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mp-tres.mpiv /size: 6498 b last modification: 2021-10-28 13:50
1%D \module
2%D   [       file=mp-tres.mpiv,
3%D        version=2017.11.08,
4%D          title=\CONTEXT\ \METAPOST\ graphics,
5%D       subtitle=Pseudo 3D,
6%D         author=Alan Braslau,
7%D           date=\currentdate,
8%D      copyright={PRAGMA ADE \& \CONTEXT\ Development Team}]
9%C
10%C This module is part of the \CONTEXT\ macro||package and is
11%C therefore copyrighted by \PRAGMA. See licen-en.pdf for
12%C details.
13
14%D This module provides simple 3D->2D projections. The code is an adaption of code
15%D by Urs Oswald, Dr.sc.math.\ ETH as presented in:
16%D
17%D \starttyping
18%D http://www.ursoswald.ch/metapost/tutorial.html.
19%D \stoptyping
20%D
21%D We need a bit more so it got extended.
22
23if
 known
 context_three
 :
 endinput
 ;
 fi
 ;
24
25boolean
 context_three
 ;
 context_three
 :
=
 true
 ;
26
27pair
 mfun_three_xy
 ;
 % this avoids the costly save and allocate
28pair
 mfun_three_yz
 ;
29pair
 mfun_three_zx
 ;
30
31transform
 Txy
 ;
32
33def
 setTxy
(
expr
 ori
,
 ang
)
 =
34    begingroup
35        save
 P
,
 t
 ;
36        pair
 P
[
]
 ;
37        transform
 t
 ;
38
39        P
0
 =
 ori
 ;
                                  % origin in MetaPost coordinates (bp)
40        P
1
 =
 (
left
 rotated
 ang
)
 scaled
 (
cosd
 ang
)
 ;
 % x axis (in mathematical coordinates)
41
42        % A sort of "cavalier projection".
43
44        % t: maps mathematical 2D coordinates onto MetaPost coordinates.
45
46        t
 :
=
 identity
 shifted
 P
0
 ;
 % Note: no shift when P0 = origin!
47
48        % Txy: maps the x-y plane of 3D space onto MetaPost coordinates,
49        % z is the vertical (MetaPost y).
50
51        % Txy:=identity
52        %   reflectedabout((0,0), (1,1))
53        %     yscaled ypart P1
54        %       slanted (xpart P1/ypart P1)
55        %         transformed t ;
56
57        % Alternatively, defined via Pxy:
58
59        % Pxy is the projection of the 3D plane z=0 onto the mathematical 2D coordinates.
60        % Pxy is determined by  3  e q u a t i o n s  describing
61        % how (1,0), (0,1), and (0,0) are mapped
62
63        save
      Pxy
 ;
64        transform
 Pxy
 ;
65           P
1
 =
 (
1
,
0
)
 transformed
 Pxy
 ;
   % Pxy: (1,0) --> P1
66        (
1
,
0
)
 =
 (
0
,
1
)
 transformed
 Pxy
 ;
   %      (0,1) --> (1,0)
67        (
0
,
0
)
 =
 (
0
,
0
)
 transformed
 Pxy
 ;
   %      (0,0) --> (0,0)
68
69        % mathematical 2D coordinates --> MetaPost coordinates
70
71        Txy
 :
=
 Pxy
 transformed
 t
 ;
72    endgroup
73enddef
 ;
74
75setTxy
(
origin
,
60
)
 ;
76
77%D We already define triplet (as rgbcolor synonym) in in \type {mp-tool.mpiv}:
78
79let
 Xpart
 =
 redpart
 ;
80let
 Ypart
 =
 greenpart
 ;
81let
 Zpart
 =
 bluepart
 ;
82
83primarydef
 p
 Xscaled
 q
 =
84  (
q
*
Xpart
 p
,
 Ypart
 p
,
 Zpart
 p
)
85enddef
 ;
86
87primarydef
 p
 Yscaled
 q
 =
88  (
Xpart
 p
,
 q
*
Ypart
 p
,
 Zpart
 p
)
89enddef
 ;
90
91primarydef
 p
 Zscaled
 q
 =
92  (
Xpart
 p
,
 Ypart
 p
,
 q
*
Zpart
 p
)
93enddef
 ;
94
95primarydef
 p
 XYZscaled
 q
 =
96  (
q
*
Xpart
 p
,
q
*
Ypart
 p
,
q
*
Zpart
 p
)
97enddef
 ;
98
99vardef
 projection
 primary
 t
 =
100    (
if
 triplet
 t
 :
101        (
Xpart
 t
,
 Ypart
 t
)
 transformed
 Txy
 shifted
 (
0
,
Zpart
 t
)
102     elseif
 pair
 t
 :
103        t
 transformed
 Txy
104     else
 :
105        origin
 transformed
 Txy
106     fi
)
107enddef
 ;
108
109vardef
 Abs
 primary
 p
 =
110    if
 triplet
 p
 :
111        sqrt
(
(
Xpart
 p
)
*
*
2
+
(
Ypart
 p
)
*
*
2
+
(
Zpart
 p
)
*
*
2
)
112    else
 :
113        length
 p
114    fi
115enddef
 ;
116
117vardef
 Unitvector
 primary
 z
 =
118    z
/
Abs
 z
119enddef
 ;
120
121primarydef
 p
 dotproduct
 q
 =
122    (
(
Xpart
 p
)
*
(
Xpart
 q
)
 +
 (
Ypart
 p
)
*
(
Ypart
 q
)
 +
 (
Zpart
 p
)
*
(
Zpart
 q
)
)
123enddef
 ;
124
125primarydef
 p
 crossproduct
 q
 =
126    (
127        (
Ypart
 p
)
*
(
Zpart
 q
)
 -
 (
Zpart
 p
)
*
(
Ypart
 q
)
,
128        (
Zpart
 p
)
*
(
Xpart
 q
)
 -
 (
Xpart
 p
)
*
(
Zpart
 q
)
,
129        (
Xpart
 p
)
*
(
Ypart
 q
)
 -
 (
Ypart
 p
)
*
(
Xpart
 q
)
130    )
131enddef
 ;
132
133primarydef
 p
 rotatedaboutX
 q
 =
134    hide
 (
135        mfun_three_yz
 :
=
 (
Ypart
 p
,
 Zpart
 p
)
 ;
136        mfun_three_yz
 :
=
 mfun_three_yz
 rotated
 q
 ;
137    )
138    (
Xpart
 p
,
 xpart
 mfun_three_yz
,
 ypart
 mfun_three_yz
)
139enddef
 ;
140
141primarydef
 p
 rotatedaboutY
 q
 =
142    hide
(
143        mfun_three_zx
 :
=
 (
Zpart
 p
,
 Xpart
 p
)
 ;
144        mfun_three_zx
 :
=
 mfun_three_zx
 rotated
 q
 ;
145    )
146    (
ypart
 mfun_three_zx
,
 Ypart
 p
,
 xpart
 mfun_three_zx
)
147enddef
 ;
148
149primarydef
 p
 rotatedaboutZ
 q
 =
150    hide
 (
151        mfun_three_xy
 :
=
 (
Xpart
 p
,
 Ypart
 p
)
 ;
152        mfun_three_xy
 :
=
 mfun_three_xy
 rotated
 q
 ;
153    )
154    (
xpart
 mfun_three_xy
,
 ypart
 mfun_three_xy
,
 Zpart
 p
)
155enddef
 ;
156
157%D We can use a rotation about an arbitrary direction t ... (easy)
158
159% primarydef p rotatedabout(expr t, a) =
160% enddef ;
161
162vardef
 draw_vector
@#
 (
expr
 v
,
 s
)
 text
 t
 =
163    if
 triplet
 v
 :
164        drawarrow
 projection
(
Origin
)
 --
 projection
(
v
)
 t
 ;
165        if
 string
 s
 :
166            label
@#
(
s
,
 projection
(
v
)
)
 t
 ;
167        fi
168    fi
169enddef
 ;
170
171%D Transform a (2D) path to a 3D plane
172
173def
 XYpath
 primary
 p
 =
174    (
for
 i
=
0
 upto
 (
length
 p
)
 if
 cycle
 p
:
 -1
 fi
 :
175        if
 i
>
0
 :
 ..
 fi
176        projection
 (
xpart
 point
 i
 of
 p
,
177                    ypart
 point
 i
 of
 p
,
178                    0
)
179        .
.
controls
180        projection
 (
xpart
 postcontrol
 i
 of
 p
,
181                    ypart
 postcontrol
 i
 of
 p
,
182                    0
)
183        and
184        projection
 (
xpart
 precontrol
 (
i
+1
)
 of
 p
,
185                    ypart
 precontrol
 (
i
+1
)
 of
 p
,
186                    0
)
187        endfor
 if
 cycle
 p
:
 .
.
cycle
 fi
)
188enddef
 ;
189
190def
 XZpath
 primary
 p
 =
191    (
for
 i
=
0
 upto
 (
length
 p
)
 if
 cycle
 p
:
 -1
 fi
 :
192        if
 i
>
0
 :
 ..
 fi
193        projection
 (
xpart
 point
 i
 of
 p
,
194                    0
,
195                    ypart
 point
 i
 of
 p
)
196        .
.
controls
197        projection
 (
xpart
 postcontrol
 i
 of
 p
,
198                    0
,
199                    ypart
 postcontrol
 i
 of
 p
)
200        and
201        projection
 (
xpart
 precontrol
 (
i
+1
)
 of
 p
,
202                    0
,
203                    ypart
 precontrol
 (
i
+1
)
 of
 p
)
204        endfor
 if
 cycle
 p
:
 .
.
cycle
 fi
)
205enddef
 ;
206
207def
 YZpath
 primary
 p
 =
208    (
for
 i
=
0
 upto
 (
length
 p
)
 if
 cycle
 p
:
 -1
 fi
 :
209        if
 i
>
0
 :
 ..
 fi
210        projection
 (
0
,
211                    xpart
 point
 i
 of
 p
,
212                    ypart
 point
 i
 of
 p
)
213        .
.
controls
214        projection
 (
0
,
215                    xpart
 postcontrol
 i
 of
 p
,
216                    ypart
 postcontrol
 i
 of
 p
)
217        and
218        projection
 (
0
,
219                    xpart
 precontrol
 (
i
+1
)
 of
 p
,
220                    ypart
 precontrol
 (
i
+1
)
 of
 p
)
221        endfor
 if
 cycle
 p
:
 .
.
cycle
 fi
)
222enddef
 ;
223
224%D Some constants...
225
226triplet
 Origin
,
 Xunitvector
,
 Yunitvector
,
 Zunitvector
 ;
227
228Origin
      :
=
 (
0
,
0
,
0
)
 ;
229Xunitvector
 :
=
 (
1
,
0
,
0
)
 ;
230Yunitvector
 :
=
 (
0
,
1
,
0
)
 ;
231Zunitvector
 :
=
 (
0
,
0
,
1
)
 ;
232
233%D We could do but don't:
234
235% let normalxpart = xpart ;
236% let normalypart = ypart ;
237
238% vardef xpart expr p = if triplet p : redpart   else : normalxpart fi p enddef ;
239% vardef ypart expr p = if triplet p : greenpart else : normalypart fi p enddef ;
240% vardef zpart expr p =                bluepart                        p enddef ;
241
242
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