| blob | b6f789bf6720f38691f64e59d88b2c1ff9d5e114 |
1 %\r
2 % Very simple model of my hand\r
3 %\r
4 % Gene Ressler\r
5 %\r
6 % In particular, this completely ignores the carpal joints.\r
7 %\r
8 % Try this with various options to sketch.\r
9 %\r
10 % -D fist \\r
11 % -D ok > none or one of these\r
12 % -D spread /\r
13 %\r
14 % -D topview \\r
15 % -D frontview > none or one of these\r
16 % -D sideview /\r
17 %\r
18 % -D repeated \r
19 %\r
20 % I am not responsible for modifications to draw\r
21 % obscene gestures.\r
22 \r
23 % parameterization of model\r
24 \r
25 % for fingers, 0 is thumb, 1 is index, \r
26 % 2 is middle, 3 is ring, 4 is little\r
27 \r
28 % lateral angle between fingers\r
29 def spread_rot \r
30 <fist> 0\r
31 <ok> 5\r
32 <spread>10\r
33 <> 0\r
34 % and between thumb and index finger\r
35 def spread_rot_0 \r
36 <fist> 40\r
37 <ok> 55\r
38 <spread> 55\r
39 <> 25\r
40 \r
41 % rotations of finger parts\r
42 % distal is the finger tip\r
43 % middle is below that\r
44 % meta is the knuckle\r
45 def distal_0_rot \r
46 <fist> 60\r
47 <ok> 45\r
48 <> -10\r
49 def middle_0_rot \r
50 <fist> 50\r
51 <ok> 40\r
52 <spread> 0\r
53 <> 10\r
54 def meta_0_rot \r
55 <fist> 40\r
56 <ok> 33\r
57 <> 0\r
58 \r
59 def distal_1_rot \r
60 <fist> 90\r
61 <ok> 60\r
62 <> 0\r
63 def meta_1_rot \r
64 <fist> 90\r
65 <ok> 55\r
66 <> 0\r
67 \r
68 def distal_2_rot\r
69 <fist> 90\r
70 <ok> 30\r
71 <> 0\r
72 def meta_2_rot\r
73 <fist> 90\r
74 <ok> 35\r
75 <> 0\r
76 \r
77 def distal_3_rot\r
78 <fist> 90\r
79 <ok> 30\r
80 <> 0\r
81 def meta_3_rot\r
82 <fist> 90\r
83 <ok> 30\r
84 <> 0\r
85 \r
86 def distal_4_rot \r
87 <fist> 90\r
88 <ok> 30\r
89 <> 0\r
90 def meta_4_rot \r
91 <fist> 90\r
92 <ok> 25\r
93 <> 0\r
94 \r
95 % end parameters\r
96 \r
97 % useful stuff\r
98 def O (0,0,0)\r
99 def I [1,0,0]\r
100 def J [0,1,0]\r
101 def K [0,0,1]\r
102 \r
103 % dependent rotations \r
104 % fingers have the last two joints wired together\r
105 def middle_1_rot distal_1_rot\r
106 def middle_2_rot distal_2_rot\r
107 def middle_3_rot distal_3_rot\r
108 def middle_4_rot distal_4_rot\r
109 \r
110 % proportions \r
111 def proximal_rad .6\r
112 def distal_rad .5\r
113 def distal_len 1.8\r
114 def joint_rad .6\r
115 def joint_gap .7\r
116 def middle_ratio 1.8\r
117 def proximal_distal_ratio proximal_rad / distal_rad\r
118 \r
119 % primitive segment of a finger is a truncated cone\r
120 def segment {\r
121 def n_faces 8\r
122 sweep { n_faces<>, rotate(360 / n_faces, [J]) } \r
123 line(proximal_rad, 0)(distal_rad, distal_len)\r
124 }\r
125 \r
126 % spheres to connect segments at joints\r
127 def joint_sphere {\r
128 def n_joint_faces 8\r
129 sweep [fillcolor=red] { n_joint_faces, rotate(360 / n_joint_faces, [J]) }\r
130 sweep { n_joint_faces, rotate(180 / n_joint_faces) } \r
131 (0, -joint_rad)\r
132 }\r
133 \r
134 % following is five separate definitions for five fingers\r
135 % with parameters, this would be much shorter!\r
136 \r
137 def distal_0 {\r
138 put { translate(joint_gap * joint_rad * [J]) \r
139 then rotate(distal_0_rot, [I]) \r
140 then translate((distal_len + joint_gap * joint_rad) * [J]) }\r
141 {segment}\r
142 put { rotate(distal_0_rot / 2, [I])\r
143 then translate((distal_len + joint_gap * joint_rad) * [J]) } \r
144 {joint_sphere}\r
145 put { scale( [J] + proximal_distal_ratio * ([I]+[K]) ) }\r
146 {segment}\r
147 } \r
148 \r
149 def finger_0 {\r
150 put { translate(joint_gap * joint_rad * [J])\r
151 then rotate(middle_0_rot, [I])\r
152 then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }\r
153 {distal_0}\r
154 put { scale(proximal_distal_ratio)\r
155 then rotate(middle_0_rot / 2, [I])\r
156 then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) } \r
157 {joint_sphere}\r
158 put { scale( middle_ratio * [J] + proximal_distal_ratio^2 * ([I]+[K]) ) }\r
159 {segment}\r
160 }\r
161 \r
162 def distal_1 {\r
163 put { translate(joint_gap * joint_rad * [J]) \r
164 then rotate(distal_1_rot, [I]) \r
165 then translate((distal_len + joint_gap * joint_rad) * [J]) }\r
166 {segment}\r
167 put { rotate(distal_1_rot / 2, [I])\r
168 then translate((distal_len + joint_gap * joint_rad) * [J]) } \r
169 {joint_sphere}\r
170 put { scale( [J] + proximal_distal_ratio * ([I]+[K]) ) }\r
171 {segment}\r
172 } \r
173 \r
174 def finger_1 {\r
175 put { translate(joint_gap * joint_rad * [J])\r
176 then rotate(middle_1_rot, [I])\r
177 then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }\r
178 {distal_1}\r
179 put { scale(proximal_distal_ratio)\r
180 then rotate(middle_1_rot / 2, [I])\r
181 then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) } \r
182 {joint_sphere}\r
183 put { scale( middle_ratio * [J] + proximal_distal_ratio^2 * ([I]+[K]) ) }\r
184 {segment}\r
185 }\r
186 \r
187 def distal_2 {\r
188 put { translate(joint_gap * joint_rad * [J]) \r
189 then rotate(distal_2_rot, [I]) \r
190 then translate((distal_len + joint_gap * joint_rad) * [J]) }\r
191 {segment}\r
192 put { rotate(distal_2_rot / 2, [I])\r
193 then translate((distal_len + joint_gap * joint_rad) * [J]) } \r
194 {joint_sphere}\r
195 put { scale( [J] + proximal_distal_ratio * ([I]+[K]) ) }\r
196 {segment}\r
197 } \r
198 \r
199 def finger_2 {\r
200 put { translate(joint_gap * joint_rad * [J])\r
201 then rotate(middle_2_rot, [I])\r
202 then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }\r
203 {distal_2}\r
204 put { scale(proximal_distal_ratio)\r
205 then rotate(middle_2_rot / 2, [I])\r
206 then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) } \r
207 {joint_sphere}\r
208 put { scale( middle_ratio * [J] + proximal_distal_ratio^2 * ([I]+[K]) ) }\r
209 {segment}\r
210 }\r
211 \r
212 def distal_3 {\r
213 put { translate(joint_gap * joint_rad * [J]) \r
214 then rotate(distal_3_rot, [I]) \r
215 then translate((distal_len + joint_gap * joint_rad) * [J]) }\r
216 {segment}\r
217 put { rotate(distal_3_rot / 2, [I])\r
218 then translate((distal_len + joint_gap * joint_rad) * [J]) } \r
219 {joint_sphere}\r
220 put { scale( [J] + proximal_distal_ratio * ([I]+[K]) ) }\r
221 {segment}\r
222 } \r
223 \r
224 def finger_3 {\r
225 put { translate(joint_gap * joint_rad * [J])\r
226 then rotate(middle_3_rot, [I])\r
227 then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }\r
228 {distal_3}\r
229 put { scale(proximal_distal_ratio)\r
230 then rotate(middle_3_rot / 2, [I])\r
231 then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) } \r
232 {joint_sphere}\r
233 put { scale( middle_ratio * [J] + proximal_distal_ratio^2 * ([I]+[K]) ) }\r
234 {segment}\r
235 }\r
236 \r
237 def distal_4 {\r
238 put { translate(joint_gap * joint_rad * [J]) \r
239 then rotate(distal_4_rot, [I]) \r
240 then translate((distal_len + joint_gap * joint_rad) * [J]) }\r
241 {segment}\r
242 put { rotate(distal_4_rot / 2, [I])\r
243 then translate((distal_len + joint_gap * joint_rad) * [J]) } \r
244 {joint_sphere}\r
245 put { scale( [J] + proximal_distal_ratio * ([I]+[K]) ) }\r
246 {segment}\r
247 } \r
248 \r
249 def finger_4 {\r
250 put { translate(joint_gap * joint_rad * [J])\r
251 then rotate(middle_4_rot, [I])\r
252 then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }\r
253 {distal_4}\r
254 put { scale(proximal_distal_ratio)\r
255 then rotate(middle_4_rot / 2, [I])\r
256 then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) } \r
257 {joint_sphere}\r
258 put { scale( middle_ratio * [J] + proximal_distal_ratio^2 * ([I]+[K]) ) }\r
259 {segment}\r
260 }\r
261 \r
262 % points on the palm of the hand\r
263 def proximal_0_loc (1.8,-5.5,0)\r
264 def proximal_1_loc (1.8,.1,0)\r
265 def proximal_2_loc (O)\r
266 def proximal_3_loc (-1.8,-.2,0)\r
267 def proximal_4_loc (-3.6,-.5,0)\r
268 def h5 (proximal_4_loc) + [-.6,-.2]\r
269 def h6 (h5) + [1,-5]\r
270 def h8 (proximal_0_loc) + [.75,-.5]\r
271 def h7 (h8) + [-.6,-.8]\r
272 def h6a (h6) + .6 * ((h7) - (h6))\r
273 def h9 (h8) + [-1.9,1]\r
274 def h10 (proximal_1_loc) + [.85,-.3]\r
275 \r
276 def hand {\r
277 \r
278 % thumb has an extra rotation for opposable-ness!\r
279 def opposition_rot rotate(-50, [J])\r
280 def thk_scale_0 1.2\r
281 put { scale([thk_scale_0,.9,thk_scale_0]) % this distorts a little; oh well\r
282 then translate((joint_gap * joint_rad) * [J])\r
283 then [[opposition_rot]]\r
284 then rotate(meta_0_rot, [I])\r
285 then rotate(-spread_rot_0, [K])\r
286 then translate((proximal_0_loc) - (O)) } \r
287 {finger_0}\r
288 \r
289 put { scale(thk_scale_0 * proximal_distal_ratio^2)\r
290 then [[opposition_rot]]\r
291 then rotate(meta_0_rot / 2, [I])\r
292 then rotate(-spread_rot_0, [K])\r
293 then translate((proximal_0_loc) - (O)) } \r
294 {joint_sphere}\r
295 \r
296 % index finger\r
297 def scale_1 .85\r
298 put { scale(scale_1) \r
299 then translate((joint_gap * joint_rad) * [J])\r
300 then rotate(meta_1_rot, [I])\r
301 then rotate(-spread_rot, [K])\r
302 then translate((proximal_1_loc) - (O)) } \r
303 {finger_1}\r
304 \r
305 put { scale(scale_1 * proximal_distal_ratio^2)\r
306 then rotate(meta_1_rot / 2, [I])\r
307 then rotate(-spread_rot, [K])\r
308 then translate((proximal_1_loc) - (O)) } \r
309 {joint_sphere}\r
310 \r
311 % middle finger\r
312 put { % no scale then\r
313 translate((joint_gap * joint_rad) * [J])\r
314 then rotate(meta_2_rot, [I])\r
315 % no spread rotation\r
316 then translate((proximal_2_loc) - (O)) } \r
317 {finger_2}\r
318 \r
319 put { scale(proximal_distal_ratio^2)\r
320 then rotate(meta_2_rot / 2, [I])\r
321 then translate((proximal_2_loc) - (O)) } \r
322 {joint_sphere}\r
323 \r
324 % ring finger\r
325 def scale_3 .85\r
326 put { scale(scale_3) \r
327 then translate((joint_gap * joint_rad) * [J])\r
328 then rotate(meta_3_rot, [I])\r
329 then rotate(spread_rot, [K])\r
330 then translate((proximal_3_loc) - (O)) } \r
331 {finger_3}\r
332 \r
333 put { scale(scale_3 * proximal_distal_ratio^2)\r
334 then rotate(meta_3_rot / 2, [I])\r
335 then rotate(spread_rot, [K])\r
336 then translate((proximal_3_loc) - (O)) } \r
337 {joint_sphere}\r
338 \r
339 % little finger\r
340 def scale_4 .7\r
341 put { scale(scale_4) \r
342 then translate((joint_gap * joint_rad) * [J])\r
343 then rotate(meta_4_rot, [I])\r
344 then rotate(2 * spread_rot, [K])\r
345 then translate((proximal_4_loc) - (O)) } \r
346 {finger_4}\r
347 \r
348 put { scale(scale_4 * proximal_distal_ratio^2)\r
349 then rotate(meta_4_rot / 2, [I])\r
350 then rotate(2 * spread_rot, [K])\r
351 then translate((proximal_4_loc) - (O)) } \r
352 {joint_sphere}\r
353 \r
354 % palm is built by sweeping a polygon through a small\r
355 % angle in order to make it thicker at the wrist\r
356 put { translate(joint_gap * joint_rad * -[J]) } % drop polytope to expose knuckles\r
357 sweep { 1, rotate(6, (0,15,0), [I]) }\r
358 put { rotate(-3, (0,15,0), [I]) } {\r
359 % need two polygons for convexity; the desired shape is concave at the thumb\r
360 polygon(proximal_1_loc)(proximal_2_loc)(proximal_3_loc)(proximal_4_loc)\r
361 (h5)(h6)(h6a)(h9)(h10)\r
362 polygon(h6a)(h7)(h8)(h9)\r
363 }\r
364 }\r
365 \r
366 % a few views\r
367 def viewxf \r
368 <frontview> view((0,0,10))\r
369 <sideview> view((10,0,0))\r
370 <topview> view((0,10,0), (O), -[K])\r
371 <> view((7,3,10))\r
372 \r
373 % either a single copy or a repeat to show different angles\r
374 def scene \r
375 <repeated>\r
376 put { [[viewxf]] then scale(.25) } {\r
377 def N 4\r
378 repeat { N, rotate(270/N, [3,2,1]), translate(14*[I]) } {hand}\r
379 }\r
380 <> put { [[viewxf]] then scale(.3) } {hand}\r
381 \r
382 {scene}\r