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
|
C***********************************************************************
C Module: plt_3D.f
C
C Copyright (C) 1996 Harold Youngren, Mark Drela
C
C This library is free software; you can redistribute it and/or
C modify it under the terms of the GNU Library General Public
C License as published by the Free Software Foundation; either
C version 2 of the License, or (at your option) any later version.
C
C This library is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
C Library General Public License for more details.
C
C You should have received a copy of the GNU Library General Public
C License along with this library; if not, write to the Free
C Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
C
C Report problems to: guppy@maine.com
C or drela@mit.edu
C***********************************************************************
C
C***********************************************************************
C --- Xplot11 3D routines
C
C Version 4.46 11/28/01
C
C Note: These are routine(s) that provide some means of displaying
C 3D objects in conjunction with the usual XPlot11 routines.
C They are by no means complete but can serve as a starting
C point for doing simple 3D graphics.
C
C***********************************************************************
subroutine VIEW(X,Y,Z,N,XP,YP,XOB,YOB,ZOB,ROBINV,XUP,YUP,ZUP)
DIMENSION X(N), Y(N), Z(N)
DIMENSION XP(N), YP(N)
C........................................................................
C
C Projects one or more points in 3-D Cartesian space
C onto a 2-D plane from the viewpoint of an observer
C at a specified location. This can be used to view
C a 3-D object (described by a set of x,y,z points)
C by projecting the points into a set of x,y points for
C plotting on a planar 2-D graphics screen.
C The viewing plane, which has its own x,y coordinate
C system, always faces the observer but can be turned
C around the viewing axis, thus simulating the observer
C tilting his head while looking at the object. This tilt
C is specified by giving a vector in x,y,z space which
C "points up" relative to the observer.
C The distance of the observer from the object is specified
C explicitly. This does not affect much the size of the viewed
C object, since the viewing plane contains the 3-D space origin
C and hence is at or near the object. It does however affect the
C apparent distortion of the object due to perspective. This
C is very useful to convey the 3-dimensionality of the object.
C If the observer is very very far away, there is no distortion
C (as in a mechanical drawing).
C
C X,Y,Z Cartesian point coordinates (input)
C N number of points (input)
C XP,YP projected point coordinates on viewing plane (output)
C XOB,YOB,ZOB Cartesian vector pointing towards observer (input)
C (magnitude irrelevant)
C ROBINV 1/(distance to observer) (input)
C XUP,YUP,ZUP Cartesian vector which points "up" from the
C observer's viewpoint (magnitude irrelevant) (input)
C
C Mark Drela July 1988
C........................................................................
C
C---- unit view vector perpendicular to viewing plane (towards observer)
XOBN = XOB/SQRT(XOB**2 + YOB**2 + ZOB**2)
YOBN = YOB/SQRT(XOB**2 + YOB**2 + ZOB**2)
ZOBN = ZOB/SQRT(XOB**2 + YOB**2 + ZOB**2)
C
C---- vector along plane's local x coordinate: (up vector)X(view vector)
XIP = YUP*ZOBN - ZUP*YOBN
YIP = ZUP*XOBN - XUP*ZOBN
ZIP = XUP*YOBN - YUP*XOBN
C
C---- normalize plane's x coordinate vector
XIHAT = XIP/SQRT(XIP**2 + YIP**2 + ZIP**2)
YIHAT = YIP/SQRT(XIP**2 + YIP**2 + ZIP**2)
ZIHAT = ZIP/SQRT(XIP**2 + YIP**2 + ZIP**2)
C
C---- unit vector along plane's y coordinate: (view vector)X(x unit vector)
XJHAT = YOBN*ZIHAT - ZOBN*YIHAT
YJHAT = ZOBN*XIHAT - XOBN*ZIHAT
ZJHAT = XOBN*YIHAT - YOBN*XIHAT
C
C---- go over all points
DO 10 I=1, N
C
RDOTR = X(I)*XOBN + Y(I)*YOBN + Z(I)*ZOBN
C
C------ viewing-axis component of vector
DRX = RDOTR*XOBN
DRY = RDOTR*YOBN
DRZ = RDOTR*ZOBN
C
C------ projected vector scaling factor due to perspective
VSCAL = 1.0 / SQRT( (XOBN-ROBINV*DRX)**2
& + (YOBN-ROBINV*DRY)**2
& + (ZOBN-ROBINV*DRZ)**2 )
C
C------ dot vector into plane coordinate system unit vectors, and scale
XP(I) = (XIHAT*X(I) + YIHAT*Y(I) + ZIHAT*Z(I))*VSCAL
YP(I) = (XJHAT*X(I) + YJHAT*Y(I) + ZJHAT*Z(I))*VSCAL
C
10 CONTINUE
C
RETURN
END
subroutine VIEWR(R,N,RP,ROB,ROBINV,RUP)
DIMENSION R(3,N)
DIMENSION RP(3,N)
DIMENSION ROB(3), RUP(3)
C........................................................................
C
C Same as VIEW, but vectors are passed in R(1:3,...) array form.
C The out-of-plane RP(3...) value is also returned.
C
C R(..) Cartesian point coordinates (input)
C N number of points (input)
C RP(..) projected point coordinates on viewing plane (output)
C ROB(.) Cartesian vector pointing towards observer (input)
C (magnitude irrelevant)
C ROBINV 1/(distance to observer) (input)
C RUP(.) Cartesian vector which points "up" from the
C observer's viewpoint (magnitude irrelevant) (input)
C
C Mark Drela July 2007
C........................................................................
REAL RIP(3), RIN(3), RJN(3), RKN(3), DR(3), RI(3)
C
C---- unit view vector perpendicular to viewing plane (towards observer)
SOB = SQRT(ROB(1)**2 + ROB(2)**2 + ROB(3)**2)
RKN(1) = ROB(1)/SOB
RKN(2) = ROB(2)/SOB
RKN(3) = ROB(3)/SOB
C
C---- vector along plane's local x coordinate: (up vector)X(view vector)
RIP(1) = RUP(2)*RKN(3) - RUP(3)*RKN(2)
RIP(2) = RUP(3)*RKN(1) - RUP(1)*RKN(3)
RIP(3) = RUP(1)*RKN(2) - RUP(2)*RKN(1)
C
C---- normalize plane's x coordinate vector
SIP = SQRT(RIP(1)**2 + RIP(2)**2 + RIP(3)**2)
RIN(1) = RIP(1)/SIP
RIN(2) = RIP(2)/SIP
RIN(3) = RIP(3)/SIP
C
C---- unit vector along plane's y coordinate: (view vector)X(x unit vector)
RJN(1) = RKN(2)*RIN(3) - RKN(3)*RIN(2)
RJN(2) = RKN(3)*RIN(1) - RKN(1)*RIN(3)
RJN(3) = RKN(1)*RIN(2) - RKN(2)*RIN(1)
C
C---- go over all points
DO 10 I=1, N
RI(1) = R(1,I)
RI(2) = R(2,I)
RI(3) = R(3,I)
RDOTR = RI(1)*RKN(1) + RI(2)*RKN(2) + RI(3)*RKN(3)
C
C------ viewing-axis component of vector
DR(1) = RDOTR*RKN(1)
DR(2) = RDOTR*RKN(2)
DR(3) = RDOTR*RKN(3)
C
C------ projected vector scaling factor due to perspective
VSCAL = 1.0 / SQRT( (RKN(1)-ROBINV*DR(1))**2
& + (RKN(2)-ROBINV*DR(2))**2
& + (RKN(3)-ROBINV*DR(3))**2 )
C
C------ dot vector into plane coordinate system unit vectors, and scale
RP(1,I) = (RIN(1)*RI(1) + RIN(2)*RI(2) + RIN(3)*RI(3))*VSCAL
RP(2,I) = (RJN(1)*RI(1) + RJN(2)*RI(2) + RJN(3)*RI(3))*VSCAL
RP(3,I) = (RKN(1)*RI(1) + RKN(2)*RI(2) + RKN(3)*RI(3))*VSCAL
10 CONTINUE
C
RETURN
END ! VIEWR
SUBROUTINE PROJMATRIX3 (ROTZ,ROTY,RMAT)
C...Purpose: To define rotation and transformation matrix. The input
C pair of angles ROTZ,ROTY specify the viewpoint by
C an angle about the Z axis (CCW) and an angle about
C the newly rotated Y axis (CCW). Both angles are
C right-handed in a conventional sense about each axis.
C
C...Input: ROTZ rotation of viewpoint about Z axis (deg)
C ROTY rotation of viewpoint about new Y axis (deg)
C
C...Output: RMAT 3x3 rotation and perspective matrix
C
DIMENSION RMAT(3,3)
C
DTR = 4.0*ATAN(1.0)/180.0
COSZ = COS(ROTZ*DTR)
SINZ = SIN(ROTZ*DTR)
COSY = COS(ROTY*DTR)
SINY = SIN(ROTY*DTR)
C
C---Rotation matrix (rotation about Z, then rotation about Y)
c xx = -( SINZ*X + COSZ*Y)
RMAT(1,1) = -SINZ
RMAT(2,1) = -COSZ
RMAT(3,1) = 0.0
C yy = SINY*COSZ*X - SINY*SINZ*Y + COSY*Z
RMAT(1,2) = SINY*COSZ
RMAT(2,2) = -SINY*SINZ
RMAT(3,2) = COSY
c zz = -(COSY*COSZ*X - COSY*SINZ*Y - SINY*Z)
RMAT(1,3) = -COSY*COSZ
RMAT(2,3) = COSY*SINZ
RMAT(3,3) = SINY
C
c xx = -( SINZ*X + COSZ*Y)
c yy = SINY*COSZ*X - SINY*SINZ*Y + COSY*Z
c zz = -(COSY*COSZ*X - COSY*SINZ*Y - SINY*Z)
C
c write(*,*) 'Rmatrix row1 ', (RMAT(1,L),L=1,3)
c write(*,*) 'Rmatrix row2 ', (RMAT(2,L),L=1,3)
c write(*,*) 'Rmatrix row3 ', (RMAT(3,L),L=1,3)
c read(*,*)
C
RETURN
END
SUBROUTINE PROJMATRIX4 (ROTZ,ROTY,RDIST,RMAT)
C...Purpose: To define rotation and perspective matrix. The input
C pair of angles ROTZ,ROTY specify the viewpoint by
C an angle about the Z axis (CCW) and an angle about
C the newly rotated Y axis (CCW). Both angles are
C right-handed in a conventional sense about each axis.
C The observer distance RDIST specifies the distance from
C the origin to the observer along the viewpoint direction.
C
C...Input: ROTZ rotation of viewpoint about Z axis (deg)
C ROTY rotation of viewpoint about new Y axis (deg)
C RDIST distance from origin to observer along viewpoint
C
C...Output: RMAT 4x4 rotation and perspective matrix
C
DIMENSION AMAT(4,4),PMAT(4,4), RMAT(4,4)
C
DTR = 4.0*ATAN(1.0)/180.0
COSZ = COS(ROTZ*DTR)
SINZ = SIN(ROTZ*DTR)
COSY = COS(ROTY*DTR)
SINY = SIN(ROTY*DTR)
C
C---Rotation matrix (rotation about Z, then rotation about Y)
c xx = -( SINZ*X + COSZ*Y)
AMAT(1,1) = -SINZ
AMAT(2,1) = -COSZ
AMAT(3,1) = 0.0
AMAT(4,1) = 0.0
C yy = SINY*COSZ*X - SINY*SINZ*Y + COSY*Z
AMAT(1,2) = SINY*COSZ
AMAT(2,2) = -SINY*SINZ
AMAT(3,2) = COSY
AMAT(4,2) = 0.0
c zz = -(COSY*COSZ*X - COSY*SINZ*Y - SINY*Z)
AMAT(1,3) = -COSY*COSZ
AMAT(2,3) = COSY*SINZ
AMAT(3,3) = SINY
AMAT(4,3) = 0.0
C
AMAT(1,4) = 0.0
AMAT(2,4) = 0.0
AMAT(3,4) = 0.0
AMAT(4,4) = 1.0
C
c xx = -( SINZ*X + COSZ*Y)
c yy = SINY*COSZ*X - SINY*SINZ*Y + COSY*Z
c zz = -(COSY*COSZ*X - COSY*SINZ*Y - SINY*Z)
c
C---Perspective matrix with projection on Z plane
PMAT(1,1) = 1.0
PMAT(2,1) = 0.0
PMAT(3,1) = 0.0
PMAT(4,1) = 0.0
C
PMAT(1,2) = 0.0
PMAT(2,2) = 1.0
PMAT(3,2) = 0.0
PMAT(4,2) = 0.0
C
PMAT(1,3) = 0.0
PMAT(2,3) = 0.0
PMAT(3,3) = 1.0
PMAT(4,3) = 0.0
C
PMAT(1,4) = 0.0
PMAT(2,4) = 0.0
PMAT(3,4) = -RDIST
PMAT(4,4) = 1.0
C
C---Product of matrices is perspective matrix
DO J=1, 4
DO K=1, 4
TMP = 0.0
DO L=1, 4
TMP = TMP + AMAT(J,L)*PMAT(L,K)
END DO
RMAT(J,K) = TMP
END DO
END DO
C
c write(*,*) 'Rmatrix row1 ', (RMAT(1,L),L=1,4)
c write(*,*) 'Rmatrix row2 ', (RMAT(2,L),L=1,4)
c write(*,*) 'Rmatrix row3 ', (RMAT(3,L),L=1,4)
c write(*,*) 'Rmatrix row4 ', (RMAT(4,L),L=1,4)
c read(*,*)
C
RETURN
END
SUBROUTINE ROTPTS3 (RMAT,PTS_IN,NPTS,PTS_OUT)
C...Purpose: To rotate array of points to a new viewpoint by
C parallel projection. The input rotation matrix
C contains the transformation data in a 3x3 matrix.
C
C...Input: RMAT 3x3 transformation matrix
C PTS_IN array (3xNPTS) of input points
C NPTS number of points in arrays
C
C...Output: PTS_OUT array (3xNPTS) of transformed points
C
DIMENSION PTS_IN(3,NPTS), PTS_OUT(3,NPTS)
DIMENSION RMAT(4,4)
C
DO I = 1, NPTS
C
DO J=1, 3
TMP = 0.0
DO K=1, 3
TMP = TMP + PTS_IN(K,I)*RMAT(K,J)
END DO
PTS_OUT(J,I) = TMP
END DO
C
END DO
C
RETURN
END
SUBROUTINE ROTPTS4 (RMAT,PTS_IN,NPTS,PTS_OUT)
C...Purpose: To rotate array of points to a new viewpoint by
C perspective projection. The input rotation matrix
C contains the transformation and perspective data in
C a 4x4 matrix in homogeneous coordinates. Note that input
C coordinates may need to be z-clipped if the user trans.
C moves the points behind the observer. A check is made
C for a singular perspective point (at observer).
C
C...Input: RMAT 4x4 rotation and perspective matrix
C PTS_IN array (3xNPTS) of input points
C NPTS number of points in arrays
C
C...Output: PTS_OUT array (3xNPTS) of transformed points
C
C...Note: You may need to translate your points to recenter them
C about the origin to get good perspective views. Points
C off to the side get pretty distorted...
C
DIMENSION PTS_IN(3,NPTS), PTS_OUT(3,NPTS)
DIMENSION RMAT(4,4), PTMP(4), PPTMP(4)
C
DO I = 1, NPTS
C
PTMP(1) = PTS_IN(1,I)
PTMP(2) = PTS_IN(2,I)
PTMP(3) = PTS_IN(3,I)
PTMP(4) = 1.0
C
DO J=1, 4
TMP = 0.0
DO K=1, 4
TMP = TMP + PTMP(K)*RMAT(K,J)
END DO
PPTMP(J) = TMP
END DO
C
IF(PPTMP(4).NE.0.0) THEN
PTS_OUT(1,I) = PPTMP(1)/PPTMP(4)
PTS_OUT(2,I) = PPTMP(2)/PPTMP(4)
PTS_OUT(3,I) = PPTMP(3)/PPTMP(4)
ELSE
WRITE(*,*) 'Homogeneous coordinate singular for pt ',I
ENDIF
C
END DO
C
RETURN
END
|
