polygon(:,1) = (/ 1.0_dp,2.0_dp,2.0_dp,1.0_dp /)
! polygon(:,2) = (/ 1.0_dp,1.0_dp,2.0_dp,2.0_dp /)
!
! point = (/ 1.5, 1.5 /)
!
! call inpoly( point, polygon, inside )
!
! --> inside = 1 ... point is inside the polygon
!
! -> see also example in test directory
! LITERATURE
! http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
! HISTORY
! Written, Juliane Mai, July 2012
! Modified, Juliane Mai, July 2012 - removing GOTO statements
INTERFACE inpoly
MODULE PROCEDURE inpoly_dp, inpoly_sp
END INTERFACE inpoly
! ------------------------------------------------------------------
PRIVATE
! ------------------------------------------------------------------
CONTAINS
! ------------------------------------------------------------------
FUNCTION areapoly_dp(coord)
IMPLICIT NONE
REAL(dp), DIMENSION(:,:), INTENT(IN) :: coord ! Coordinates of the polygon in question
REAL(dp) :: areapoly_dp
! Local variables
INTEGER(i4) :: i,k ! loop
INTEGER(i4) :: Nedges ! number of coordinates
REAL(dp) :: xsum ! for summing up
REAL(dp) :: ysum ! for summing up
xsum = 0.0_dp
ysum = 0.0_dp
Nedges = size(coord,1)
do i = 1, Nedges
if (i .eq. Nedges) then
k = 1_i4
else
k = i + 1_i4
end if
xsum = xsum + ( coord(i,1) * coord(k,2) )
ysum = ysum + ( coord(i,2) * coord(k,1) )
end do
areapoly_dp = 0.5_sp * (xsum - ysum)
RETURN
END FUNCTION areapoly_dp
FUNCTION areapoly_sp(coord)
IMPLICIT NONE
REAL(sp), dimension(:,:), INTENT(IN) :: coord ! Coordinates of the polygon in question
REAL(sp) :: areapoly_sp
! Local variables
INTEGER(i4) :: i,k ! loop
INTEGER(i4) :: Nedges ! number of coordinates
REAL(sp) :: xsum ! for summing up
REAL(sp) :: ysum ! for summing up
xsum = 0.0_sp
ysum = 0.0_sp
Nedges = size(coord,1)
do i = 1, Nedges
if (i .eq. Nedges) then
k = 1_i4
else
k = i + 1_i4
end if
xsum = xsum + ( coord(i,1) * coord(k,2) )
ysum = ysum + ( coord(i,2) * coord(k,1) )
end do
areapoly_sp = 0.5_sp * (xsum - ysum)
END FUNCTION areapoly_sp
! ------------------------------------------------------------------
! ------------------------------------------------------------------
FUNCTION center_of_mass_dp(coord)
IMPLICIT NONE
REAL(dp), dimension(:,:), INTENT(IN) :: coord ! Coordinates of polygon in question
REAL(dp),dimension(2) :: center_of_mass_dp
! Local variables
INTEGER(i4) :: i,k ! loop
INTEGER(i4) :: Nedges ! number of coordinates
REAL(dp) :: area ! area of the polygon
REAL(dp) :: xsum ! for summing up
REAL(dp) :: ysum ! for summing up
REAL(dp) :: hotspot_x ! for summing up
REAL(dp) :: hotspot_y ! for summing up
xsum = 0.0_dp
ysum = 0.0_dp
Nedges = size(coord,1)
area = areapoly_dp(coord)
do i = 1, Nedges
if (i .eq. Nedges ) then
k = 1_i4
else
k = i + 1_i4
end if
! multiply x coord by the y coord of next vertex
xsum = xsum + ((coord(i,1) + coord(k,1)) * &
((coord(i,1) * coord(k,2) - coord(k,1) * coord(i,2))))
ysum = ysum + ((coord(i,2) + coord(k,2)) * &
((coord(i,1) * coord(k,2) - coord(k,1) * coord(i,2))))
end do
hotspot_x = 1.0_dp / (6.0_dp * area) * xsum
hotspot_y = 1.0_dp / (6.0_dp * area) * ysum
center_of_mass_dp(1) = hotspot_x
center_of_mass_dp(2) = hotspot_y
RETURN
END FUNCTION center_of_mass_dp
FUNCTION center_of_mass_sp(coord)
IMPLICIT NONE
REAL(sp),dimension(:,:), INTENT(IN) :: coord ! Coordinates of polygon in question
REAL(sp),dimension(2) :: center_of_mass_sp
! Local variables
INTEGER(i4) :: i,k ! loop
INTEGER(i4) :: Nedges ! number of coordinates
REAL(sp) :: area ! area of the polygon
REAL(sp) :: xsum ! for summing up
REAL(sp) :: ysum ! for summing up
REAL(sp) :: hotspot_x ! for summing up
REAL(sp) :: hotspot_y ! for summing up
xsum = 0.0_sp
ysum = 0.0_sp
Nedges = size(coord,1)
area = areapoly_sp(coord)
do i = 1, Nedges
if (i .eq. Nedges ) then
k = 1_i4
else
k = i + 1_i4
end if
! multiply x coord by the y coord of next vertex
xsum = xsum + ((coord(i,1) + coord(k,1)) * &
((coord(i,1) * coord(k,2) - coord(k,1) * coord(i,2))))
ysum = ysum + ((coord(i,2) + coord(k,2)) * &
((coord(i,1) * coord(k,2) - coord(k,1) * coord(i,2))))
end do
hotspot_x = 1.0_sp / (6.0_sp * area) * xsum
hotspot_y = 1.0_sp / (6.0_sp * area) * ysum
center_of_mass_sp(1) = hotspot_x
center_of_mass_sp(2) = hotspot_y
RETURN
END FUNCTION center_of_mass_sp
! ------------------------------------------------------------------
SUBROUTINE inpoly_dp(P,coord,erg)
!
REAL(dp), dimension(2), INTENT(IN) :: P ! Point in question
REAL(dp), dimension(:,:), INTENT(IN) :: coord ! Coordinates of the polygon
INTEGER(i4), INTENT(OUT) :: erg ! Result:
! inside: erg = 1
! outside: erg = -1
! on vertex/edge: erg = 0
! Local variables
REAL(dp), dimension(:), allocatable :: X, Y
REAL(dp) :: lx, ly
LOGICAL :: MX,MY,NX,NY, test1, test2
INTEGER(i4) :: N, I, J
N = size(coord,1)
allocate(x(N))
allocate(y(N))
do i=1,N
X(I)=coord(I,1)-P(1)
Y(I)=coord(I,2)-P(2)
! Edge
if ( eq(X(I),0.0_dp) .and. eq(Y(I),0.0_dp) ) then
erg=0_i4
return
end if
end do
erg=-1_i4
DO I=1,N
J=1+MOD(I,N)
! vertical Vertex
If ( eq(coord(I,1),coord(J,1)) .and. eq(coord(I,1),P(1)) ) then
ly = (P(2)-coord(J,2)) / (coord(I,2)-coord(J,2))
If ( ge(ly,0.0_dp) .and. le(ly,1.0_dp) ) then
erg=0_i4
return
end if
end if
! horizontal Vertex
If ( eq(coord(I,2),coord(J,2)) .and. eq(coord(I,2),P(2)) ) then
lx = (P(1)-coord(J,1)) / (coord(I,1)-coord(J,1))
If ( ge(lx,0.0_dp ) .and. le(lx,1.0_dp) ) then
erg=0_i4
return
end if
end if
!
MX = ge(X(I),0.0_dp)
NX = ge(X(J),0.0_dp)
MY = ge(Y(I),0.0_dp)
NY = ge(Y(J),0.0_dp)
test1 = .NOT.((MY.OR.NY).AND.(MX.OR.NX)).OR.(MX.AND.NX)
test2 = .NOT.(MY.AND.NY.AND.(MX.OR.NX).AND..NOT.(MX.AND.NX))
if (.not. test1) then
if (test2) then
IF ((Y(I)*X(J)-X(I)*Y(J))/(X(J)-X(I)) .lt. 0.0_dp) then
cycle
ELSE
IF ((Y(I)*X(J)-X(I)*Y(J))/(X(J)-X(I)) .gt. 0.0_dp) then
erg = -erg
cycle
ELSE
erg = 0_i4
return
END IF
END IF
else
erg=-erg
end if
end if
END DO
deallocate(x)
deallocate(y)
END SUBROUTINE inpoly_dp
SUBROUTINE inpoly_sp(P,coord,erg)
!
REAL(sp), dimension(2), INTENT(IN) :: P ! Point in question
REAL(sp), dimension(:,:), INTENT(IN) :: coord ! Coordinates of the polygon
INTEGER(i4), INTENT(OUT) :: erg ! Result:
! inside: erg = 1
! outside: erg = -1
! on vertex/edge: erg = 0
! Local variables
REAL(sp), dimension(:), allocatable :: X, Y
REAL(sp) :: lx, ly
LOGICAL :: MX,MY,NX,NY, test1, test2
INTEGER(i4) :: N, I, J
N = size(coord,1)
allocate(x(N))
allocate(y(N))
do i=1,N
X(I)=coord(I,1)-P(1)
Y(I)=coord(I,2)-P(2)
! Edge
if ( eq(X(I),0.0_sp) .and. eq(Y(I),0.0_sp) ) then
erg=0_i4
return
end if
end do
erg=-1_i4
DO I=1,N
J=1+MOD(I,N)
! vertical Vertex
If ( eq(coord(I,1),coord(J,1)) .and. eq(coord(I,1),P(1)) ) then
ly = (P(2)-coord(J,2)) / (coord(I,2)-coord(J,2))
If ( ge(ly,0.0_sp) .and. le(ly,1.0_sp) ) then
erg=0_i4
return
end if
end if
! horizontal Vertex
If ( eq(coord(I,2),coord(J,2)) .and. eq(coord(I,2),P(2)) ) then
lx = (P(1)-coord(J,1)) / (coord(I,1)-coord(J,1))
If ( ge(lx,0.0_sp ) .and. le(lx,1.0_sp) ) then
erg=0_i4
return
end if
end if
!
MX = ge(X(I),0.0_sp)
NX = ge(X(J),0.0_sp)
MY = ge(Y(I),0.0_sp)
NY = ge(Y(J),0.0_sp)
test1 = .NOT.((MY.OR.NY).AND.(MX.OR.NX)).OR.(MX.AND.NX)
test2 = .NOT.(MY.AND.NY.AND.(MX.OR.NX).AND..NOT.(MX.AND.NX))
if (.not. test1) then
if (test2) then
IF ((Y(I)*X(J)-X(I)*Y(J))/(X(J)-X(I)) .lt. 0.0_sp) then
cycle
ELSE
IF ((Y(I)*X(J)-X(I)*Y(J))/(X(J)-X(I)) .gt. 0.0_sp) then
erg = -erg
cycle
ELSE
erg = 0_i4
return
END IF
END IF
else
erg=-erg
end if
end if
END DO
deallocate(x)
deallocate(y)
END SUBROUTINE inpoly_sp
END MODULE mo_poly