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
|
% fieldlinesnormapaper.mp
% L. Nobre G.
% 2009
input featpost3Dplus2D;
Spread := 25;
f := (20,0,0);
color posa, posb, perpd;
numeric limy, limz, bord;
posa = (0,-3,3); %%%%%%%% allways make Y(posa) < Y(posb) %%%%%%%%%%%
posb = (0,3,-2); %%%%%%%%%%%% never make Y(posa) = Y(posb) %%%%%%%%%
perpd = (1,0,0);
limy = 7;
limz = 5;
bord = 2.5;
def vecfunc( expr posit )=
begingroup
save field;
color field, horiz, verti, vech, vecv;
numeric modula, modulb, ypos, zpos, hd, hf, vd, vf, zref, yref;
modula = conorm( posit-posa );
modulb = conorm( posit-posb );
field = N( ( posit-posa )/(modula**3)-( posit-posb )/(modulb**3) );
ypos = Y( posit );
zpos = Z( posit );
if Z(posa) <> Z(posb):
(ypos,zref) = whatever[(Y(posa),Z(posa)),(Y(posb),Z(posb))];
(yref,zpos) = whatever[(Y(posa),Z(posa)),(Y(posb),Z(posb))];
if ( abs(zpos) > limz-bord ):
hd = abs(zpos)-limz+bord;
if ypos < yref:
if zpos > 0:
vech = -green;
else:
vech = green;
fi;
else:
if zpos > 0:
vech = green;
else:
vech = -green;
fi;
fi;
else:
hd = 0;
vech = black;
fi;
else:
zref = Z(posa);
vech = green;
if ( abs(zpos) > limz-bord ):
hd = abs(zpos)-limz+bord;
else:
hd = 0;
fi;
fi;
if ( abs(ypos) > limy-bord ):
vd = abs(ypos)-limy+bord;
if zpos > zref:
if ypos < 0:
vecv = blue;
else:
vecv = -blue;
fi;
else:
if ypos < 0:
vecv = -blue;
else:
vecv = blue;
fi;
fi;
else:
vd = 0;
vecv = black;
fi;
hf = (hd/bord)**2;
vf = (vd/bord)**2;
( N(field*(0.975-hf)*(0.975-vf)+hf*vech+vf*vecv) )
endgroup
enddef;
def potfunc( expr posit )=
begingroup
color field;
field = vecfunc( posit );
( ncrossprod( field, perpd ) )
endgroup
enddef;
beginfig(1);
numeric i, lena, lenb, numa, numb, sa, sb, diffstep, ray;
numeric j, gridstep, fac;
color stp, grdp, locv;
path oneline;
pen grossa, fina;
grossa = pencircle scaled 3pt;
fina = pencircle scaled 2pt;
lena = 60;
lenb = 40;
numa = 15;
numb = 30;
diffstep = 0.1;
ray = 0.5;
sa = 40;
sb = 5;
fac = 0.275;
gridstep = 0.3;
for i=-limy+0.5*gridstep step gridstep until limy-0.5*gridstep:
for j=-limz+0.5*gridstep step gridstep until limz-0.5*gridstep:
grdp := (0,i,j);
locv := 0.5*fac*vecfunc( grdp );
drawarrow rp(grdp-locv)--rp(grdp+locv);
endfor;
endfor;
for i=sa step numa until (360-sa):
stp := posa+( 0, ray*cosd(i), ray*sind(i) );
oneline := fieldlinepath( lena, stp, diffstep, vecfunc );
draw oneline withpen grossa;
draw oneline withpen fina withcolor background;
endfor;
for i=sb step numb until (360-sb):
stp := posb+( 0, ray*cosd(i), ray*sind(i) );
oneline := fieldlinepath( lenb, stp, -diffstep, vecfunc );
draw oneline withpen grossa;
draw oneline withpen fina withcolor background;
endfor;
drawoptions(withpen grossa);
draw rp(posa);
draw rp(posb);
draw rp((0,-limy,-limz))--rp((0, limy,-limz))--
rp((0, limy, limz))--rp((0,-limy, limz))--cycle;
drawoptions();
endfig;
beginfig(2);
numeric i, lena, numa, diffstep, fac, gridstep, margnum;
color stp, grdp, locv;
path oneline, twoline, bordeline;
pen grossa, fina;
grossa = pencircle scaled 3pt;
fina = pencircle scaled 2pt;
lena = 85;
numa = 13;
margnum = 2;
diffstep = 0.2;
fac = 0.275;
gridstep = 0.3;
for i=-limy+0.5*gridstep step gridstep until limy-0.5*gridstep:
for j=-limz+0.5*gridstep step gridstep until limz-0.5*gridstep:
grdp := (0,i,j);
locv := 0.5*fac*potfunc( grdp );
drawarrow rp(grdp-locv)--rp(grdp+locv);
endfor;
endfor;
for i=margnum upto numa-margnum:
stp := (i/numa)[posa,posb];
oneline := fieldlinepath( lena, stp, diffstep, potfunc );
twoline := fieldlinepath( lena, stp, -diffstep, potfunc );
draw oneline withpen grossa;
draw twoline withpen grossa;
endfor;
drawoptions(withpen grossa);
draw rp(posa);
draw rp(posb);
bordeline = rp((0,-limy,-limz))--rp((0, limy,-limz))--
rp((0, limy, limz))--rp((0,-limy, limz))--cycle;
clip currentpicture to bordeline;
draw bordeline;
drawoptions(withpen fina);
numeric side;
path aux, electri;
side = 10mm;
aux = origin--(side,0)--(side,side)--cycle;
z0 = 0.667[origin,(side,0.5*side)];
electri = aux shifted (-z0) rotated (45+angle(rp(posb)-rp(posa)));
fill electri shifted rp(posb);
fill electri rotated 180 shifted rp(posa);
endfig;
end.
|
