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
|
*DECK NXTITA
FUNCTION NXTITA(POSTRI ,PINPOS,VOLINT)
*
*----------
*
*Purpose:
* Compute the volume of intersection between
* a 2--D triangle and an annular pin.
*
*Copyright:
* Copyright (C) 2010 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
*Author(s): G. Marleau.
*
*Parameters: input
* POSTRI spatial description of the triangle with:
* POSTRI(1,J) $X$ location of corner $j$ of triangle;
* POSTRI(2,J) $Y$ location of corner $j$ of triangle.
* PINPOS spatial description of the annular pin region with:
* PINPOS(0) the radius of the annular pin;
* PINPOS(1) the $X$ position of the annular pin center;
* PINPOS(2) the $Y$ position of the annular pin center.
*
*Parameters: output
* NXTITA type of intersection between haxagon and annular pin, where:
* = 0 means that there is no intersection
* between the two regions;
* = 1 means that the hexagon
* is all located inside the annular pin;
* = 2 means that the annular pin
* is all located inside the hexagon;
* =-1 means that the intersection between
* the hexagon and the annular pin is partial.
* VOLINT 2-D volume of intersection (area) between hexagon and
* annular pin.
*
*Reference:
* G. Marleau,
* New Geometries Processing in DRAGON: The NXT: Module,
* Report IGE-260, Polytechnique Montreal,
* Montreal, 2005.
*
*----
*
IMPLICIT NONE
*----
* Subroutine arguments
*----
INTEGER NXTITA
DOUBLE PRECISION POSTRI(2,3),PINPOS(0:2)
DOUBLE PRECISION VOLINT
*----
* Local parameters
*----
INTEGER IOUT
CHARACTER NAMSBR*6
PARAMETER (IOUT=6,NAMSBR='NXTITA')
INTEGER IPRINT
PARAMETER (IPRINT=100)
DOUBLE PRECISION DCUTOF
PARAMETER (DCUTOF=1.0D-8)
DOUBLE PRECISION DZERO,DONE,DHALF,DSQ3O2
PARAMETER (DZERO=0.0D0,DONE=1.0D0,
> DHALF=0.5D0,DSQ3O2=0.86602540378444D0)
*----
* Functions
*----
DOUBLE PRECISION XDRCST,PI
*----
* Local variables
*----
INTEGER IDIR,IFACE,NFPINS,NCIN,NKPINS,ICOR,ICORIN(3),IC
DOUBLE PRECISION VOLOUT,RADP2,X1,Y1,X2,Y2,VOLTRI,ALPHA
DOUBLE PRECISION CPPP(2),CORPOS(2),DIRFAC(2,3),DIRLIN(2,3),RADC,
> DIRN,DISTM,DISTC,DNOR(3),DTAN(3),
> VT,AFPINT(3),XFPINT(3),
> YFPINT(3),TC1(2),TC2(2),DISTS,DISTF
*----
* Print header if required
*----
IF(IPRINT .GE. 200) THEN
WRITE(IOUT,6000) NAMSBR
WRITE(IOUT,6010) (POSTRI(1,ICOR),POSTRI(2,ICOR),ICOR=1,3)
WRITE(IOUT,6011) (PINPOS(IFACE),IFACE=0,2)
ENDIF
*----
* Initialize PI, NXTITA and VOLINT
*----
PI=XDRCST('Pi',' ')
NXTITA=0
VOLINT=DZERO
VOLOUT=DZERO
*----
* Evaluate distance from FACES to pin center
*----
RADP2=PINPOS(0)**2
NFPINS=0
NCIN=0
NKPINS=0
*----
* Compute volume of triangle
*----
X1=POSTRI(1,2)-POSTRI(1,1)
X2=POSTRI(1,3)-POSTRI(1,1)
Y1=POSTRI(2,2)-POSTRI(2,1)
Y2=POSTRI(2,3)-POSTRI(2,1)
VOLTRI=ABS(X1*Y2-X2*Y1)/2.0D0
*----
* Analyze each face
*----
CPPP(1)=POSTRI(1,2)
CPPP(2)=POSTRI(2,2)
CORPOS(1)=POSTRI(1,3)
CORPOS(2)=POSTRI(2,3)
DO IFACE=1,3
ICOR=IFACE
ICORIN(ICOR)=0
* write(6,'(A6,5x,2i5)') 'FACE ',IFACE,ICOR
AFPINT(IFACE)=DZERO
XFPINT(IFACE)=DZERO
YFPINT(IFACE)=DZERO
DNOR(IFACE)=DZERO
DTAN(IFACE)=DZERO
RADC=DZERO
DISTM=DZERO
*----
* Find direction of face and its normal directed inward
* the triangle
*----
DIRLIN(1,IFACE)=(POSTRI(1,IFACE)-CORPOS(1))
DIRLIN(2,IFACE)=(POSTRI(2,IFACE)-CORPOS(2))
DIRN=SQRT(DIRLIN(1,IFACE)**2+DIRLIN(2,IFACE)**2)
DIRLIN(1,IFACE)=DIRLIN(1,IFACE)/DIRN
DIRLIN(2,IFACE)=DIRLIN(2,IFACE)/DIRN
DIRFAC(1,IFACE)=-DIRLIN(2,IFACE)
DIRFAC(2,IFACE)=DIRLIN(1,IFACE)
* write(6,*) 'Corner and pin position with respect to corner'
* write(6,'(4F20.10)')
* > CORPOS(1),CORPOS(2),PINPOS(1)-CORPOS(1),
* > PINPOS(2)-CORPOS(2)
* write(6,*) 'Face tangent and normal'
* write(6,'(4F20.10)')
* > DIRLIN(1,IFACE),DIRLIN(2,IFACE),DIRFAC(1,IFACE),DIRFAC(2,IFACE)
DO IDIR=1,2
DISTC=PINPOS(IDIR)-CORPOS(IDIR)
DISTM=DISTM+(CPPP(IDIR)-CORPOS(IDIR))*DIRFAC(IDIR,IFACE)
DNOR(IFACE)=DNOR(IFACE)+DISTC*DIRFAC(IDIR,IFACE)
DTAN(IFACE)=DTAN(IFACE)+DISTC*DIRLIN(IDIR,IFACE)
RADC=RADC+DISTC**2
ENDDO
* write(6,*) 'Distance of center to face',DNOR(IFACE)
IF(DNOR(IFACE) .GT. DISTM+PINPOS(0)) THEN
NXTITA=0
VOLINT=DZERO
IF(IPRINT .GE. 200) THEN
WRITE(IOUT,6012) NAMSBR,NXTITA,VOLINT
WRITE(IOUT,6001) NAMSBR
ENDIF
RETURN
ELSE IF(DNOR(IFACE) .LT. -PINPOS(0)) THEN
NXTITA=0
VOLINT=DZERO
IF(IPRINT .GE. 200) THEN
WRITE(IOUT,6012) NAMSBR,NXTITA,VOLINT
WRITE(IOUT,6001) NAMSBR
ENDIF
RETURN
ELSE IF(DNOR(IFACE) .GE. PINPOS(0)) THEN
NFPINS=NFPINS+1
NKPINS=NKPINS+1
ELSE
*----
* Point of intersection of current face with pin
*----
XFPINT(IFACE)=DNOR(IFACE)
YFPINT(IFACE)=SQRT(RADP2-XFPINT(IFACE)**2)
AFPINT(IFACE)=ACOS(XFPINT(IFACE)/PINPOS(0))
VT=XFPINT(IFACE)*YFPINT(IFACE)
DISTS=DTAN(IFACE)-YFPINT(IFACE)
DISTF=DTAN(IFACE)+YFPINT(IFACE)
* write(6,*) 'DISTS/DISTF/DIRN=',DISTS,DISTF,DIRN
IF(DISTS .LE. DIRN .AND. DISTF .GT. DZERO) THEN
* write(6,'(A9,2X,7F20.10)')
* > 'Volout 1=',XFPINT(IFACE),YFPINT(IFACE),
* > AFPINT(IFACE),VT,VOLOUT,
* > RADP2*AFPINT(IFACE)-VT,VOLOUT+RADP2*AFPINT(IFACE)-VT
VOLOUT=VOLOUT+RADP2*AFPINT(IFACE)-VT
ELSE
NKPINS=NKPINS+1
* write(6,'(A9,2X,7F20.10)')
* > 'Volout 3=',XFPINT(IFACE),YFPINT(IFACE),
* > AFPINT(IFACE),VT,VOLOUT,
* > RADP2*AFPINT(IFACE)-VT,VOLOUT
VOLOUT=VOLOUT
ENDIF
ENDIF
IF(RADC .LT. RADP2) THEN
*----
* Identify corners in pin
*----
ICORIN(ICOR)=1
NCIN=NCIN+1
ENDIF
CPPP(1)=CORPOS(1)
CPPP(2)=CORPOS(2)
CORPOS(1)=POSTRI(1,IFACE)
CORPOS(2)=POSTRI(2,IFACE)
ENDDO
IF(NFPINS .EQ. 3) THEN
*----
* Pin completely inside triangle
*----
NXTITA=2
VOLINT=PI*RADP2
ELSE IF(NCIN .EQ. 3) THEN
*----
* Triangle completely inside pin
*----
NXTITA=1
VOLINT=VOLTRI
ELSE IF(NKPINS .EQ. 3) THEN
*----
* No intersection between triangle and pin
*----
NXTITA=0
VOLINT=DZERO
ELSE
*----
* For corners inside pin, find intersection of outside surfaces
* and remove from VOLOUT
*----
NXTITA=-1
DO ICOR=1,3
* write(6,*) 'ICORIN=',ICOR,ICORIN(ICOR)
IF(ICORIN(ICOR) .EQ. 1) THEN
*----
* Point of intersection of previous face with pin in the positive
* direction
*----
IFACE=ICOR-1
IF(IFACE .LE. 0) IFACE=3+IFACE
IC=ICOR-2
IF(IC .LE. 0) IC=3+IC
DO IDIR=1,2
TC2(IDIR)=POSTRI(IDIR,IC)
> +(DTAN(IFACE)+YFPINT(IFACE))*DIRLIN(IDIR,IFACE)
ENDDO
* write(6,*) 'TC2=',TC2(1),TC2(2)
*----
* Point of intersection of current face with pin in the negative
* direction
*----
IFACE=ICOR
IC=ICOR-1
IF(IC .LE. 0) IC=3+IC
DO IDIR=1,2
TC1(IDIR)=POSTRI(IDIR,IC)
> +(DTAN(IFACE)-YFPINT(IFACE))*DIRLIN(IDIR,IFACE)
ENDDO
* write(6,*) 'TC1=',TC1(1),TC1(2)
*----
* Triangle outside is identified by CORPOS(*,IC),TC1,TC2
* Compute its volume
*----
X1=TC1(1)-POSTRI(1,IC)
X2=TC2(1)-POSTRI(1,IC)
Y1=TC1(2)-POSTRI(2,IC)
Y2=TC2(2)-POSTRI(2,IC)
VOLTRI=ABS(X1*Y2-X2*Y1)/2.0D0
* write(6,*) 'Triangle 1=',X1,X2,Y1,Y2,VOLTRI
*----
* Add contribution from annular sector between T1 and T2
* Compute distance of T1 to T2
*----
Y2=DZERO
DO IDIR=1,2
Y2=Y2+(TC1(IDIR)-TC2(IDIR))**2
ENDDO
Y2=Y2/4.0D0
X2=SQRT(RADP2-Y2)
Y2=SQRT(Y2)
ALPHA=ACOS(X2/PINPOS(0))
* write(6,*) 'Triangle 2=',X2,Y2,ALPHA,
* > VOLOUT,RADP2*ALPHA,X2*Y2,RADP2*ALPHA-X2*Y2+VOLTRI
VOLOUT=VOLOUT-RADP2*ALPHA+X2*Y2-VOLTRI
ENDIF
ENDDO
VOLINT=PI*RADP2-VOLOUT
* write(6,*) 'Triangle 3=',VOLINT,PI*RADP2,VOLOUT
ENDIF
IF(IPRINT .GE. 200) THEN
WRITE(IOUT,6012) NAMSBR,NXTITA,VOLINT
WRITE(IOUT,6001) NAMSBR
ENDIF
RETURN
*----
* Output formats
*----
6000 FORMAT('(* Output from --',A6,'-- follows ')
6001 FORMAT(' Output from --',A6,'-- completed *)')
6010 FORMAT('POSTRI={',5(F20.10,','),F20.10,'};')
6011 FORMAT('PINPOS={',2(F20.10,','),F20.10,'};')
6012 FORMAT(A6,'={',I5,',',F20.10,'};')
END
|
