-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy path3d23.mp
151 lines (126 loc) · 3.53 KB
/
3d23.mp
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
% tex/conc/mp/3d23.mp 2009-1-5 Alan U. Kennington.
% $Id: tex/conc/mp/3d23.mp 892fc608c5 2009-01-04 13:50:37Z Alan U. Kennington $
% 3d graphic: A bucket.
input 3dmax.mp
% input mapmax.mp
verbatimtex
\input akmath
etex
%%%%%%%%%%%%%%%%%%%%%%%%%
% figure 1 %
%%%%%%%%%%%%%%%%%%%%%%%%%
beginfig(1);
numeric A[][]; % The current 4x3 transformation matrix.
numeric p[][], q[][]; % Lists of 3-vectors.
pair v[], w[]; % Coordinate pairs on the drawing canvas.
numeric s; % The screen scale factor.
path pat[];
color col[];
Z_set(p0)(0, -35, 22); % Position of viewer.
Z_set(q0)(0, 0, 0); % Centre of picture.
A_set_pq(A)(p0)(q0);
% A_print(A);
s := 640;
unit := 10;
pickup pencircle scaled 0.5;
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
% Points in 3-d.
Z_set(p10)(0cm, 0cm, 0cm); % Origin.
Z_set(p11)(unit, 0cm, 0cm); % X axis.
Z_set(p12)(0cm, unit, 0cm); % Y axis.
Z_set(p13)(0cm, 0cm, 0.9unit); % Z axis.
% Points in 2-d.
A_calc_w(A)(w11)(p11)(s);
A_calc_w(A)(w12)(p12)(s);
A_calc_w(A)(w13)(p13)(s);
A_calc_w(A)(w10)(p10)(s);
% showvariable w;
% drawarrow w10--w11;
% drawarrow w10--w12;
% drawarrow w10--w13;
% label.rt(btex $x_1$ etex, w11);
% label.rt(btex $x_2$ etex, w12);
% label.lft(btex $x_3$ etex, w13+(-2pt,0));
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
% The bucket.
hh := 0.4unit;
rr := 0.2unit;
rrr := 1.14rr;
dd := rrr - rr; % Thickness at bottom of bucket.
np := 22;
Z_set(p20)(0unit, 0unit, 0unit); % Origin.
Z_add_set(p21)(p20)(0, 0, hh);
for ii = 0 upto np - 1:
w0 := (0, rr) rotated ((ii / np) * 360);
w1 := (0, rrr) rotated ((ii / np) * 360);
Z_add_set(p[30+ii])(p20)(xpart(w0), ypart(w0), 0);
Z_add_set(p[30+ii+np])(p20)(xpart(w1), ypart(w1), -dd);
Z_add_set(p[30+ii+2np])(p21)(xpart(w0), ypart(w0), 0);
Z_add_set(p[30+ii+3np])(p21)(xpart(w1), ypart(w1), 0);
endfor
% Points in 2-d.
A_calc_w(A)(w20)(p20)(s);
A_calc_w(A)(w21)(p21)(s);
for ii = 0 upto np - 1:
A_calc_w(A)(w[30+ii])(p[30+ii])(s);
A_calc_w(A)(w[30+ii+np])(p[30+ii+np])(s);
% draw w[30+ii+np];
% label.lft(decimal ii, w[30+ii+np]);
A_calc_w(A)(w[30+ii+2np])(p[30+ii+2np])(s);
A_calc_w(A)(w[30+ii+3np])(p[30+ii+3np])(s);
endfor
pat1 :=
for ii = 0 upto np - 1:
w[30+ii]..
endfor
cycle;
pat2 :=
for ii = 0 upto np - 1:
w[30+ii+np]..
endfor
cycle;
pat3 :=
for ii = 0 upto np - 1:
w[30+ii+2np]..
endfor
cycle;
pat4 :=
for ii = 0 upto np - 1:
w[30+ii+3np]..
endfor
cycle;
v1 := 0.5[point (np/4) of pat1, point (np/4) of pat2];
v2 := 0.5[point (np/4) of pat3, point (np/4) of pat4];
v3 := 0.5[v1, v2];
v4 := v3 + (-40pt, 20pt);
v5 := 1.5[point (3np/4) of pat1, point (3np/4) of pat2];
v6 := 1.5[point (3np/4) of pat3, point (3np/4) of pat4];
v7 := 0.5[v5, v6];
v8 := v7 + (40pt, 20pt);
% drawarrow w20--w21;
rat := 0.36;
draw pat1 dashed evenly scaled rat;
draw subpath (np/4, 3np/4) of pat2;
draw subpath (3np/4, 5np/4) of pat2 dashed evenly scaled rat;
draw pat3;
draw pat4;
v11 := point (np/4) of pat1;
v12 := point (np/4) of pat2;
v13 := point (np/4) of pat3;
v14 := point (np/4) of pat4;
v21 := point (3np/4) of pat1;
v22 := point (3np/4) of pat2;
v23 := point (3np/4) of pat3;
v24 := point (3np/4) of pat4;
draw v11--v13 dashed evenly scaled rat;
draw v12--v14;
draw v21--v23 dashed evenly scaled rat;
draw v22--v24;
% Labels.
drawarrow v4--v3;
label.top(btex boundary etex, v4);
label(btex inside etex, w21);
drawarrow v8--v7;
label.top(btex outside etex, v8);
endfig;
end