380 lines
12 KiB
PostScript
380 lines
12 KiB
PostScript
%!
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% If you're concerned that the cpu in your PostScript printer will atrophy
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% from disuse, here is another Escher-like contribution to to keep it busy
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% for a while. It uses PostScript color commands, but will still work on
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% a monochrome printer (but isn't very pretty in black & white).
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%
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% The butterflies are arranged in a hexagonal grid (wallpaper group p6),
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% and the moveto, lineto, curveto commands used to render the tesselation
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% are redefined so as to impose a nonlinear transform that shrinks the
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% infinite plane to an ellipse. This is a sleazy way to mimic Escher's
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% "circle limit" sorts of things.
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%
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% The butterfly permimeter was made by imposing all the symmetry constraints
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% on a path, and then that path was filled in using Adobe Illustrator
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%
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% The routines Xform and next_color are easy to change if you want to hack
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% with them. The code was written to sacrifice efficiency for readability.
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%
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% Bob Wallis
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%
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% UUCP {sun,pyramid,cae780,apple}!weitek!wallis
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%statusdict begin waittimeout 6000 lt % if you have a slow printer, you
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% {0 60 6000 setdefaulttimeouts} % might need to uncomment this
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%if end
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/nlayers 1 def % 1 takes about 10 minutes on a LW+; 2 takes 4x longer
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/warp 1 def % 1 -> ellipsoidal distortion; 0 -> flat Euclidean
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/inch {72 mul} def
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/x4 152 def /y4 205.6 def % 6 fold rotation center of bfly
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/x12 387.20 def /y12 403.84 def % 3 fold center of bfly
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/dx x4 x12 sub def % [dx,dy] = distance between the
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/dy y4 y12 sub def % two fixed points above
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/Dm dx dup mul dy dup mul % magnitude of basis vectors of
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add sqrt 3 sqrt mul % parallelogram lattice
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def % = |dx,dy| * sqrt(3)
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/Da dy dx atan 30 add def
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/D1x Dm Da cos mul def % [D1x, D1y] = basis vector vector #1
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/D1y Dm Da sin mul def % = [Dm,0] exp(j30)
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/Da dy dx atan 30 sub def
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/D2x Dm Da cos mul def % [D2x, D2y] = basis vector vector #2
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/D2y Dm Da sin mul def % = [Dm,0] exp(-j30)
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/m { moveto} def
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/L {lineto} def
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/S {stroke} def
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/c {curveto} def
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/f {closepath fill} def
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/F {closepath fill} def
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/g { setgray} def
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/FillStroke { % fill interior & stroke black border
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closepath gsave fill grestore 0 setgray stroke
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} def
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%
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% Description of 1 butterfly
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%
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/body {
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314.96 280.19 m
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383.4 261.71 445.11 243.23 513.52 224.68 c
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463.68 256.59 490.26 328.83 446.99 360.76 c
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423.71 347.32 397.08 339.7 367.07 337.9 c
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388.93 358.28 414.14 372.84 442.73 381.58 c
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426.68 398.18 394.07 389.7 387.2 403.84 c
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371.52 404.96 362.56 372.48 340.16 366.88 c
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346.88 396.01 346.88 425.12 340.16 454.24 c
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326.72 427.35 320 400.48 320 373.6 c
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270.71 352.1 221.44 411.23 168.88 384.02 c
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189.04 388.03 202.48 380.4 212.57 366.95 c
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216.72 350.85 209.23 341.46 190.1 338.79 c
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177.34 343.57 167.94 354.17 161.9 370.59 c
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176.06 305.52 132.02 274.05 152 205.6 c
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201.29 257.12 250.56 234.72 299.84 279.52 c
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288.64 266.08 284.16 252.64 286.4 239.2 c
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298.27 223.97 310.15 222.18 322.02 233.82 c
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328.62 249.28 328.51 264.74 314.96 280.19 c
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FillStroke
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} def
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/eyes {
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294.8125 238.3246 m
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296.9115 238.3246 298.6132 242.7964 298.6132 248.3125 c
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298.6132 253.8286 296.9115 258.3004 294.8125 258.3004 c
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292.7135 258.3004 291.0118 253.8286 291.0118 248.3125 c
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291.0118 242.7964 292.7135 238.3246 294.8125 238.3246 c
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closepath gsave 1 g fill grestore 0 g S
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319.5 241.1782 m
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321.7455 241.1782 323.5659 245.4917 323.5659 250.8125 c
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323.5659 256.1333 321.7455 260.4468 319.5 260.4468 c
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317.2545 260.4468 315.4341 256.1333 315.4341 250.8125 c
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315.4341 245.4917 317.2545 241.1782 319.5 241.1782 c
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closepath gsave 1 g fill grestore 0 g S
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0 g
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296.875 242.0939 m
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297.4608 242.0939 297.9356 243.479 297.9356 245.1875 c
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297.9356 246.896 297.4608 248.2811 296.875 248.2811 c
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296.2892 248.2811 295.8143 246.896 295.8143 245.1875 c
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295.8143 243.479 296.2892 242.0939 296.875 242.0939 c
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f
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0 g
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318.5 243.7707 m
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319.281 243.7707 319.9142 245.0766 319.9142 246.6875 c
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319.9142 248.2984 319.281 249.6043 318.5 249.6043 c
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317.719 249.6043 317.0858 248.2984 317.0858 246.6875 c
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317.0858 245.0766 317.719 243.7707 318.5 243.7707 c
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f
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} def
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/stripes {
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292 289 m
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252 294 241 295 213 279 c
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185 263 175 252 159 222 c
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S
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285 313 m
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239 326 226 325 206 315 c
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186 305 164 278 161 267 c
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S
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298 353 m
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262 342 251 339 237 355 c
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223 371 213 380 201 383 c
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S
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330 288 m
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384 293 385 292 418 280 c
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451 268 452 264 473 247 c
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S
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342 306 m
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381 311 386 317 410 311 c
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434 305 460 287 474 262 c
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S
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345 321 m
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352 357 359 367 379 377 c
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399 387 409 385 426 382 c
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S
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327.75 367.75 m
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336.5 392.25 333.682 403.348 335.25 415.5 c
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S
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320 364.75 m
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322 361.75 323.5 360.5 326.25 360 c
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329 359.5 332 360.5 334 362.75 c
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S
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316.25 356.5 m
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318.75 353.25 320 353 323.25 352.25 c
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326.5 351.5 329 352 331.5 353.25 c
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S
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312.5 349 m
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316.75 345.5 318.25 344.5 321.25 343.75 c
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324.25 343 327 344 329.75 346 c
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S
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310.75 340.75 m
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314.25 336.5 316.25 335.25 320 335.25 c
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323.75 335.25 327 336.5 329.25 338 c
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S
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308.5 332 m
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311.75 328.5 312.5 327.25 317 327 c
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321.5 326.75 325.75 328.25 327.75 329.75 c
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S
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305 322 m
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309.5 317.75 310.75 317 315 316.5 c
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319.25 316 322.25 318 324.75 320 c
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S
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302.25 311 m
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307 307.5 307.75 306.25 312.75 306 c
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317.75 305.75 320 307.25 323.75 309.5 c
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S
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301.25 298.25 m
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304.5 292.75 305.25 292 308.25 292 c
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311.25 292 313.75 293.75 315.75 295.75 c
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S
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} def
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/nostrils {
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0 g
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304.062 227.775 m
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304.599 227.775 305.034 228.883 305.034 230.25 c
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305.034 231.616 304.599 232.724 304.062 232.724 c
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303.525 232.724 303.09 231.616 303.09 230.25 c
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303.09 228.883 303.525 227.775 304.062 227.775 c
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f
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304.062 230.25 m
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F
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309.562 228.275 m
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310.099 228.275 310.534 229.383 310.534 230.75 c
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310.534 232.116 310.099 233.224 309.562 233.224 c
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309.025 233.224 308.59 232.116 308.59 230.75 c
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308.59 229.383 309.025 228.275 309.562 228.275 c
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f
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} def
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/thorax
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{
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327.5 300 m
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316.5 283 315.5 275.5 308 277.5 c
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294 311.5 299 313.5 304 334 c
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309 354.5 315.5 362 322.5 372 c
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329.5 382 327.5 376.5 331 376 c
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334.5 375.5 339.1367 379.1109 339 369 c
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338.5 332 333.4999 324.5 330.5 311.5 c
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0 g S
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} def
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/spots {
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next_color
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192 242.201 m
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202.1535 242.201 210.3848 251.0655 210.3848 262 c
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210.3848 272.9345 202.1535 281.799 192 281.799 c
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181.8465 281.799 173.6152 272.9345 173.6152 262 c
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173.6152 251.0655 181.8465 242.201 192 242.201 c
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FillStroke
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next_color
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447.5 250.2365 m
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459.6061 250.2365 469.4203 257.5181 469.4203 266.5 c
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469.4203 275.4819 459.6061 282.7635 447.5 282.7635 c
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435.3939 282.7635 425.5797 275.4819 425.5797 266.5 c
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425.5797 257.5181 435.3939 250.2365 447.5 250.2365 c
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FillStroke
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next_color
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401 369.1005 m
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409.5914 369.1005 416.5563 373.5327 416.5563 379 c
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416.5563 384.4673 409.5914 388.8995 401 388.8995 c
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392.4086 388.8995 385.4436 384.4673 385.4436 379 c
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385.4436 373.5327 392.4086 369.1005 401 369.1005 c
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FillStroke
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next_color
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249 348.2721 m
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261.4966 348.2721 271.6274 353.9707 271.6274 361 c
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271.6274 368.0293 261.4966 373.7279 249 373.7279 c
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236.5034 373.7279 226.3726 368.0293 226.3726 361 c
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226.3726 353.9707 236.5034 348.2721 249 348.2721 c
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FillStroke
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} def
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/ncolor 6 def
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/cidx 0 def
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/next_color {
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cidx ncolor div % hue
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.75 % saturation (change these if you like)
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.8 % lightness
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sethsbcolor
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/cidx cidx 1 add ncolor mod def
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} def
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/cidx 0 def
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/max_r2 % radius^2 for center of outermost ring of butterflies
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Dm nlayers mul 1.05 mul dup mul
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def
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/max_radius max_r2 sqrt def
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/max_radius_inv 1 max_radius div def
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/Dm_inv 1 Dm div def
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%
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% Ellipsoidal distortion, maps "nlayers" concentric rings of cells into
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% an ellipse centered on page
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% D length of 1 basis vector separating hexagonal cells
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% z0 center of 6-fold rotation = origin of shrink xform
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% z' = (z - z0)/D new coord system
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% |z'| = sqrt(x^2 + [(8.5/11)*y]^2) aspect ratio of paper
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% z" = z' * a/M(|z'|) shrink by "a/M(|z|)" as fcn of radius
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% At the max radius, we want the shrunk ellipse to be "W" units wide so it
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% just fits our output format - solve for scale factor "a"
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% zmax = n+0.5 for n layers of cells
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% zmax * [a/M(zmax)] = W 1/2 width of output on paper
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% a = M(zmax)*W/zmax solve for "a"
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%/M{dup mul 1 add sqrt}bind def % M(u) = sqrt(1+|u|^2) = one possible shrink
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/M { 1.5 add } bind def % M(u) = (1.5+|u|) = another possible one
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/W 3.8 inch def % 1/2 width of ellipse
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/zmax 0.5 nlayers add def % radius at last layer of hexagons
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/a zmax M W mul zmax div def % a = M(zmax)*W/zmax
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/Xform { % [x0,y0] = ctr ellipse
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Matrix transform
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/y exch def
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/x exch def
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/z x dup mul y .773 mul dup mul add sqrt def % ellipse radius
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/Scale a z M div def % z=a/M(|z|)
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x Scale mul x0 add % magnify back up
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y Scale mul y0 add % [x0+x*s, y0+y*s]
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} bind def
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/Helvetica findfont 8 scalefont setfont
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4.25 inch 0.5 inch moveto
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(RHW) stringwidth pop -0.5 mul 0 rmoveto
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(RHW) show % autograph
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warp 1 eq { % redefine commands to use Xform
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/moveto { Xform //moveto} def
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/lineto { Xform //lineto} def
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/curveto {
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Xform 6 -2 roll
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Xform 6 -2 roll
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Xform 6 -2 roll
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//curveto
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} def
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}if
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/bfly { % paint 1 butterfly
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next_color body
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1 setgray eyes
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stripes
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0 setgray nostrils
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0.5 setgray thorax next_color
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spots
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} def
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/x0 x4 def % center
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/y0 y4 def
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/T1matrix % xlate to center of image
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x0 neg y0 neg matrix translate
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def
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/Smatrix % scale so that 1 basis vector = 1.0
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Dm_inv dup matrix scale
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def
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/HexCell { % 6 butterflys rotated about center of
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/cidx 0 def % 6 fold symmetry
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/color 0 def
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/T2matrix dx dy matrix translate def
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0 60 300 {
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/angle exch def
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/Rmatrix angle matrix rotate def
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/Matrix % translate, rotate, scale - used by Xform
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T1matrix Rmatrix matrix concatmatrix
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T2matrix matrix concatmatrix
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Smatrix matrix concatmatrix
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def
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gsave
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warp 0 eq % then may use usual PostScript machinery
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{ % else using Xform
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x0 y0 translate angle rotate
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.5 dup scale
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dx x0 sub dy y0 sub translate
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} if
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bfly
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next_color
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grestore
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} for
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} def
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%320 x4 sub 240 y4 sub translate
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4.25 inch x4 sub 5.5 inch y4 sub translate
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0 setlinewidth
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/N 2 def
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N neg 1 N {
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/i exch def % translate to
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N neg 1 N { % i*D1 + j*D2
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/j exch def % and draw HexCell
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gsave
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/dx i D1x mul j D2x mul add def % translate HexCell by
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/dy i D1y mul j D2y mul add def % [dx,dy]
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/r2 dx dup mul dy dup mul add def % r^2 = |dx,dy|^2
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r2 max_r2 lt % inside radius?
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{ % yes
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1 r2 max_r2 div sub sqrt 2 div
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setlinewidth % make skinnier lines
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HexCell % 6 butterflies
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}
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if
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grestore
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} for
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} for
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showpage
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