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
|
divert(-1)
lib3D.m4 Macros for rotation, projection, and other
operations on argument triples representing
3D vectors or colors.
* Circuit_macros Version 10.0, copyright (c) 2022 J. D. Aplevich under *
* the LaTeX Project Public Licence in file Licence.txt. The files of *
* this distribution may be redistributed or modified provided that this *
* copyright notice is included and provided that modifications are clearly *
* marked to distinguish them from this distribution. There is no warranty *
* whatsoever for these files. *
define(`lib3D_')
ifdef(`libgen_',,`include(libgen.m4)divert(-1)')
=============================================================================
`setview(azimuth, elevation, rotation)
Set view angles (degrees) for projection onto
a plane. The view vector is obtained by looking
in along the x axis, then rotating about -x,
-y, and z in that order. 3D vectors are
projected onto the resulting yz plane
using the project() macro. If rotation = 0,
the projection matrix P is
P =( -sin(az), cos(az), 0 )
(-sin(el)cos(az),-sin(az)sin(el),cos(el))'
define(`setview',`
`# setview($@)'
define(`m4azim',ifelse(`$1',,0,prod_($1,dtor_)))dnl
define(`m4elev',ifelse(`$2',,0,prod_($2,dtor_)))dnl
define(`m4rot', ifelse(`$3',,0,prod_($3,dtor_)))dnl
define(`m4azimr',`ifelse(`$1',,0,`prod_(`$1',dtor_)')')dnl
define(`m4elevr',`ifelse(`$2',,0,`prod_(`$2',dtor_)')')dnl
define(`m4rotx',`ifelse(`$3',,0,`prod_(`$3',dtor_)')')dnl
define(`m4caz',
`ifelse(`$1',,1,`$1',0,1,`$1',90,0,`$1',-90, 0,m4cos(m4azim))')dnl
define(`m4saz',
`ifelse(`$1',,0,`$1',0,0,`$1',90,1,`$1',-90,-1,m4sin(m4azim))')dnl
define(`m4cel',
`ifelse(`$2',,1,`$2',0,1,`$2',90,0,`$2',-90, 0,m4cos(m4elev))')dnl
define(`m4sel',
`ifelse(`$2',,0,`$2',0,0,`$2',90,1,`$2',-90,-1,m4sin(m4elev))')dnl
define(`m4cro',`ifelse(`$3',,1,`$3',0,1,`$3',90,0,`$3',-90, 0,m4cos(m4rot))')dnl
define(`m4sro',`ifelse(`$3',,0,`$3',0,0,`$3',90,1,`$3',-90,-1,m4sin(m4rot))')dnl
view3D1=m4caz*m4cel;dnl
view3D2=m4saz*m4cel;dnl
view3D3=m4sel
ifdef(`setlight_',,`light3D1=view3D1; light3D2=view3D2; light3D3=view3D3')
dnl Unit vectors projected on the view plane
UPx_: project(1,0,0)
UPy_: project(0,1,0)
UPz_: project(0,0,1)
`# setview end'
')
define(`m4cos',`ifelse(`$1',0,1,cos(`$1'))')
define(`m4sin',`ifelse(`$1',0,0,sin(`$1'))')
The resulting view vector
#efine(`View3D',`PtoBase3D(1,0,0)')
define(`View3D',`view3D1,view3D2,view3D3')
`Extract the x-y, x-z, or y-z coordinate pair
from a triple'
define(`Pr_xy',`$1,$2')
define(`Pr_xz',`$1,$3')
define(`Pr_yz',`$2,$3')
Projection coords back to orig 3D coords
define(`PtoBase3D',
`rot3Dz(m4azim,rot3Dy(-m4elev,rot3Dx(-m4rot,`$1',`$2',`$3')))')
This does the 3D to 2D axonometric projection
i.e. project(x,y,z) produces coordinate pair
u,v on the 2D plane defined by the view angles
and Project(x,y,z) produces position (u,v)
ifdpic(
`define(`project',
`Pr_yz(rot3Dx(m4rot,rot3Dy(m4elev,rot3Dz(-m4azim,`$1',`$2',`$3'))))')
define(`Project',`(ifelse(`$1',0,
`ifelse(`$2',0,`ifelse(`$3',0,`(0,0)',UPz_*(`$3'))',
`UPy_*(`$2')`'ifelse(`$3',0,,+UPz_*(`$3'))')',
`UPx_*(`$1')`'ifelse(`$2',0,,+UPy_*(`$2'))`'ifelse(`$3',0,,+UPz_*(`$3'))'))')',
`define(`project',
`Pr_yz(rot3Dx(m4rot,rot3Dy(m4elev,rot3Dz(-m4azim,`$1',`$2',`$3'))))')
define(`Project',`(project($@))')')
`Rotation about x axis rot3Dx(angle,x1,x2,x3)'
define(`rot3Dx',``$2',diff_(prod_(m4cos(`$1'),`$3'),prod_(m4sin(`$1'),`$4')),dnl
sum_(prod_(m4sin(`$1'),`$3'),prod_(m4cos(`$1'),`$4'))')
`Rotation about y axis rot3Dy(angle,x1,x2,x3)'
define(`rot3Dy',`sum_(prod_(m4cos(`$1'),`$2'),prod_(m4sin(`$1'),`$4')),`$3',dnl
diff_(prod_(m4cos(`$1'),`$4'),prod_(m4sin(`$1'),`$2'))')
`Rotation about z axis rot3Dz(angle,x1,x2,x3)'
define(`rot3Dz',`diff_(prod_(m4cos(`$1'),`$2'),prod_(m4sin(`$1'),`$3')),dnl
sum_(prod_(m4sin(`$1'),`$2'),prod_(m4cos(`$1'),`$3')),`$4'')
`Cross product cross3D(x1,y1,z1,x2,y2,z2)'
define(`cross3D',`diff_(prod_(`$2',`$6'),prod_(`$3',`$5')),dnl
diff_(prod_(`$3',`$4'),prod_(`$1',`$6')),dnl
diff_(prod_(`$1',`$5'),prod_(`$2',`$4'))')
`Dot product dot3D(x1,y1,z1,x2,y2,z2)'
define(`dot3D',`(sum_(
sum_(prod_(`$1',`$4'),prod_(`$2',`$5')),prod_(`$3',`$6')))')
Vector addition, subtraction, scalar product
define(`sum3D',`sum_(`$1',`$4'),sum_(`$2',`$5'),sum_(`$3',`$6')')
define(`diff3D',`diff_(`$1',`$4'),diff_(`$2',`$5'),diff_(`$3',`$6')')
define(`sprod3D',`prod_(`$1',`$2'),prod_(`$1',`$3'),prod_(`$1',`$4')')
Extract direction cosine
`eg v = dcosine3D(1,x,y,z) assigns x to v'
define(`dcosine3D',`(ifelse(`$1',1,`$2',`$1',2,`$3',`$4'))')
Euclidian length
define(`length3D',`sqrt((`$1')^2+(`$2')^2+(`$3')^2)')
Unit vector
define(`unit3D',`sprod3D(1/length3D(`$1',`$2',`$3'),`$1',`$2',`$3')')
Proportion: between3D(x,Vec1,Vec2), i.e.
Vec1 * (1-x) + Vec2 * x
define(`between3D',`sum3D(sprod3D((1-(`$1')),`$2',`$3',`$4'),
sprod3D( `$1',`$5',`$6',`$7'))')
`assign3D([u],[v],[w],x,y,z); eg
assign3D(u,v,w,cross3D(x1,y1,z1,x2,y2,z2))
assigns u = 4th arg, v = 5th arg, w = 6th arg,
for nonblank u, v, or w'
define(`assign3D',`assign3($@)')
`vassign3D(name,x,y,z); eg
vassign3D(u,x,y,z)
assigns u[1] = x, u[2] = y, u[3] = z'
define(`vassign3D',`for i_vassign3D = 1 to 3 do {
exec sprintf("`$1'[i_vassign3D] = $%g",i_vassign3D+3) }')
Write out the 3 arguments for debug
define(`print3D',`print sprintf("`$1'(%g,%g,%g)",`$2',`$3',`$4')')
`setlight (azimuth, elevation, rotation)
Set angles (degrees) for 3D highlighting.
Defaults are the previous values for
setview(). The Light3D vector is defined
as for View3D.'
define(`setlight',`define(`setlight_')
define(`m4hzim',`ifelse(`$1',,m4azimr,`prod_(`$1',dtor_)')')dnl
define(`m4hlev',`ifelse(`$2',,m4elevr,`prod_(`$2',dtor_)')')dnl
define(`m4hot',`ifelse(`$3',,m4rotx,`prod_(`$3',dtor_)')')dnl
define(`m4chz',`ifelse(`$1',0,1,`$1',90,0,`$1',-90, 0,cos(m4hzim))')dnl
define(`m4shz',`ifelse(`$1',0,0,`$1',90,1,`$1',-90,-1,sin(m4hzim))')dnl
define(`m4chl',`ifelse(`$2',0,1,`$2',90,0,`$2',-90, 0,cos(m4hlev))')dnl
define(`m4shl',`ifelse(`$2',0,0,`$2',90,1,`$2',-90,-1,sin(m4hlev))')dnl
define(`m4cho',`ifelse(`$3',0,1,`$3',90,0,`$3',-90, 0,cos(m4hot))')dnl
define(`m4sho',`ifelse(`$3',0,0,`$3',90,1,`$3',-90,-1,sin(m4hot))')dnl
light3D1=m4chz*m4chl
light3D2=m4shz*m4chl
light3D3=m4shl
')
The resulting vector
#efine(`Light3D',`PtoBase3D(1,0,0)')
define(`Light3D',
`ifdef(`setlight_',`light3D1,light3D2,light3D3',`view3D1,view3D2,view3D3')')
`Fector(x,y,z,nx,ny,nz) with .Origin at pos
Arrow with flat 3D head. The second vector,
(i.e. args nx,ny,nz) is the normal to the
head flat surface'
define(`Fector',
`[ Origin: 0,0
define(`M4F_V',``$1',`$2',`$3'')dnl the whole vector V
lV = length3D(M4F_V)
define(`M4F_T',``$4',`$5',`$6'')dnl normal to the top surface
lT = length3D(M4F_T)
define(`M4F_Vn',`sprod3D(1/lV,M4F_V)')dnl unit vector Vn
aln = 0.15*scale ;dnl arrowhead length
awd = 0.09*scale ;dnl " width
adp = 0.0375*scale ;dnl " depth (thickness)
define(`M4F_Vt',`sprod3D((lV-aln),M4F_Vn)')dnl head base vector
Start: Origin
End: project(M4F_V)
rpoint_(from Origin to End)
lTdp = adp/2/lT
vtx = dcosine3D(1,M4F_Vt); vty = dcosine3D(2,M4F_Vt) # Vt coords
vtz = dcosine3D(3,M4F_Vt)
dnl half-thickness vector in direction of T
tx = prod_(lTdp,`$4'); ty = prod_(lTdp,`$5')
tz = prod_(lTdp,`$6')
dnl half-width vector right
rf = awd/2/lT/lV
rx = rf*dcosine3D(1,cross3D(M4F_V,M4F_T))
ry = rf*dcosine3D(2,cross3D(M4F_V,M4F_T))
rz = rf*dcosine3D(3,cross3D(M4F_V,M4F_T))
dnl top and bottom points of V
TV: project(sum3D(M4F_V, tx,ty,tz))
BV: project(diff3D(M4F_V, tx,ty,tz))
dnl top, bottom right, left of base
TR: project(sum3D(vtx,vty,vtz, sum3D(tx,ty,tz,rx,ry,rz)))
BR: project(sum3D(vtx,vty,vtz, diff3D(rx,ry,rz,tx,ty,tz)))
BL: project(diff3D(vtx,vty,vtz, sum3D(rx,ry,rz,tx,ty,tz)))
TL: project(diff3D(vtx,vty,vtz, diff3D(rx,ry,rz,tx,ty,tz)))
lthickness = linethick
dnl base
if dot3D(M4F_V,View3D) < 0 then {
thinlines_
ifgpic(`gshade(0.5,BR,BL,TL,TR,BR,BL)',
`line thick 0 fill_(0.5) from BR to BL then to TL then to TR then to BR')
line from BR to BL ; line to TL ; line to TR ; line to BR
linethick_(lthickness)
}
dnl shaft
linethick_(1.2)
psset_(arrows=c-c)
line from Origin to project(vtx,vty,vtz)
psset_(arrows=-)
thinlines_
dnl top or bottom
if dot3D(M4F_T,View3D) > 0 then {
ifgpic(`gshade(1,TR,TL,TV,TR,TL)',
`line thick 0 fill_(1) from TV to TR then to TL then to TV')
line from TV to TR ; line to TL ; line to TV
} else {
ifgpic(`gshade(0,BR,BL,BV,BR,BL)',
`line thick 0 fill_(0) from BV to BR then to BL then to BV')
line from BV to BR ; line to BL ; line to BV
}
dnl starboard normal; draw right face
define(`M4F_S',
`cross3D(diff3D(sprod3D(aln,M4F_Vn),rx,ry,rz),M4F_T)')dnl
if dot3D(M4F_S,View3D) > 0 then {
ifgpic(`gshade(1,TV,BV,BR,TR,TV,BV)',
`line thick 0 fill_(1) from TV to BV then to BR then to TR then to TV')
line from TV to BV ; line to BR ; line to TR ; line to TV
}
dnl port normal; draw left face
define(`M4F_P',
`cross3D(M4F_T,sum3D(sprod3D(aln,M4F_Vn),rx,ry,rz))')dnl
if dot3D(M4F_P,View3D) > 0 then {
ifgpic(`gshade(1,TV,BV,BL,TL,TV,BV)',
`line thick 0 fill_(1) from TV to BV then to BL then to TL then to TV')
line from TV to BV ; line to BL ; line to TL ; line to TV
}
linethick_(lthickness)
`$7'] ') # End Fector
`shadedball( rad,
highlight rad, highlight degrees,
initial shade, final shade )
The highlight is by default at
radius rad*3/5 and angle 110 deg
(or arg2 deg); if setlight has been
invoked then the highlight is as
given by its azimuth and elevation arguments'
define(`shadedball',`[ C: (0,0); r = ifelse(`$1',,circlerad,`$1')
ifdef(`setlight_',
`H: (project(sprod3D(r,light3D1,light3D2,light3D3)))
hr = distance(C,H)',
`hr = ifelse(`$2',,r*3/5,`$2'); ha = ifelse(`$3',,110,`$3')
H: (cosd(ha)*hr,sind(ha)*hr)')
u0 = ifelse(`$4',,1,`$4'); uf = ifelse(`$5',,0.25,`$5')
rm = r+hr; n = int(rm/(linethick bp__))
for i=1 to n-1 do { x = i/n*rm; u = u0+(i/n)^2*(uf-u0)
if x <= (r-hr) then {
circle rad x thick linethick*1.6 outlined rgbstring(u,u,u) at H } \
else { arc cw thick linethick*ifpgf(2,1.6) outlined rgbstring(u,u,u) \
from Cintersect(H,x,C,r) to Cintersect(H,x,C,r,R) with .c at H } }
circle rad r ifpgf(+linethick bp__/2) at C
`$6']')
divert(0)dnl
|
