-
Notifications
You must be signed in to change notification settings - Fork 2
/
3d.ps
355 lines (333 loc) · 11 KB
/
3d.ps
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
% these procedures have been posted in comp.lang.postscript
% by Bill Lee, [email protected], on Apr 19 1995
% subject: arc with arrow head
% changes by Cristian Barbarosie in 2018 [email protected]
%* _____________________________ Arrows ____________________________________
%* Procedure to draw the path for an arrow head. Note: the arrowhead will be
%* added to the current path. The arrowhead will also be drawn and filled.
%*
%* Usage: Linewidth deltaX deltaY ArrowHead
%*
%* where: LineWidth is the width in points of the arrow head lines
%*
%* deltaX and deltaY define the direction that the arrow points
%*
%* Note: If Linewidth is zero, a value of 1 will be substituted
%*
/rArrowHead {
exch atan matrix currentmatrix exch rotate exch
dup 0 eq
{ pop 1 } if
dup scale
-7 2 rlineto
1 -2 rlineto
-1 -2 rlineto
7 2 rlineto
currentpoint
gsave
newpath moveto
-7 2 rlineto
1 -2 rlineto
-1 -2 rlineto
closepath
fill
grestore
setmatrix
} def
%* Procedure to draw the path for an arrow head. Note: the arrowhead will be
%* added to the current path. The arrowhead will also be drawn and filled.
%*
%* Usage: Linewidth PreviousX PreviousY ArrowHead
%*
%* where: LineWidth is the width in points of the arrow head lines
%*
%* PreviousX and PreviousY along with the currentpoint
%* define the direction that the arrow points
%*
%* Note: If Linewidth is zero, a value of 1 will be substituted
%*
/ArrowHead {
currentpoint
4 2 roll exch 4 -1 roll exch
sub 3 1 roll sub
rArrowHead
} def
%* _____________________________ RLineto^ ____________________________________
%* Procedure to add a relative line to the current path and then add the
%* path for an arrow on its end.
%*
%* Usage: x y RLineto^
%*
%* where: x and y are the offsets from the current point
%*
/RLineto^ {
currentlinewidth currentpoint 5 3 roll
rlineto
ArrowHead
} def
%* _____________________________ Lineto^ ____________________________________
%* Procedure to add a line to the current path and then add the
%* path for an arrow on its end.
%*
%* Usage: x y Lineto^
%*
%* where: x and y are the new points for the path
%*
/Lineto^ {
currentlinewidth currentpoint 5 3 roll
lineto
ArrowHead
} def
%* _____________________________ Arc^ ____________________________________
%* Procedure to add an arc to the current path and then add the
%* path for arrow on its end.
%*
%* Usage: x y r ang1 ang2 Arc^
%*
%* where: x, y, ang1, ang2, and r are the normal parameters
%* for drawing an arc.
%*
/Arc^ {
5 copy arc
exch pop 2 sub
dup cos 2 index mul 4 index add
exch sin 2 index mul 3 index add
currentlinewidth 3 1 roll
ArrowHead pop pop pop
} def
%* _____________________________ Arcn^ ____________________________________
%* Procedure to add an arc to the current path and then add the
%* path for arrow on its end.
%*
%* Usage: x y r ang1 ang2 Arcn^
%*
%* where: x, y, ang1, ang2, and r are the normal parameters
%* for drawing an arcn.
%*
/Arcn^ {
5 copy arcn
exch pop 2 add
dup cos 2 index mul 4 index add
exch sin 2 index mul 3 index add
currentlinewidth 3 1 roll
ArrowHead pop pop pop
} def
% _______________________________________________________
%
% procedures for projecting 3d objects into the plane
% _______________________________________________________
/A11 1 def /A12 0 def /A13 0 def
/A21 0 def /A22 -1 def /A23 0 def
/A31 0 def /A32 0 def /A33 1 def
/sq2 0.5 sqrt def
/seta 0.285 def
/rotxy
{ % rodamos com n graus no plano xy
dup cos /c exch def
sin /s exch def
% A11 = c A11 - s A21
% A12 = c A12 - s A22
% A13 = c A13 - s A23
% A21 = s A11 + c A21
% A22 = s A12 + c A22
% A23 = s A13 + c A23
/nA11 c A11 mul s A21 mul sub def
/nA12 c A12 mul s A22 mul sub def
/nA13 c A13 mul s A23 mul sub def
/A21 s A11 mul c A21 mul add def
/A22 s A12 mul c A22 mul add def
/A23 s A13 mul c A23 mul add def
/A11 nA11 def /A12 nA12 def /A13 nA13 def } def
/rotxz
{ % rodamos com n graus no plano xz
dup cos /c exch def
sin /s exch def
% A11 = c A11 - s A31
% A12 = c A12 - s A32
% A13 = c A13 - s A33
% A31 = s A11 + c A31
% A32 = s A12 + c A32
% A33 = s A13 + c A33
/nA11 c A11 mul s A31 mul sub def
/nA12 c A12 mul s A32 mul sub def
/nA13 c A13 mul s A33 mul sub def
/A31 s A11 mul c A31 mul add def
/A32 s A12 mul c A32 mul add def
/A33 s A13 mul c A33 mul add def
/A11 nA11 def /A12 nA12 def /A13 nA13 def } def
/rotyz
{ % rodamos com n graus no plano yz
dup cos /c exch def
sin /s exch def
% A21 = c A21 - s A31
% A22 = c A22 - s A32
% A23 = c A23 - s A33
% A31 = s A21 + c A31
% A32 = s A22 + c A32
% A33 = s A23 + c A33
/nA21 c A21 mul s A31 mul sub def
/nA22 c A22 mul s A32 mul sub def
/nA23 c A23 mul s A33 mul sub def
/A31 s A21 mul c A31 mul add def
/A32 s A22 mul c A32 mul add def
/A33 s A23 mul c A33 mul add def
/A21 nA21 def /A22 nA22 def /A23 nA23 def } def
/proj
{ % primeiro rodamos o boneco
% depois projectamos eliminando simplesmente a segunda coordenada
/z exch def /y exch def /x exch def
A11 x mul A12 y mul add A13 z mul add
A31 x mul A32 y mul add A33 z mul add } def
% para desenhar um circulo, fazemos oito curvas Bezier
% recebemos o centro e um vector ortogonal ao plano do circulo
% cuja norma e' igual ao raio do circulo
% queremos oito vectores ortogonais a ( x y z )
% observamos que ( y -x 0 ) ( z 0 -x ) ( 0 z -y ) sao ortogonais a ( x y z )
% mas nao sao ortogonais entre si e alguns podem ser nulos
% se tivermos dois desses tres vectores, v e w, fazemos a soma e a diferenca
% entao v+u e v-u sao ortogonais entre si e tambem sao ortogonais a ( x y z )
% temos entao tres candidatos a pares v+u, v-u
% escolhemos o par que tiver min(|v+u|,|v-u|) maior
/constroi_2_vec % x y z sao usados como macros, nao na pilha !
{ % v = ( y -x 0 ) w = ( z 0 -x )
/r1 0 def
/a1x y def /a1y x -1 mul def /a1z 0 def
a1x a1y a1z normalizar 0 eq not {
/a1z exch def /a1y exch def /a1x exch def
/c1x z def /c1y 0 def /c1z x -1 mul def
c1x c1y c1z normalizar 0 eq not {
/c1z exch def /c1y exch def /c1x exch def
/ra a1x c1x add dup mul a1y c1y add dup mul add a1z c1z add dup mul add def % |v+w|
/rb a1x c1x sub dup mul a1y c1y sub dup mul add a1z c1z sub dup mul add def % |v-w|
ra rb lt { ra } { rb } ifelse /r1 exch def } if } if
% v = ( -y x 0 ) w = ( 0 z -y )
/r2 0 def
/a2x y -1 mul def /a2y x def /a2z 0 def
a2x a2y a2z normalizar 0 eq not {
/a2z exch def /a2y exch def /a2x exch def
/c2x 0 def /c2y z def /c2z y -1 mul def
c2x c2y c2z normalizar 0 eq not {
/c2z exch def /c2y exch def /c2x exch def
/ra a2x c2x add dup mul a2y c2y add dup mul add a2z c2z add dup mul add def % |v+w|
/rb a2x c2x sub dup mul a2y c2y sub dup mul add a2z c2z sub dup mul add def % |v-w|
ra rb lt { ra } { rb } ifelse /r2 exch def } if } if
% v = ( z 0 -x ) w = ( 0 z -y )
/r3 0 def
/a3x z def /a3y 0 def /a3z x -1 mul def
a3x a3y a3z normalizar 0 eq not {
/a3z exch def /a3y exch def /a3x exch def
/c3x 0 def /c3y z def /c3z y -1 mul def
c3x c3y c3z normalizar 0 eq not {
/c3z exch def /c3y exch def /c3x exch def
/ra a3x c3x add dup mul a3y c3y add dup mul add a3z c3z add dup mul add def % |v+w|
/rb a3x c3x sub dup mul a3y c3y sub dup mul add a3z c3z sub dup mul add def % |v-w|
ra rb lt { ra } { rb } ifelse /r3 exch def } if } if
r1 r2 gt
{ r1 r3 gt
{ % r1 is max
% v = ( y -x 0 ) w = ( z 0 -x )
/ax a1x def /cx c1x def
/ay a1y def /cy c1y def
/az a1z def /cz c1z def }
{ % r3 is max
% v = ( -z 0 x ) w = ( 0 z -y )
/ax a3x def /cx c3x def
/ay a3y def /cy c3y def
/az a3z def /cz c3z def } ifelse }
{ r2 r3 gt
{ % r2 is max
% v = ( -y x 0 ) w = ( 0 z -y )
/ax a2x def /cx c2x def
/ay a2y def /cy c2y def
/az a2z def /cz c2z def }
{ % r3 is max
% v = ( -z 0 x ) w = ( 0 z -y )
/ax a3x def /cx c3x def
/ay a3y def /cy c3y def
/az a3z def /cz c3z def } ifelse }
ifelse
/bx ax cx add def
/by ay cy add def
/bz az cz add def
bx by bz normalizar pop
/bz exch def /by exch def /bx exch def
/dx cx ax sub def
/dy cy ay sub def
/dz cz az sub def
dx dy dz normalizar pop
/dz exch def /dy exch def /dx exch def }
def
/normalizar % r e' usado como macro, nao na pilha !
{ /zz exch def /yy exch def /xx exch def
/norm xx xx mul yy yy mul add zz zz mul add sqrt def
norm 0 eq not
{ xx norm div r mul yy norm div r mul zz norm div r mul } if
norm
} def
% deixa tres numeros na pilha
/circulo
{ /z exch def /y exch def /x exch def
/center_z exch def /center_y exch def /center_x exch def
/r x x mul y y mul add z z mul add sqrt def
constroi_2_vec % precisa de x y z r
center_x ax add center_y ay add center_z az add proj moveto
center_x ax add cx seta mul add
center_y ay add cy seta mul add
center_z az add cz seta mul add proj
center_x bx add dx seta mul sub
center_y by add dy seta mul sub
center_z bz add dz seta mul sub proj
center_x bx add center_y by add center_z bz add proj curveto
center_x bx add dx seta mul add
center_y by add dy seta mul add
center_z bz add dz seta mul add proj
center_x cx add ax seta mul add
center_y cy add ay seta mul add
center_z cz add az seta mul add proj
center_x cx add center_y cy add center_z cz add proj curveto
center_x cx add ax seta mul sub
center_y cy add ay seta mul sub
center_z cz add az seta mul sub proj
center_x dx add bx seta mul add
center_y dy add by seta mul add
center_z dz add bz seta mul add proj
center_x dx add center_y dy add center_z dz add proj curveto
center_x dx add bx seta mul sub
center_y dy add by seta mul sub
center_z dz add bz seta mul sub proj
center_x ax sub cx seta mul add
center_y ay sub cy seta mul add
center_z az sub cz seta mul add proj
center_x ax sub center_y ay sub center_z az sub proj curveto
% semi-circle
center_x ax sub cx seta mul sub
center_y ay sub cy seta mul sub
center_z az sub cz seta mul sub proj
center_x bx sub dx seta mul add
center_y by sub dy seta mul add
center_z bz sub dz seta mul add proj
center_x bx sub center_y by sub center_z bz sub proj curveto
center_x bx sub dx seta mul sub
center_y by sub dy seta mul sub
center_z bz sub dz seta mul sub proj
center_x cx sub ax seta mul sub
center_y cy sub ay seta mul sub
center_z cz sub az seta mul sub proj
center_x cx sub center_y cy sub center_z cz sub proj curveto
center_x cx sub ax seta mul add
center_y cy sub ay seta mul add
center_z cz sub az seta mul add proj
center_x dx sub bx seta mul sub
center_y dy sub by seta mul sub
center_z dz sub bz seta mul sub proj
center_x dx sub center_y dy sub center_z dz sub proj curveto
center_x dx sub bx seta mul add
center_y dy sub by seta mul add
center_z dz sub bz seta mul add proj
center_x ax add cx seta mul sub
center_y ay add cy seta mul sub
center_z az add cz seta mul sub proj
center_x ax add center_y ay add center_z az add proj curveto
} def
%____________________________________________________________________________
%____________________________________________________________________________