Contents of file 'poincare/example-ccr.mp':
1 % This Filename: example-ccr.mp [MetaPost source]
2 % Creation time: Thu Jan 23 20:19:30 2014
3 %
4 % Copyright (C) 1997-2005, Fredrik Jonsson <fj@optics.kth.se>
5 %
6 % Input Filename [Stokes parameters]: example-cc.dat
7 % This MetaPost source code was automatically generated by poincare
8 % Full set of command line options that generated this code:
9 % --verbose --normalize --bezier --inputfile example-cc.dat --outputfile
10 % example-ccr.mp --axislengths 0.3 1.7 0.3 2.4
11 % 0.3 1.5 --axislabels s_1(t) bot s_2(t)
12 % bot s_3(t) rt --rotatephi 15.0 --rotatepsi
13 % -60.0 --shading 0.75 0.99 --rhodivisor 50
14 % --phidivisor 80 --scalefactor 20.0 --paththickness 0.8
15 % --arrowthickness 0.4 --arrowheadangle 20.0 --draw_paths_as_arrows --reverse_arrow_paths
16
17 %
18 % Description: Map of Stokes parameters, visualized as trajectories
19 % onto the Poincare sphere. This file contains MetaPost
20 % source code, to be compiled with John Hobby's MetaPost
21 % compiler or used with anything that understands MetaPost
22 % source code.
23 %
24 % If you want to create PostScript output, or include the resulting
25 % output in a TeX document, this example illustrates the procedure,
26 % assuming 'poincaremap.mp' to be the name of the file containing the
27 % MetaPost code to be visualized: (commands run on command-line)
28 %
29 % mp poincaremap.mp;
30 % echo "\input epsf\centerline{\epsfbox{poincaremap.1}}\bye" > tmp.tex;
31 % tex tmp.tex;
32 % dvips tmp.dvi -o poincaremap.ps;
33 %
34 % Here, the first command compiles the MetaPost source code, and leaves
35 % an Encapsulated PostScript file named 'poincaremap.1', containing TeX
36 % control codes for characters, etc. This file does not contain any
37 % definitions for characters or TeX-specific items, and it cannot be
38 % viewed or printed simply as is stands; it must rather be included into
39 % TeX code in order to provide something useful.
40 % The second command creates a temporary minimal TeX-file 'tmp.tex',
41 % that only includes the previously generated Encapsulated PostScript
42 % code.
43 % The third command compiles the TeX-code into device-independent,
44 % or DVI, output, stored in the file 'tmp.dvi'.
45 % Finally, the last command converts the DVI output into a free-
46 % standing PostScript file 'poincaremap.ps', to be printed or viewed
47 % with some PostScript viewer, such as GhostView.
48 %
49 scalefactor := 20.000000 mm;
50 rot_psi := -60.000000; % Rotation angle round z-axis (first rotation)
51 rot_phi := 15.000000; % Rotation angle round y-axis (second rotation)
52 alpha := -24.146108; % == arctan(sin(rot_phi)*tan(rot_psi))
53 beta := -8.498781; % == arctan(sin(rot_phi)/tan(rot_psi))
54
55 %
56 % Parameters specifying the location of the light source; for Phong
57 % shading of the sphere.
58 %
59 % phi_source: Angle (in deg.) to light source counterclockwise
60 % 'from three o'clock', viewed from the observer.
61 %
62 % theta_source: Angle (in deg.) between light source and observer,
63 % seen from the centre of the sphere.
64 %
65 % Parameters specifying the shading 'intensity' in terms of maximum
66 % (for the highlighs) and minimum (for the deep shadowed regions)
67 % values for the Phong shading. '0.0' <=> 'black'; '1.0' <=> 'white'
68 %
69 % upper_value: Maximum value of whiteness.
70 % lower_value: Minimum value of whiteness.
71 %
72 phi_source := 30.000000;
73 theta_source := 30.000000;
74 upper_value := 0.990000;
75 lower_value := 0.750000;
76 radius := scalefactor;
77 delta_rho := radius/50.000000;
78 delta_phi := 360.0/80.000000;
79 beginfig(1);
80 path p;
81 path equator;
82 transform T;
83 c1:=lower_value;
84 c2:=upper_value-lower_value;
85 nx_source := sind(theta_source)*cosd(phi_source);
86 ny_source := sind(theta_source)*sind(phi_source);
87 nz_source := cosd(theta_source);
88 phistop := 360.0;
89 rhostop := radius - delta_rho/2.0;
90 %
91 % Draw the shaded Poincare sphere projected on 2D screen coordinates
92 %
93 for rho=0.0cm step delta_rho until rhostop:
94 for phi=0.0 step delta_phi until phistop:
95 rhomid := rho + delta_rho/2.0;
96 phimid := phi + delta_phi/2.0;
97 x1 := rho*cosd(phi);
98 y1 := rho*sind(phi);
99 x2 := (rho+delta_rho)*cosd(phi);
100 y2 := (rho+delta_rho)*sind(phi);
101 x3 := (rho+delta_rho)*cosd(phi+delta_phi);
102 y3 := (rho+delta_rho)*sind(phi+delta_phi);
103 x4 := rho*cosd(phi+delta_phi);
104 y4 := rho*sind(phi+delta_phi);
105 p:=makepath makepen ((x1,y1)--(x2,y2)--(x3,y3)--(x4,y4)--(x1,y1));
106 quot := (rhomid/radius);
107 nx_object := quot*cosd(phimid);
108 ny_object := quot*sind(phimid);
109 nz_object := sqrt(1-quot*quot);
110 prod:=nx_object*nx_source+ny_object*ny_source
111 +nz_object*nz_source;
112 if prod < 0.0:
113 value := c1;
114 else:
115 value := c1 + c2*prod*prod;
116 fi
117 fill p withcolor value[black,white];
118 endfor
119 endfor
120
121 %
122 % Draw the 'equators' of the Poincare sphere
123 %
124 equator := halfcircle scaled (2.0*radius);
125 eqcolval := .45; % '0.0' <=> 'white'; '1.0' <=> 'black'
126
127 pickup pencircle scaled 0.600000 pt;
128 %
129 % Draw equator $S_3=0$...
130 %
131 T := identity yscaled sind(rot_phi) rotated 180.0;
132 draw equator transformed T withcolor eqcolval [white,black];
133
134 %
135 % ... then equator $S_2=0$...
136 %
137 T := identity yscaled (cosd(rot_phi)*sind(rot_psi))
138 rotated (270.0 + alpha);
139 draw equator transformed T withcolor eqcolval [white,black];
140
141 %
142 % ... and finally equator $S_1=0$.
143 %
144 T := identity yscaled (cosd(rot_phi)*cosd(rot_psi))
145 rotated (270.0 - beta);
146 draw equator transformed T withcolor eqcolval [white,black];
147
148 oldahangle:=ahangle;
149 ahangle:=20.000000;
150 pickup pencircle scaled 0.800000 pt;
151 pickup pencircle scaled 0.400000 pt;
152 pickup pencircle scaled 0.400000 pt;
153 pickup pencircle scaled 0.800000 pt;
154 p := makepath makepen (0.9883,0.1506)..(0.9814,0.1857)
155 ..(0.9727,0.2205)..(0.9622,0.2550)..(0.9499,0.2893)
156 ..(0.9359,0.3230)..(0.9202,0.3564)..(0.9029,0.3893)
157 ..(0.8841,0.4216)..(0.8638,0.4534)..(0.8422,0.4845)
158 ..(0.8192,0.5150)..(0.7950,0.5447)..(0.7696,0.5738)
159 ..(0.7433,0.6020)..(0.7160,0.6295)..(0.6879,0.6561)
160 ..(0.6591,0.6818)..(0.6296,0.7067);
161 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
162 pickup pencircle scaled 0.400000 pt;
163 pickup pencircle scaled 0.800000 pt;
164 p := makepath makepen (0.6147,0.7187)..(0.5845,0.7422)
165 ..(0.5540,0.7647)..(0.5233,0.7862)..(0.4924,0.8067)
166 ..(0.4615,0.8262)..(0.4309,0.8447)..(0.4005,0.8621)
167 ..(0.3703,0.8785)..(0.3408,0.8939)..(0.3117,0.9082)
168 ..(0.2833,0.9214)..(0.2556,0.9336)..(0.2291,0.9447)
169 ..(0.2034,0.9547)..(0.1788,0.9637)..(0.1554,0.9717)
170 ..(0.1333,0.9787)..(0.1125,0.9846)..(0.0932,0.9895)
171 ..(0.0753,0.9934)..(0.0591,0.9964)..(0.0444,0.9984);
172 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
173 pickup pencircle scaled 0.400000 pt;
174 pickup pencircle scaled 0.400000 pt;
175 pickup pencircle scaled 0.800000 pt;
176 p := makepath makepen (0.8294,-0.5586)..(0.8482,-0.5290)
177 ..(0.8655,-0.4987)..(0.8812,-0.4679)..(0.8953,-0.4363)
178 ..(0.9078,-0.4042)..(0.9185,-0.3715)..(0.9274,-0.3385)
179 ..(0.9346,-0.3049)..(0.9398,-0.2710)..(0.9432,-0.2368)
180 ..(0.9447,-0.2024)..(0.9444,-0.1676)..(0.9421,-0.1327)
181 ..(0.9379,-0.0977)..(0.9319,-0.0627)..(0.9240,-0.0275)
182 ..(0.9142,0.0075)..(0.9026,0.0425)..(0.8893,0.0774)
183 ..(0.8742,0.1121)..(0.8574,0.1467);
184 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
185 pickup pencircle scaled 0.400000 pt;
186 pickup pencircle scaled 0.800000 pt;
187 p := makepath makepen (0.8485,0.1637)..(0.8293,0.1978)
188 ..(0.8086,0.2316)..(0.7865,0.2649)..(0.7630,0.2978)
189 ..(0.7382,0.3303)..(0.7123,0.3622)..(0.6852,0.3935)
190 ..(0.6571,0.4244)..(0.6281,0.4545)..(0.5983,0.4841)
191 ..(0.5678,0.5130)..(0.5367,0.5411)..(0.5052,0.5685)
192 ..(0.4732,0.5951)..(0.4411,0.6210)..(0.4088,0.6460)
193 ..(0.3764,0.6702)..(0.3442,0.6935)..(0.3122,0.7159)
194 ..(0.2806,0.7375)..(0.2493,0.7582)..(0.2186,0.7780);
195 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
196 pickup pencircle scaled 0.400000 pt;
197 pickup pencircle scaled 0.800000 pt;
198 p := makepath makepen (0.2035,0.7875)..(0.1738,0.8060)
199 ..(0.1449,0.8234)..(0.1170,0.8400)..(0.0901,0.8557)
200 ..(0.0644,0.8704)..(0.0398,0.8843)..(0.0166,0.8972)
201 ..(-0.0053,0.9092)..(-0.0258,0.9204)..(-0.0447,0.9306)
202 ..(-0.0621,0.9400)..(-0.0777,0.9485)..(-0.0917,0.9562)
203 ..(-0.1040,0.9631)..(-0.1145,0.9692)..(-0.1231,0.9744)
204 ..(-0.1299,0.9789)..(-0.1349,0.9827)..(-0.1379,0.9857)
205 ..(-0.1391,0.9881)..(-0.1384,0.9897)..(-0.1359,0.9907);
206 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
207 pickup pencircle scaled 0.400000 pt;
208 pickup pencircle scaled 0.800000 pt;
209 p := makepath makepen (0.3182,-0.9375)..(0.3467,-0.9272)
210 ..(0.3749,-0.9158)..(0.4030,-0.9032)..(0.4306,-0.8894)
211 ..(0.4578,-0.8745)..(0.4842,-0.8585)..(0.5100,-0.8414)
212 ..(0.5351,-0.8231)..(0.5591,-0.8038)..(0.5821,-0.7835)
213 ..(0.6040,-0.7622)..(0.6246,-0.7399)..(0.6440,-0.7166)
214 ..(0.6619,-0.6925)..(0.6784,-0.6676)..(0.6935,-0.6416)
215 ..(0.7069,-0.6150)..(0.7185,-0.5877)..(0.7286,-0.5596)
216 ..(0.7368,-0.5308)..(0.7433,-0.5015)..(0.7479,-0.4716);
217 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
218 pickup pencircle scaled 0.400000 pt;
219 pickup pencircle scaled 0.800000 pt;
220 p := makepath makepen (0.7495,-0.4564)..(0.7513,-0.4257)
221 ..(0.7513,-0.3945)..(0.7494,-0.3629)..(0.7455,-0.3310)
222 ..(0.7398,-0.2987)..(0.7321,-0.2663)..(0.7227,-0.2335)
223 ..(0.7114,-0.2006)..(0.6983,-0.1676)..(0.6835,-0.1345)
224 ..(0.6669,-0.1014)..(0.6487,-0.0684)..(0.6289,-0.0353)
225 ..(0.6076,-0.0024)..(0.5848,0.0303)..(0.5606,0.0628)
226 ..(0.5351,0.0952)..(0.5084,0.1272)..(0.4806,0.1588)
227 ..(0.4517,0.1902)..(0.4220,0.2211)..(0.3913,0.2517);
228 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
229 pickup pencircle scaled 0.400000 pt;
230 pickup pencircle scaled 0.800000 pt;
231 p := makepath makepen (0.3758,0.2667)..(0.3441,0.2965)
232 ..(0.3119,0.3258)..(0.2793,0.3545)..(0.2463,0.3827)
233 ..(0.2131,0.4103)..(0.1798,0.4372)..(0.1465,0.4635)
234 ..(0.1133,0.4892)..(0.0805,0.5141)..(0.0479,0.5385)
235 ..(0.0158,0.5621)..(-0.0156,0.5849)..(-0.0464,0.6071)
236 ..(-0.0764,0.6285)..(-0.1055,0.6492)..(-0.1336,0.6691)
237 ..(-0.1605,0.6883)..(-0.1864,0.7067)..(-0.2109,0.7244)
238 ..(-0.2340,0.7414)..(-0.2558,0.7576)..(-0.2760,0.7731);
239 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
240 pickup pencircle scaled 0.400000 pt;
241 pickup pencircle scaled 0.800000 pt;
242 p := makepath makepen (-0.2855,0.7806)..(-0.3033,0.7951)
243 ..(-0.3195,0.8088)..(-0.3339,0.8218)..(-0.3465,0.8342)
244 ..(-0.3574,0.8458)..(-0.3665,0.8568)..(-0.3737,0.8672)
245 ..(-0.3790,0.8769)..(-0.3824,0.8860)..(-0.3840,0.8946)
246 ..(-0.3837,0.9025)..(-0.3815,0.9099)..(-0.3774,0.9168)
247 ..(-0.3716,0.9231)..(-0.3639,0.9289)..(-0.3545,0.9343)
248 ..(-0.3434,0.9392);
249 draw p scaled radius withcolor 0.650000 [black,white];
250 pickup pencircle scaled 0.400000 pt;
251 pickup pencircle scaled 0.800000 pt;
252 p := makepath makepen (0.3199,-0.8838)..(0.3410,-0.8694)
253 ..(0.3609,-0.8539)..(0.3795,-0.8374)..(0.3966,-0.8199)
254 ..(0.4124,-0.8014)..(0.4266,-0.7819)..(0.4391,-0.7615)
255 ..(0.4500,-0.7402)..(0.4592,-0.7182)..(0.4666,-0.6953)
256 ..(0.4722,-0.6717)..(0.4761,-0.6473)..(0.4780,-0.6223)
257 ..(0.4781,-0.5966)..(0.4762,-0.5704)..(0.4726,-0.5436)
258 ..(0.4670,-0.5163)..(0.4596,-0.4886)..(0.4502,-0.4605)
259 ..(0.4392,-0.4319)..(0.4263,-0.4031)..(0.4116,-0.3740);
260 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
261 pickup pencircle scaled 0.400000 pt;
262 pickup pencircle scaled 0.800000 pt;
263 p := makepath makepen (0.4035,-0.3595)..(0.3863,-0.3300)
264 ..(0.3674,-0.3005)..(0.3469,-0.2707)..(0.3251,-0.2410)
265 ..(0.3016,-0.2112)..(0.2769,-0.1815)..(0.2509,-0.1516)
266 ..(0.2237,-0.1220)..(0.1954,-0.0925)..(0.1661,-0.0631)
267 ..(0.1359,-0.0339)..(0.1049,-0.0050)..(0.0732,0.0237)
268 ..(0.0409,0.0521)..(0.0083,0.0802)..(-0.0248,0.1079)
269 ..(-0.0582,0.1353)..(-0.0916,0.1622)..(-0.1250,0.1887)
270 ..(-0.1584,0.2149)..(-0.1915,0.2405)..(-0.2243,0.2657);
271 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
272 pickup pencircle scaled 0.400000 pt;
273 pickup pencircle scaled 0.800000 pt;
274 p := makepath makepen (-0.2404,0.2781)..(-0.2726,0.3025)
275 ..(-0.3039,0.3265)..(-0.3347,0.3499)..(-0.3645,0.3728)
276 ..(-0.3935,0.3951)..(-0.4214,0.4168)..(-0.4482,0.4381)
277 ..(-0.4737,0.4589)..(-0.4979,0.4790)..(-0.5208,0.4987)
278 ..(-0.5422,0.5178)..(-0.5621,0.5363)..(-0.5803,0.5544)
279 ..(-0.5970,0.5718)..(-0.6118,0.5888)..(-0.6250,0.6053)
280 ..(-0.6363,0.6213)..(-0.6458,0.6368)..(-0.6534,0.6517)
281 ..(-0.6592,0.6663)..(-0.6631,0.6804)..(-0.6651,0.6940);
282 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
283 pickup pencircle scaled 0.400000 pt;
284 pickup pencircle scaled 0.800000 pt;
285 p := makepath makepen (-0.6654,0.7006)..(-0.6646,0.7137)
286 ..(-0.6618,0.7263)..(-0.6573,0.7384)..(-0.6508,0.7503)
287 ..(-0.6427,0.7617)..(-0.6328,0.7727)..(-0.6211,0.7835);
288 draw p scaled radius withcolor 0.650000 [black,white];
289 pickup pencircle scaled 0.400000 pt;
290 pickup pencircle scaled 0.800000 pt;
291 p := makepath makepen (0.1994,-0.8401)..(0.2052,-0.8235)
292 ..(0.2090,-0.8060)..(0.2110,-0.7878)..(0.2112,-0.7687)
293 ..(0.2095,-0.7491)..(0.2058,-0.7287)..(0.2004,-0.7077)
294 ..(0.1931,-0.6862)..(0.1839,-0.6641)..(0.1729,-0.6415)
295 ..(0.1602,-0.6185)..(0.1456,-0.5950)..(0.1294,-0.5712)
296 ..(0.1116,-0.5470)..(0.0921,-0.5226)..(0.0712,-0.4979)
297 ..(0.0488,-0.4729)..(0.0251,-0.4479)..(-0.0000,-0.4226)
298 ..(-0.0262,-0.3972)..(-0.0536,-0.3718)..(-0.0820,-0.3463);
299 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
300 pickup pencircle scaled 0.400000 pt;
301 pickup pencircle scaled 0.800000 pt;
302 p := makepath makepen (-0.0965,-0.3337)..(-0.1262,-0.3082)
303 ..(-0.1567,-0.2827)..(-0.1879,-0.2573)..(-0.2196,-0.2322)
304 ..(-0.2517,-0.2070)..(-0.2841,-0.1821)..(-0.3168,-0.1572)
305 ..(-0.3495,-0.1326)..(-0.3822,-0.1082)..(-0.4148,-0.0840)
306 ..(-0.4471,-0.0601)..(-0.4790,-0.0364)..(-0.5105,-0.0130)
307 ..(-0.5413,0.0100)..(-0.5714,0.0328)..(-0.6008,0.0553)
308 ..(-0.6292,0.0775)..(-0.6566,0.0993)..(-0.6829,0.1208)
309 ..(-0.7080,0.1420)..(-0.7318,0.1628)..(-0.7542,0.1834);
310 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
311 pickup pencircle scaled 0.400000 pt;
312 pickup pencircle scaled 0.800000 pt;
313 p := makepath makepen (-0.7649,0.1935)..(-0.7850,0.2136)
314 ..(-0.8037,0.2333)..(-0.8207,0.2527)..(-0.8361,0.2718)
315 ..(-0.8497,0.2906)..(-0.8616,0.3090)..(-0.8716,0.3271)
316 ..(-0.8798,0.3451)..(-0.8862,0.3626)..(-0.8906,0.3800)
317 ..(-0.8931,0.3971)..(-0.8938,0.4139)..(-0.8925,0.4305)
318 ..(-0.8894,0.4469)..(-0.8844,0.4630)..(-0.8776,0.4790);
319 draw p scaled radius withcolor 0.650000 [black,white];
320 pickup pencircle scaled 0.400000 pt;
321 pickup pencircle scaled 0.400000 pt;
322 pickup pencircle scaled 0.800000 pt;
323 p := makepath makepen (0.0028,-0.8231)..(-0.0091,-0.8070)
324 ..(-0.0227,-0.7903)..(-0.0380,-0.7732)..(-0.0549,-0.7556)
325 ..(-0.0735,-0.7376)..(-0.0934,-0.7192)..(-0.1149,-0.7005)
326 ..(-0.1376,-0.6815)..(-0.1616,-0.6622)..(-0.1868,-0.6427)
327 ..(-0.2131,-0.6230)..(-0.2404,-0.6030)..(-0.2686,-0.5829)
328 ..(-0.2975,-0.5627)..(-0.3272,-0.5424)..(-0.3574,-0.5219)
329 ..(-0.3881,-0.5014)..(-0.4190,-0.4810)..(-0.4503,-0.4605)
330 ..(-0.4817,-0.4400)..(-0.5130,-0.4194)..(-0.5442,-0.3990);
331 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
332 pickup pencircle scaled 0.400000 pt;
333 pickup pencircle scaled 0.800000 pt;
334 p := makepath makepen (-0.5598,-0.3888)..(-0.5906,-0.3684)
335 ..(-0.6211,-0.3481)..(-0.6510,-0.3279)..(-0.6803,-0.3078)
336 ..(-0.7089,-0.2878)..(-0.7366,-0.2679)..(-0.7634,-0.2480)
337 ..(-0.7892,-0.2283)..(-0.8138,-0.2087)..(-0.8372,-0.1892)
338 ..(-0.8593,-0.1699)..(-0.8799,-0.1507)..(-0.8992,-0.1316)
339 ..(-0.9168,-0.1126)..(-0.9329,-0.0937)..(-0.9472,-0.0749)
340 ..(-0.9599,-0.0561)..(-0.9708,-0.0376)..(-0.9799,-0.0191)
341 ..(-0.9872,-0.0006)..(-0.9925,0.0178)..(-0.9960,0.0363);
342 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
343 pickup pencircle scaled 0.400000 pt;
344 pickup pencircle scaled 0.800000 pt;
345 p := makepath makepen (-0.9971,0.0454)..(-0.9977,0.0637);
346 draw p scaled radius withcolor 0.650000 [black,white];
347 pickup pencircle scaled 0.400000 pt;
348 pickup pencircle scaled 0.400000 pt;
349 pickup pencircle scaled 0.800000 pt;
350 p := makepath makepen (-0.1949,-0.8393)..(-0.2198,-0.8262)
351 ..(-0.2457,-0.8129)..(-0.2725,-0.7993)..(-0.3001,-0.7855)
352 ..(-0.3283,-0.7714)..(-0.3571,-0.7571)..(-0.3862,-0.7427)
353 ..(-0.4157,-0.7281)..(-0.4454,-0.7133)..(-0.4752,-0.6984)
354 ..(-0.5050,-0.6833)..(-0.5347,-0.6681)..(-0.5640,-0.6529)
355 ..(-0.5930,-0.6375)..(-0.6215,-0.6221)..(-0.6495,-0.6066)
356 ..(-0.6767,-0.5910)..(-0.7031,-0.5753)..(-0.7286,-0.5596)
357 ..(-0.7530,-0.5438)..(-0.7764,-0.5279)..(-0.7986,-0.5119);
358 drawarrow reverse p scaled radius withcolor 0.650000 [black,white];
359 pickup pencircle scaled 0.400000 pt;
360 pickup pencircle scaled 0.800000 pt;
361 p := makepath makepen (-0.8092,-0.5039)..(-0.8294,-0.4879)
362 ..(-0.8482,-0.4717)..(-0.8655,-0.4554)..(-0.8812,-0.4392)
363 ..(-0.8953,-0.4227)..(-0.9078,-0.4062)..(-0.9185,-0.3895)
364 ..(-0.9274,-0.3727);
365 draw p scaled radius withcolor 0.650000 [black,white];
366 pickup pencircle scaled 0.400000 pt;
367 pickup pencircle scaled 0.400000 pt;
368 pickup pencircle scaled 0.400000 pt;
369 pickup pencircle scaled 0.800000 pt;
370 p := makepath makepen (-0.3182,-0.8824)..(-0.3467,-0.8739)
371 ..(-0.3749,-0.8651)..(-0.4030,-0.8561)..(-0.4306,-0.8469)
372 ..(-0.4578,-0.8375)..(-0.4842,-0.8279)..(-0.5100,-0.8181)
373 ..(-0.5351,-0.8080)..(-0.5591,-0.7977)..(-0.5821,-0.7873)
374 ..(-0.6040,-0.7766)..(-0.6246,-0.7657)..(-0.6440,-0.7545)
375 ..(-0.6619,-0.7431)..(-0.6784,-0.7315)..(-0.6935,-0.7195)
376 ..(-0.7069,-0.7073);
377 draw p scaled radius withcolor 0.650000 [black,white];
378 pickup pencircle scaled 0.400000 pt;
379 pickup pencircle scaled 0.400000 pt;
380 pickup pencircle scaled 0.400000 pt;
381 pickup pencircle scaled 0.400000 pt;
382 pickup pencircle scaled 0.800000 pt;
383 p := makepath makepen (-0.3199,-0.9361)..(-0.3410,-0.9317)
384 ..(-0.3609,-0.9270)..(-0.3795,-0.9219)..(-0.3966,-0.9165)
385 ..(-0.4124,-0.9107);
386 draw p scaled radius withcolor 0.650000 [black,white];
387 pickup pencircle scaled 0.400000 pt;
388 pickup pencircle scaled 0.400000 pt;
389 pickup pencircle scaled 0.400000 pt;
390 pickup pencircle scaled 0.400000 pt;
391 pickup pencircle scaled 0.400000 pt;
392 pickup pencircle scaled 0.400000 pt;
393 pickup pencircle scaled 0.400000 pt;
394 pickup pencircle scaled 0.800000 pt;
395 p := makepath makepen (0.5770,0.8167)..(0.5490,0.8358)
396 ..(0.5204,0.8538)..(0.4915,0.8707)..(0.4623,0.8865)
397 ..(0.4330,0.9012)..(0.4038,0.9147)..(0.3745,0.9271)
398 ..(0.3455,0.9384);
399 draw p scaled radius withcolor 0.650000 [black,white];
400 pickup pencircle scaled 0.400000 pt;
401 ahangle:=oldahangle;
402 oldahangle:=ahangle;
403 ahangle:=20.000000;
404 pickup pencircle scaled 0.800000 pt;
405 pickup pencircle scaled 0.800000 pt;
406 p := makepath makepen (-0.0028,-0.9968)..(0.0091,-0.9941)
407 ..(0.0227,-0.9906)..(0.0380,-0.9861)..(0.0549,-0.9807)
408 ..(0.0735,-0.9744)..(0.0934,-0.9671)..(0.1149,-0.9588)
409 ..(0.1376,-0.9496)..(0.1616,-0.9393)..(0.1868,-0.9281)
410 ..(0.2131,-0.9158)..(0.2404,-0.9025)..(0.2686,-0.8882)
411 ..(0.2975,-0.8729)..(0.3272,-0.8566)..(0.3574,-0.8393)
412 ..(0.3881,-0.8209)..(0.4190,-0.8016)..(0.4503,-0.7813)
413 ..(0.4817,-0.7600)..(0.5130,-0.7377)..(0.5442,-0.7145);
414 drawarrow reverse p scaled radius withcolor black;
415 pickup pencircle scaled 0.400000 pt;
416 pickup pencircle scaled 0.800000 pt;
417 p := makepath makepen (0.5598,-0.7026)..(0.5906,-0.6780)
418 ..(0.6211,-0.6526)..(0.6510,-0.6262)..(0.6803,-0.5991)
419 ..(0.7089,-0.5712)..(0.7366,-0.5425)..(0.7634,-0.5130)
420 ..(0.7892,-0.4828)..(0.8138,-0.4520)..(0.8372,-0.4205)
421 ..(0.8593,-0.3884)..(0.8799,-0.3558)..(0.8992,-0.3226)
422 ..(0.9168,-0.2891)..(0.9329,-0.2550)..(0.9472,-0.2207)
423 ..(0.9599,-0.1859)..(0.9708,-0.1510)..(0.9799,-0.1158)
424 ..(0.9872,-0.0804)..(0.9925,-0.0449)..(0.9960,-0.0092);
425 drawarrow reverse p scaled radius withcolor black;
426 pickup pencircle scaled 0.400000 pt;
427 pickup pencircle scaled 0.800000 pt;
428 p := makepath makepen (0.9971,0.0085)..(0.9977,0.0441)
429 ..(0.9965,0.0798)..(0.9933,0.1153)..(0.9883,0.1506);
430 draw p scaled radius withcolor black;
431 pickup pencircle scaled 0.400000 pt;
432 pickup pencircle scaled 0.400000 pt;
433 pickup pencircle scaled 0.800000 pt;
434 p := makepath makepen (0.1949,-0.9806)..(0.2198,-0.9749)
435 ..(0.2457,-0.9680)..(0.2725,-0.9600)..(0.3001,-0.9509)
436 ..(0.3283,-0.9406)..(0.3571,-0.9292)..(0.3862,-0.9167)
437 ..(0.4157,-0.9031)..(0.4454,-0.8883)..(0.4752,-0.8724)
438 ..(0.5050,-0.8554)..(0.5347,-0.8373)..(0.5640,-0.8182)
439 ..(0.5930,-0.7980)..(0.6215,-0.7769)..(0.6495,-0.7546)
440 ..(0.6767,-0.7314)..(0.7031,-0.7072)..(0.7286,-0.6821)
441 ..(0.7530,-0.6561)..(0.7764,-0.6293)..(0.7986,-0.6016);
442 drawarrow reverse p scaled radius withcolor black;
443 pickup pencircle scaled 0.400000 pt;
444 pickup pencircle scaled 0.800000 pt;
445 p := makepath makepen (0.8092,-0.5875)..(0.8294,-0.5586);
446 draw p scaled radius withcolor black;
447 pickup pencircle scaled 0.400000 pt;
448 pickup pencircle scaled 0.400000 pt;
449 pickup pencircle scaled 0.400000 pt;
450 pickup pencircle scaled 0.400000 pt;
451 pickup pencircle scaled 0.400000 pt;
452 pickup pencircle scaled 0.400000 pt;
453 pickup pencircle scaled 0.800000 pt;
454 p := makepath makepen (-0.3434,0.9392)..(-0.3306,0.9436)
455 ..(-0.3163,0.9475)..(-0.3004,0.9511)..(-0.2831,0.9543)
456 ..(-0.2643,0.9570);
457 drawarrow reverse p scaled radius withcolor black;
458 pickup pencircle scaled 0.400000 pt;
459 pickup pencircle scaled 0.400000 pt;
460 pickup pencircle scaled 0.400000 pt;
461 pickup pencircle scaled 0.400000 pt;
462 pickup pencircle scaled 0.800000 pt;
463 p := makepath makepen (-0.6211,0.7835)..(-0.6079,0.7939)
464 ..(-0.5930,0.8040)..(-0.5766,0.8138)..(-0.5587,0.8233)
465 ..(-0.5395,0.8325)..(-0.5190,0.8414)..(-0.4973,0.8500)
466 ..(-0.4744,0.8584)..(-0.4506,0.8666)..(-0.4257,0.8745)
467 ..(-0.4001,0.8821)..(-0.3738,0.8895)..(-0.3469,0.8967)
468 ..(-0.3195,0.9036)..(-0.2917,0.9103);
469 drawarrow reverse p scaled radius withcolor black;
470 pickup pencircle scaled 0.400000 pt;
471 pickup pencircle scaled 0.400000 pt;
472 pickup pencircle scaled 0.400000 pt;
473 pickup pencircle scaled 0.800000 pt;
474 p := makepath makepen (-0.8776,0.4790)..(-0.8689,0.4947)
475 ..(-0.8585,0.5102)..(-0.8464,0.5256)..(-0.8326,0.5409)
476 ..(-0.8172,0.5559)..(-0.8002,0.5708);
477 drawarrow reverse p scaled radius withcolor black;
478 pickup pencircle scaled 0.400000 pt;
479 pickup pencircle scaled 0.800000 pt;
480 p := makepath makepen (-0.7911,0.5782)..(-0.7720,0.5928)
481 ..(-0.7514,0.6074)..(-0.7296,0.6218)..(-0.7066,0.6361)
482 ..(-0.6825,0.6503)..(-0.6574,0.6643)..(-0.6314,0.6782)
483 ..(-0.6046,0.6919)..(-0.5770,0.7056)..(-0.5490,0.7191)
484 ..(-0.5204,0.7325)..(-0.4915,0.7458)..(-0.4623,0.7589)
485 ..(-0.4330,0.7718)..(-0.4038,0.7846)..(-0.3745,0.7972)
486 ..(-0.3455,0.8096)..(-0.3169,0.8218)..(-0.2887,0.8338)
487 ..(-0.2610,0.8455)..(-0.2340,0.8571)..(-0.2078,0.8683);
488 drawarrow reverse p scaled radius withcolor black;
489 pickup pencircle scaled 0.400000 pt;
490 pickup pencircle scaled 0.400000 pt;
491 pickup pencircle scaled 0.400000 pt;
492 pickup pencircle scaled 0.800000 pt;
493 p := makepath makepen (-0.9977,0.0637)..(-0.9965,0.0819)
494 ..(-0.9933,0.1002)..(-0.9883,0.1184)..(-0.9814,0.1366)
495 ..(-0.9727,0.1547)..(-0.9622,0.1729)..(-0.9499,0.1912)
496 ..(-0.9359,0.2094)..(-0.9202,0.2278)..(-0.9029,0.2461)
497 ..(-0.8841,0.2644)..(-0.8638,0.2828)..(-0.8422,0.3012)
498 ..(-0.8192,0.3198)..(-0.7950,0.3383)..(-0.7696,0.3570)
499 ..(-0.7433,0.3755)..(-0.7160,0.3942)..(-0.6879,0.4130)
500 ..(-0.6591,0.4317)..(-0.6296,0.4505);
501 drawarrow reverse p scaled radius withcolor black;
502 pickup pencircle scaled 0.400000 pt;
503 pickup pencircle scaled 0.800000 pt;
504 p := makepath makepen (-0.6147,0.4599)..(-0.5845,0.4788)
505 ..(-0.5540,0.4976)..(-0.5233,0.5165)..(-0.4924,0.5353)
506 ..(-0.4615,0.5541)..(-0.4309,0.5728)..(-0.4005,0.5914)
507 ..(-0.3703,0.6100)..(-0.3408,0.6284)..(-0.3117,0.6468)
508 ..(-0.2833,0.6649)..(-0.2556,0.6830)..(-0.2291,0.7007)
509 ..(-0.2034,0.7183)..(-0.1788,0.7356)..(-0.1554,0.7526)
510 ..(-0.1333,0.7693)..(-0.1125,0.7857)..(-0.0932,0.8017)
511 ..(-0.0753,0.8173)..(-0.0591,0.8324)..(-0.0444,0.8471);
512 drawarrow reverse p scaled radius withcolor black;
513 pickup pencircle scaled 0.400000 pt;
514 pickup pencircle scaled 0.400000 pt;
515 pickup pencircle scaled 0.800000 pt;
516 p := makepath makepen (-0.9274,-0.3727)..(-0.9346,-0.3558)
517 ..(-0.9398,-0.3387)..(-0.9432,-0.3215)..(-0.9447,-0.3042)
518 ..(-0.9444,-0.2866)..(-0.9421,-0.2689)..(-0.9379,-0.2510)
519 ..(-0.9319,-0.2329)..(-0.9240,-0.2146)..(-0.9142,-0.1961)
520 ..(-0.9026,-0.1773)..(-0.8893,-0.1584)..(-0.8742,-0.1391)
521 ..(-0.8574,-0.1196);
522 drawarrow reverse p scaled radius withcolor black;
523 pickup pencircle scaled 0.400000 pt;
524 pickup pencircle scaled 0.800000 pt;
525 p := makepath makepen (-0.8485,-0.1098)..(-0.8293,-0.0900)
526 ..(-0.8086,-0.0699)..(-0.7865,-0.0495)..(-0.7630,-0.0289)
527 ..(-0.7382,-0.0080)..(-0.7123,0.0130)..(-0.6852,0.0344)
528 ..(-0.6571,0.0560)..(-0.6281,0.0779)..(-0.5983,0.1000)
529 ..(-0.5678,0.1224)..(-0.5367,0.1449)..(-0.5052,0.1677)
530 ..(-0.4732,0.1906)..(-0.4411,0.2138)..(-0.4088,0.2371)
531 ..(-0.3764,0.2606)..(-0.3442,0.2841)..(-0.3122,0.3078)
532 ..(-0.2806,0.3316)..(-0.2493,0.3553)..(-0.2186,0.3793);
533 drawarrow reverse p scaled radius withcolor black;
534 pickup pencircle scaled 0.400000 pt;
535 pickup pencircle scaled 0.800000 pt;
536 p := makepath makepen (-0.2035,0.3911)..(-0.1738,0.4150)
537 ..(-0.1449,0.4388)..(-0.1170,0.4626)..(-0.0901,0.4863)
538 ..(-0.0644,0.5098)..(-0.0398,0.5332)..(-0.0166,0.5563)
539 ..(0.0053,0.5793)..(0.0258,0.6020)..(0.0447,0.6243)
540 ..(0.0621,0.6463)..(0.0777,0.6680)..(0.0917,0.6892)
541 ..(0.1040,0.7099)..(0.1145,0.7302)..(0.1231,0.7499)
542 ..(0.1299,0.7690)..(0.1349,0.7876)..(0.1379,0.8054)
543 ..(0.1391,0.8227)..(0.1384,0.8391)..(0.1359,0.8548);
544 drawarrow reverse p scaled radius withcolor black;
545 pickup pencircle scaled 0.400000 pt;
546 pickup pencircle scaled 0.800000 pt;
547 p := makepath makepen (-0.7069,-0.7073)..(-0.7185,-0.6949)
548 ..(-0.7286,-0.6822)..(-0.7368,-0.6691)..(-0.7433,-0.6557)
549 ..(-0.7479,-0.6420);
550 drawarrow reverse p scaled radius withcolor black;
551 pickup pencircle scaled 0.400000 pt;
552 pickup pencircle scaled 0.800000 pt;
553 p := makepath makepen (-0.7495,-0.6351)..(-0.7513,-0.6208)
554 ..(-0.7513,-0.6062)..(-0.7494,-0.5912)..(-0.7455,-0.5759)
555 ..(-0.7398,-0.5602)..(-0.7321,-0.5441)..(-0.7227,-0.5275)
556 ..(-0.7114,-0.5105)..(-0.6983,-0.4931)..(-0.6835,-0.4752)
557 ..(-0.6669,-0.4569)..(-0.6487,-0.4382)..(-0.6289,-0.4189)
558 ..(-0.6076,-0.3992)..(-0.5848,-0.3790)..(-0.5606,-0.3584)
559 ..(-0.5351,-0.3373)..(-0.5084,-0.3157)..(-0.4806,-0.2937)
560 ..(-0.4517,-0.2711)..(-0.4220,-0.2481)..(-0.3913,-0.2246);
561 drawarrow reverse p scaled radius withcolor black;
562 pickup pencircle scaled 0.400000 pt;
563 pickup pencircle scaled 0.800000 pt;
564 p := makepath makepen (-0.3758,-0.2128)..(-0.3441,-0.1887)
565 ..(-0.3119,-0.1641)..(-0.2793,-0.1391)..(-0.2463,-0.1138)
566 ..(-0.2131,-0.0881)..(-0.1798,-0.0620)..(-0.1465,-0.0356)
567 ..(-0.1133,-0.0087)..(-0.0805,0.0183)..(-0.0479,0.0457)
568 ..(-0.0158,0.0733)..(0.0156,0.1011)..(0.0464,0.1291)
569 ..(0.0764,0.1572)..(0.1055,0.1856)..(0.1336,0.2140)
570 ..(0.1605,0.2424)..(0.1864,0.2708)..(0.2109,0.2992)
571 ..(0.2340,0.3276)..(0.2558,0.3559)..(0.2760,0.3840);
572 drawarrow reverse p scaled radius withcolor black;
573 pickup pencircle scaled 0.400000 pt;
574 pickup pencircle scaled 0.800000 pt;
575 p := makepath makepen (0.2855,0.3980)..(0.3033,0.4259)
576 ..(0.3195,0.4535)..(0.3339,0.4808)..(0.3465,0.5078)
577 ..(0.3574,0.5345)..(0.3665,0.5606)..(0.3737,0.5864)
578 ..(0.3790,0.6116)..(0.3824,0.6362)..(0.3840,0.6604)
579 ..(0.3837,0.6838)..(0.3815,0.7066)..(0.3774,0.7286)
580 ..(0.3716,0.7499)..(0.3639,0.7704)..(0.3545,0.7901)
581 ..(0.3434,0.8088)..(0.3306,0.8267)..(0.3163,0.8436)
582 ..(0.3004,0.8596)..(0.2831,0.8745)..(0.2643,0.8884);
583 drawarrow reverse p scaled radius withcolor black;
584 pickup pencircle scaled 0.400000 pt;
585 pickup pencircle scaled 0.800000 pt;
586 p := makepath makepen (-0.4124,-0.9107)..(-0.4266,-0.9045)
587 ..(-0.4391,-0.8979)..(-0.4500,-0.8908)..(-0.4592,-0.8834)
588 ..(-0.4666,-0.8755)..(-0.4722,-0.8671)..(-0.4761,-0.8582)
589 ..(-0.4780,-0.8489)..(-0.4781,-0.8390)..(-0.4762,-0.8286)
590 ..(-0.4726,-0.8176)..(-0.4670,-0.8061)..(-0.4596,-0.7940)
591 ..(-0.4502,-0.7813)..(-0.4392,-0.7679)..(-0.4263,-0.7540)
592 ..(-0.4116,-0.7395);
593 drawarrow reverse p scaled radius withcolor black;
594 pickup pencircle scaled 0.400000 pt;
595 pickup pencircle scaled 0.800000 pt;
596 p := makepath makepen (-0.4035,-0.7320)..(-0.3863,-0.7165)
597 ..(-0.3674,-0.7003)..(-0.3469,-0.6834)..(-0.3251,-0.6660)
598 ..(-0.3016,-0.6478)..(-0.2769,-0.6289)..(-0.2509,-0.6093)
599 ..(-0.2237,-0.5892)..(-0.1954,-0.5682)..(-0.1661,-0.5467)
600 ..(-0.1359,-0.5244)..(-0.1049,-0.5016)..(-0.0732,-0.4779)
601 ..(-0.0409,-0.4538)..(-0.0083,-0.4289)..(0.0248,-0.4035)
602 ..(0.0582,-0.3774)..(0.0916,-0.3508)..(0.1250,-0.3236)
603 ..(0.1584,-0.2958)..(0.1915,-0.2675)..(0.2243,-0.2387);
604 drawarrow reverse p scaled radius withcolor black;
605 pickup pencircle scaled 0.400000 pt;
606 pickup pencircle scaled 0.800000 pt;
607 p := makepath makepen (0.2404,-0.2242)..(0.2726,-0.1947)
608 ..(0.3039,-0.1648)..(0.3347,-0.1345)..(0.3645,-0.1038)
609 ..(0.3935,-0.0729)..(0.4214,-0.0417)..(0.4482,-0.0102)
610 ..(0.4737,0.0216)..(0.4979,0.0534)..(0.5208,0.0855)
611 ..(0.5422,0.1176)..(0.5621,0.1497)..(0.5803,0.1818)
612 ..(0.5970,0.2138)..(0.6118,0.2459)..(0.6250,0.2777)
613 ..(0.6363,0.3094)..(0.6458,0.3408)..(0.6534,0.3719)
614 ..(0.6592,0.4028)..(0.6631,0.4332)..(0.6651,0.4632);
615 drawarrow reverse p scaled radius withcolor black;
616 pickup pencircle scaled 0.400000 pt;
617 pickup pencircle scaled 0.800000 pt;
618 p := makepath makepen (0.6654,0.4780)..(0.6646,0.5073)
619 ..(0.6618,0.5361)..(0.6573,0.5642)..(0.6508,0.5917)
620 ..(0.6427,0.6186)..(0.6328,0.6447)..(0.6211,0.6700)
621 ..(0.6079,0.6946)..(0.5930,0.7183)..(0.5766,0.7412)
622 ..(0.5587,0.7631)..(0.5395,0.7840)..(0.5190,0.8040)
623 ..(0.4973,0.8230)..(0.4744,0.8409)..(0.4506,0.8578)
624 ..(0.4257,0.8736)..(0.4001,0.8882)..(0.3738,0.9017)
625 ..(0.3469,0.9140)..(0.3195,0.9252)..(0.2917,0.9352);
626 drawarrow reverse p scaled radius withcolor black;
627 pickup pencircle scaled 0.400000 pt;
628 pickup pencircle scaled 0.800000 pt;
629 p := makepath makepen (-0.1994,-0.9798)..(-0.2052,-0.9776)
630 ..(-0.2090,-0.9749)..(-0.2110,-0.9716)..(-0.2112,-0.9676)
631 ..(-0.2095,-0.9630)..(-0.2058,-0.9577)..(-0.2004,-0.9516)
632 ..(-0.1931,-0.9449)..(-0.1839,-0.9375)..(-0.1729,-0.9293)
633 ..(-0.1602,-0.9203)..(-0.1456,-0.9105)..(-0.1294,-0.8999)
634 ..(-0.1116,-0.8886)..(-0.0921,-0.8764)..(-0.0712,-0.8633)
635 ..(-0.0488,-0.8495)..(-0.0251,-0.8347)..(0.0000,-0.8192)
636 ..(0.0262,-0.8027)..(0.0536,-0.7854)..(0.0820,-0.7672);
637 drawarrow reverse p scaled radius withcolor black;
638 pickup pencircle scaled 0.400000 pt;
639 pickup pencircle scaled 0.800000 pt;
640 p := makepath makepen (0.0965,-0.7578)..(0.1262,-0.7383)
641 ..(0.1567,-0.7180)..(0.1879,-0.6968)..(0.2196,-0.6748)
642 ..(0.2517,-0.6519)..(0.2841,-0.6283)..(0.3168,-0.6038)
643 ..(0.3495,-0.5786)..(0.3822,-0.5525)..(0.4148,-0.5257)
644 ..(0.4471,-0.4983)..(0.4790,-0.4701)..(0.5105,-0.4412)
645 ..(0.5413,-0.4117)..(0.5714,-0.3815)..(0.6008,-0.3509)
646 ..(0.6292,-0.3196)..(0.6566,-0.2878)..(0.6829,-0.2556)
647 ..(0.7080,-0.2229)..(0.7318,-0.1899)..(0.7542,-0.1564);
648 drawarrow reverse p scaled radius withcolor black;
649 pickup pencircle scaled 0.400000 pt;
650 pickup pencircle scaled 0.800000 pt;
651 p := makepath makepen (0.7649,-0.1396)..(0.7850,-0.1058)
652 ..(0.8037,-0.0716)..(0.8207,-0.0373)..(0.8361,-0.0029)
653 ..(0.8497,0.0317)..(0.8616,0.0662)..(0.8716,0.1008)
654 ..(0.8798,0.1354)..(0.8862,0.1698)..(0.8906,0.2042)
655 ..(0.8931,0.2383)..(0.8938,0.2721)..(0.8925,0.3057)
656 ..(0.8894,0.3388)..(0.8844,0.3717)..(0.8776,0.4041)
657 ..(0.8689,0.4360)..(0.8585,0.4673)..(0.8464,0.4981)
658 ..(0.8326,0.5282)..(0.8172,0.5577)..(0.8002,0.5864);
659 drawarrow reverse p scaled radius withcolor black;
660 pickup pencircle scaled 0.400000 pt;
661 pickup pencircle scaled 0.800000 pt;
662 p := makepath makepen (0.7911,0.6005)..(0.7720,0.6281)
663 ..(0.7514,0.6549)..(0.7296,0.6808)..(0.7066,0.7059)
664 ..(0.6825,0.7300)..(0.6574,0.7531)..(0.6314,0.7753)
665 ..(0.6046,0.7965)..(0.5770,0.8167);
666 draw p scaled radius withcolor black;
667 pickup pencircle scaled 0.800000 pt;
668 p := makepath makepen (0.3455,0.9384)..(0.3169,0.9485)
669 ..(0.2887,0.9574)..(0.2610,0.9651)..(0.2340,0.9717)
670 ..(0.2078,0.9772);
671 drawarrow reverse p scaled radius withcolor black;
672 pickup pencircle scaled 0.400000 pt;
673 ahangle:=oldahangle;
674 %
675 % Draw the $S_1$-, $S_2$- and $S_3$-axis of the Poincare sphere.
676 % First of all, calculate the transformations of the intersections
677 % for the unity sphere.
678 %
679 % Used variables:
680 %
681 % behind_distance : Specifies the relative distance of the coordi-
682 % axes to be plotted behind origo (in negative di-
683 % rection of respective axis.
684 %
685 % outside_distance_s1 : The relative distance from origo to the point
686 % of the arrow head of the coordinate axis S1.
687 % If this is set to 1.0, the arrow head will
688 % point directly at the Poincare sphere.
689 %
690 % outside_distance_s2 : Same as above, except that this one controls
691 % the S2 coordinate axis instead.
692 %
693 % outside_distance_s3 : Same as above, except that this one controls
694 % the S3 coordinate axis instead.
695 %
696 % insidecolval : Specifies the shade of gray to use for the parts
697 % of the coordinate axes that are inside the Poin-
698 % care sphere. Values must be between 0 and 1,
699 % where: '0.0' <=> 'white'; '1.0' <=> 'black'
700 %
701 behind_distance_s1 := -0.300000;
702 behind_distance_s2 := -0.300000;
703 behind_distance_s3 := -0.300000;
704 outside_distance_s1 := 1.700000;
705 outside_distance_s2 := 2.400000;
706 outside_distance_s3 := 1.500000;
707 insidecolval := .85; % '0.0' <=> 'white'; '1.0' <=> 'black'
708
709 pickup pencircle scaled 0.600000 pt;
710 %
711 % Start with drawing the x-axis...
712 %
713 x_bis_start := radius*behind_distance_s1*cosd(rot_psi)*cosd(rot_phi);
714 y_bis_start := radius*behind_distance_s1*sind(rot_psi);
715 z_bis_start := -radius*behind_distance_s1*cosd(rot_psi)*sind(rot_phi);
716 x_bis_intersect := radius*cosd(rot_psi)*cosd(rot_phi);
717 y_bis_intersect := radius*sind(rot_psi);
718 z_bis_intersect := -radius*cosd(rot_psi)*sind(rot_phi);
719 p := makepath makepen (y_bis_intersect,z_bis_intersect)--
720 (outside_distance_s1*y_bis_intersect,
721 outside_distance_s1*z_bis_intersect);
722 drawarrow p;
723 label.bot(btex $s_1(t)$ etex,
724 (outside_distance_s1*y_bis_intersect,
725 outside_distance_s1*z_bis_intersect));
726
727 %
728 % ... then draw the y-axis ...
729 %
730 x_bis_start := -radius*behind_distance_s2*sind(rot_psi)*cosd(rot_phi);
731 y_bis_start := radius*behind_distance_s2*cosd(rot_psi);
732 z_bis_start := radius*behind_distance_s2*sind(rot_psi)*sind(rot_phi);
733 x_bis_intersect := -radius*sind(rot_psi)*cosd(rot_phi);
734 y_bis_intersect := radius*cosd(rot_psi);
735 z_bis_intersect := radius*sind(rot_psi)*sind(rot_phi);
736 p := makepath makepen (y_bis_intersect,z_bis_intersect)--
737 (outside_distance_s2*y_bis_intersect,
738 outside_distance_s2*z_bis_intersect);
739 drawarrow p;
740 label.bot(btex $s_2(t)$ etex,
741 (outside_distance_s2*y_bis_intersect,
742 outside_distance_s2*z_bis_intersect));
743
744 %
745 % ... then, finally, draw the z-axis.
746 %
747 x_bis_start := radius*behind_distance_s3*sind(rot_phi);
748 y_bis_start := 0.0;
749 z_bis_start := radius*behind_distance_s3*cosd(rot_phi);
750 x_bis_intersect := radius*sind(rot_phi);
751 y_bis_intersect := 0.0;
752 z_bis_intersect := radius*cosd(rot_phi);
753 p := makepath makepen (y_bis_intersect,z_bis_intersect)--
754 (outside_distance_s3*y_bis_intersect,
755 outside_distance_s3*z_bis_intersect);
756 drawarrow p;
757 label.rt(btex $s_3(t)$ etex,
758 (outside_distance_s3*y_bis_intersect,
759 outside_distance_s3*z_bis_intersect));
760
761 endfig;
762 end
763
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