├── .gitignore ├── README.md ├── .github └── workflows │ └── build.yml ├── fiziko.mkiv ├── LICENSE.md ├── fiziko.tex └── fiziko.mp /.gitignore: -------------------------------------------------------------------------------- 1 | .DS_Store 2 | *.log 3 | *.tu? 4 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # fiziko 2 | 3 | ![pulley](https://user-images.githubusercontent.com/7447349/45599924-c3a3f700-b9fc-11e8-9996-f27555c4ded5.png) 4 | 5 | This MetaPost library was initially written to automate some elements of black and white illustrations for a physics textbook. First and foremost it provides functions to draw things like lines of variable width, shaded spheres and tubes of different kinds, which can be used to produce images of a variety of objects. The library also contains functions to draw some objects constructed from these primitives. 6 | 7 | ![knots](https://user-images.githubusercontent.com/7447349/69825221-8e5d8080-121f-11ea-956e-cb58f7483d6b.png) 8 | 9 | Here's a [blog post](https://m.habr.com/en/post/454376/) describing the project in more detail. 10 | -------------------------------------------------------------------------------- /.github/workflows/build.yml: -------------------------------------------------------------------------------- 1 | # This is a basic workflow to help you get started with Actions 2 | 3 | name: CI 4 | 5 | # Controls when the workflow will run 6 | on: 7 | # Triggers the workflow on push or pull request events but only for the "master" branch 8 | push: 9 | branches: [ "master" ] 10 | pull_request: 11 | branches: [ "master" ] 12 | 13 | # Allows you to run this workflow manually from the Actions tab 14 | workflow_dispatch: 15 | 16 | # A workflow run is made up of one or more jobs that can run sequentially or in parallel 17 | jobs: 18 | build: 19 | runs-on: ubuntu-latest 20 | container: texlive/texlive:latest 21 | steps: 22 | - uses: actions/checkout@v3 23 | 24 | # Runs a single command using the runners shell 25 | - name: Build the pdf 26 | run: lualatex -interaction=nonstopmode fiziko.tex 27 | 28 | - uses: actions/upload-artifact@v3 29 | with: 30 | name: pdf 31 | path: fiziko.pdf 32 | -------------------------------------------------------------------------------- /fiziko.mkiv: -------------------------------------------------------------------------------- 1 | \startMPinclusions 2 | input fiziko.mp; 3 | \stopMPinclusions 4 | 5 | \setuptyping[ 6 | option=mp, 7 | numbering=file, 8 | keeptogether=yes, 9 | ] 10 | \setuplinenumbering[ 11 | style={\ss\bfxx}, 12 | color=gray, 13 | ] 14 | \setupinteraction[ 15 | state=start 16 | ] 17 | 18 | \usesymbols[cc] 19 | 20 | \startsetups document:start 21 | \startalignment[middle] 22 | \documentvariable{author}\par 23 | \blank[3*line] 24 | 25 | {\ss\bfa\documentvariable{title}} 26 | 27 | \vfill 28 | 29 | \documentvariable{abstract} 30 | 31 | \vfill 32 | 33 | \goto{\documentvariable{url}}[url(\documentvariable{url})]\par 34 | \blank[line] 35 | 36 | \documentvariable{license} 37 | 38 | \stopalignment 39 | \page 40 | \completecontent[criterium=all] 41 | \page 42 | \stopsetups 43 | 44 | 45 | \startdocument[ 46 | author=Sergey Slyusarev, 47 | title={\type{fiziko}\par v.0.2.1 package for \MetaPost}, 48 | abstract={This document describes a bunch of macros provided by the \quotation{fiziko} library for \MetaPost.}, 49 | license={This document is distributed under the CC-BY-SA 4.0 license\par\symbol[cc][by]~\symbol[cc][sa]}, 50 | url={https://github.com/jemmybutton/fiziko}, 51 | ] 52 | 53 | \section{Introduction} 54 | This MetaPost library was initially written to automate some elements of black and white illustrations for a physics textbook. First and foremost it provides functions to draw things like lines of variable width, shaded spheres and tubes of different kinds, which can be used to produce images of a variety of objects. The library also contains functions to draw some objects constructed from these primitives. 55 | 56 | \section{Usage} 57 | Simply include this in the beginning of your \MetaPost\ document: 58 | 59 | \startMP[numbering=no] 60 | input fiziko.mp 61 | \stopMP 62 | 63 | \section{Global variables} 64 | A few global variables control different aspects of the behavior of the provided macros. Not all possible values are meaningful and some will definitely result in ugly pictures or errors. 65 | 66 | \subsection{minStrokeWidth} 67 | This variable controls minimal thickness of lines that are used for shading. Below this value lines are not getting thinner, but become dashed instead, maintaining roughly the same amount of ink per unit length as a thinner line would take. Default value is one fifth of a point. There are several things that depend on this value, so it’s convenient to change it using a macro: 68 | 69 | \startMP[numbering=no] 70 | defineMinStrokeWidth(1/2pt); 71 | \stopMP 72 | 73 | \subsection{lightDirection} 74 | This variable controls direction from which light falls on shaded objects. It’s of \type{pair} type and is set in radians. Default direction is top-left: 75 | 76 | \startMP[numbering=no] 77 | lightDirection := (-1/8pi, 1/8pi); 78 | \stopMP 79 | 80 | \subsection{lightDirection} 81 | This variable determines whether the light is inverted. This comes in handy when you need to have your shaded objects white on black. It's of \type{boolean} type. Default value is false: 82 | 83 | \def\BufferName{lightDirection} 84 | \startbuffer[\BufferName] 85 | draw sphere.c(1cm); 86 | invertedLight := true; 87 | fill ((unitsquare shifted (-1/2,-1/2)) scaled 3/2cm) shifted (3/2cm, 0) withcolor black; 88 | draw sphere.c(1cm) shifted (3/2cm, 0) withcolor white; 89 | invertedLight := false; 90 | \stopbuffer 91 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 92 | 93 | 94 | \section{\quotation{Lower level} macros} 95 | Currently, algorithms are quite stupid and will produce decent results only in certain simple circumstances. 96 | 97 | \subsection{offsetPath (\emph{path})(\emph{offset function})} 98 | This macro returns offset path (of type \type{path}) to a current path with a distance from the original path controlled by some arbitrary function; typically, it is a function of path length, set as either \type{offsetPathTime} or \type{offsetPathLength}. Former is simply \type{time} on current path and changes from 0 to \type{length(path)}, and latter changes from 0 to 1 over the path \type{arctime} (as a function of \type{arclength}). 99 | 100 | \def\BufferName{offsetPath} 101 | \startbuffer[\BufferName] 102 | path p, q; 103 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 104 | q := offsetPath(p)(1cm*sin(offsetPathLength*pi)); 105 | draw p; 106 | draw q dashed evenly; 107 | \stopbuffer 108 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 109 | 110 | \subsection{brush (\emph{path})(\emph{offset function})} 111 | This macro returns a \type{picture} of a line of variable width along given path, which is controlled by some arbitrary function, analogous to \type{offsetPath}. If line is getting thinner than \type{minStrokeWith}, it is drawn dashed. 112 | 113 | \def\BufferName{brush} 114 | \startbuffer[\BufferName] 115 | path p; 116 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 117 | draw brush (p)(2minStrokeWidth*sin(offsetPathLength*pi)); 118 | \stopbuffer 119 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 120 | 121 | \subsection{sphere.c (\emph{diameter})} 122 | This macro returns a \type{picture} of a sphere with specified diameter shaded with concentric strokes. Strokes are arranged to fit those of \type{tube.l}. 123 | 124 | \def\BufferName{sphere.c} 125 | \startbuffer[\BufferName] 126 | for i := 1 step 1 until 6: 127 | draw sphere.c(i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 128 | endfor; 129 | \stopbuffer 130 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 131 | 132 | \subsection{sphere.s (\emph{diameter})} 133 | This macro returns a \type{picture} of a sphere with specified diameter shaded with stipples. 134 | 135 | \def\BufferName{sphere.s} 136 | \startbuffer[\BufferName] 137 | for i := 1 step 1 until 6: 138 | draw sphere.s(i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 139 | endfor; 140 | \stopbuffer 141 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 142 | 143 | \subsection{sphereLat (\emph{diameter, angle})} 144 | This macro returns a \type{picture} of a shaded sphere with specified diameter. Unlike \type{sphere.c} macro, this one draws latitudinal strokes around axis rotated at specified \type{angle}. 145 | 146 | \def\BufferName{sphereLat} 147 | \startbuffer[\BufferName] 148 | for i := 1 step 1 until 6: 149 | draw sphereLat(i*1/4cm, -90 + i*30) 150 | shifted (1/2cm*(i*(i+1))/2, 0); 151 | endfor; 152 | \stopbuffer 153 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 154 | 155 | \subsection{tube.l (\emph{path})(\emph{offset function})} 156 | This macro returns a \type{picture} of a shaded \quotation{tube} of a variable width along a given path, which is controlled by some arbitrary function, analogous to \type{offsetPath}. \quotation{Tube} drawn by this macro is shaded be longitudal strokes. Once tube is generated, you can call \type{tubeOutline} path global variable, if you need one. 157 | 158 | \def\BufferName{tube.l} 159 | \startbuffer[\BufferName] 160 | path p; 161 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 162 | draw tube.l (p)(1/2cm*sin(offsetPathLength*pi)); 163 | \stopbuffer 164 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 165 | 166 | \subsection{tube.t (\emph{path})(\emph{offset function})} 167 | This macro returns a \type{picture} of a shaded \quotation{tube} of variable width along given path, which is controlled by some arbitrary function, analogous to \type{offsetPath}. \quotation{Tube} drawn by this macro is shaded be transverse strokes. Once tube is generated, you can call \type{tubeOutline} path global variable, if you need one. 168 | 169 | \def\BufferName{tube.t} 170 | \startbuffer[\BufferName] 171 | path p; 172 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 173 | draw tube.t (p)(1/2cm*sin(offsetPathLength*pi)); 174 | \stopbuffer 175 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 176 | 177 | \subsection{tube.s (\emph{path})(\emph{offset function})} 178 | This macro returns a \type{picture} of a shaded \quotation{tube} of variable width along given path, which is controlled by some arbitrary function, analogous to \type{offsetPath}. \quotation{Tube} drawn by this macro is shaded with stipples. Once tube is generated, you can call \type{tubeOutline} path global variable, if you need one. 179 | 180 | \def\BufferName{tube.s} 181 | \startbuffer[\BufferName] 182 | path p; 183 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 184 | draw tube.s (p)(1/2cm*sin(offsetPathLength*pi)); 185 | \stopbuffer 186 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 187 | 188 | \subsection{tube.e (\emph{path})(\emph{offset function})} 189 | This macro returns the outline of a tube as a path. 190 | 191 | \section{\quotation{Higher level} macros} 192 | Using macros described in the previous section it is possible to construct more complex images. Macros for drawing some often used images are present in this package. 193 | 194 | \subsection{eye (\emph{angle})} 195 | This macro returns a \type{picture} of an eye pointed at the direction \type{angle} (in degrees). Eye size is controlled by a global variable \type{eyescale}, which has default value of \type{eyescale := 1/2cm;}. 196 | 197 | \def\BufferName{eye} 198 | \startbuffer[\BufferName] 199 | save eyescale; 200 | for i := 1 step 1 until 6: 201 | eyescale := 1/6cm*i; 202 | draw eye(i*60) shifted (1/2cm*(i*(i+1))/2, 0); 203 | endfor; 204 | \stopbuffer 205 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 206 | 207 | \subsection{pulley (\emph{diameter, angle})} 208 | This macro returns a \type{picture} of a pulley with specified \type{diameter} and its support pointed at the direction \type{angle} (in degrees). Note that pulley’s support protrudes from its center by \type{pulleySupportSize*diameter} and by default \type{pulleySupportSize} = 3/2. Once pulley is generated, you can call \type{pulleyOutline} path global variable, if you need one. 209 | 210 | \def\BufferName{pulley} 211 | \startbuffer[\BufferName] 212 | draw (-1/8cm, 0)--(12cm, 0); 213 | for i := 1 step 1 until 6: 214 | r := 1/7cm*i; 215 | draw image( 216 | draw pulley(2r, 0) shifted (0, -4/3r); 217 | draw (r, -4/3r) -- (r, -2cm); 218 | drawarrow (-r, -4/3r) -- (-r, -2cm); 219 | ) shifted (1/2cm*(i*(i+1))/2, 0); 220 | endfor; 221 | \stopbuffer 222 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 223 | 224 | \subsection{pulleyWheel (\emph{diameter})} 225 | This macro returns a \type{picture} of a pulley wheel with specified \type{diameter}. 226 | 227 | \def\BufferName{pulleyWheel} 228 | \startbuffer[\BufferName] 229 | for i := 1 step 1 until 6: 230 | r := 1/7cm*i; 231 | draw image( 232 | draw pulleyWheel(2r); 233 | draw (r, 0) -- (r, 1cm); 234 | drawarrow (-r, 0) -- (-r, 1cm); 235 | ) shifted (1/2cm*(i*(i+1))/2, 0); 236 | endfor; 237 | \stopbuffer 238 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 239 | 240 | \subsection{wheel (\emph{diameter, angle})} 241 | This macro returns a \type{picture} of a wheel with specified \type{diameter} and its support pointed at the direction \type{angle} (in degrees). 242 | 243 | \def\BufferName{wheel} 244 | \startbuffer[\BufferName] 245 | draw (-1/8cm, 0)--(12cm, 0); 246 | for i := 1 step 1 until 6: 247 | r := 1/7cm*i; 248 | draw wheel(2r, 0) shifted (0, -r) shifted (1/2cm*(i*(i+1))/2, 0); 249 | endfor; 250 | \stopbuffer 251 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 252 | 253 | \subsection{weight.s (\emph{height})} 254 | This macro returns a \type{picture} of a weight of a specific \type{height} that is standing on the point \type{(0, 0)}. 255 | 256 | \def\BufferName{weight.s} 257 | \startbuffer[\BufferName] 258 | for i := 1 step 1 until 6: 259 | draw weight.s(1/4cm + i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 260 | endfor; 261 | draw (-1/8cm, 0)--(12cm, 0); 262 | \stopbuffer 263 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 264 | 265 | \subsection{weight.h (\emph{height})} 266 | This macro returns a \type{picture} of a weight of a specific \type{height} that is is hanging from the point \type{(0, 0)}. 267 | 268 | \def\BufferName{weight.h} 269 | \startbuffer[\BufferName] 270 | for i := 1 step 1 until 6: 271 | draw weight.h(1/4cm + i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 272 | endfor; 273 | draw (12cm, 0)--(-1/8cm, 0); 274 | \stopbuffer 275 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 276 | 277 | \subsection{spring (\emph{point a, point b, number of steps})} 278 | This macro returns a \type{picture} of a spring stretched between points \type{a} and \type{b} (of type \type{pair}), with specified \type{number of steps}. Spring width is controlled by global variable \type{springwidth} with the default value \type{springwidth := 1/8cm;}. 279 | 280 | \def\BufferName{spring} 281 | \startbuffer[\BufferName] 282 | pair a, b; 283 | a := (0, 0); 284 | for i := 1 step 1 until 6: 285 | springwidth := 1/16cm + i*1/48cm; 286 | b := (i*1/3cm, - i*1/5cm); 287 | draw spring (a, b, 10) shifted (2/5cm*(i*(i+1))/2, 0); 288 | endfor; 289 | \stopbuffer 290 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 291 | 292 | \subsection{solidSurface (\emph{path})} 293 | This macro returns a \type{picture} of a solid surface on the right side of a given \type{path}. 294 | 295 | \def\BufferName{solidSurface} 296 | \startbuffer[\BufferName] 297 | path p; 298 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 299 | draw solidSurface(p); 300 | \stopbuffer 301 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 302 | 303 | \subsection{solid (\emph{path, angle, type})} 304 | Fills given \type{path} with strokes of specific type at a given \type{angle}. \type{type} can be 0 (\quotation{solid} strokes) and 1 (\quotation{glass} strokes). 305 | 306 | \def\BufferName{solid} 307 | \startbuffer[\BufferName] 308 | path p[]; 309 | p1 := unitsquare scaled 2cm; 310 | p2 := p1 shifted (4cm, 0); 311 | draw solid(p1, 45, 0); 312 | draw solid(p2, -45, 1); 313 | \stopbuffer 314 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 315 | 316 | \subsection{woodBlock (\emph{width, height})} 317 | Returns a \type{picture} of a rectangular block of wood with its bottom-left corner in the origin. 318 | 319 | \def\BufferName{woodBlock} 320 | \startbuffer[\BufferName] 321 | draw woodBlock(10cm, 1/2cm); 322 | \stopbuffer 323 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 324 | 325 | \subsection{woodenThing (\emph{path, angle})} 326 | Returns a \type{picture} of a wood texture at a given \type{angle} fitted into a given \type{path}. 327 | 328 | \def\BufferName{woodenThing} 329 | \startbuffer[\BufferName] 330 | path p, q; 331 | p := dir(-60) scaled 1/2 -- dir(90) scaled 2/3 -- dir (-120) scaled 3/5 -- cycle; 332 | for i := 1 step 1 until 6: 333 | q := (p scaled 3/2cm) rotated (i*60); 334 | draw woodenThing (q, i*60) shifted (2cm*i, 0); 335 | endfor; 336 | \stopbuffer 337 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 338 | 339 | \subsection{woodenSurface (\emph{path, angle})} 340 | Returns a \type{picture} similar to that of a solid surface on the right side of a given \type{path}, but with wood texture . 341 | 342 | \def\BufferName{woodenSurface} 343 | \startbuffer[\BufferName] 344 | path p; 345 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 346 | draw woodenSurface(p); 347 | \stopbuffer 348 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 349 | 350 | \subsection{globe (\emph{radius, longitude, latitude})} 351 | This macro returns a \type{picture} of the globe of specified \type{radius} centered at specific \type{longitude} and \type{latitude}; 352 | 353 | \def\BufferName{globe} 354 | \startbuffer[\BufferName] 355 | for i := 1 step 1 until 6: 356 | draw globe(i*1/4cm, i*60, -90 + i*30) 357 | shifted (1/2cm*(i*(i+1))/2, 0); 358 | endfor; 359 | \stopbuffer 360 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 361 | 362 | \subsection{Knots} 363 | There are two macros to handle knot drawing: \type{addStrandToKnot} and \type{knotFromStrands}. Currently the algorithm is not especially stable. 364 | 365 | \subsubsection{addStrandToKnot (\emph{knotName}) (\emph{path, ropeWidth, ropeType, intersectionOrder})} 366 | This macro adds a strand to knot named \type{knotName} and returns nothing. Strand follows the given \type{path} and has a given \type{ropeWidth}. \type{ropeType} can be \type{"l"}, \type{"t"} (as in \type{tube.l} and \type{tube.t}) or \type{"e"} (for an unshaded strand). \type{intersectionOrder} is a string of comma separated numbers which represent a \quotation{layer} to which intersections along the strand go. 367 | 368 | \subsubsection{knotFromStrands (\emph{knotName})} 369 | This macro returns a picture of a knot with a given \type{knotName}. 370 | 371 | \def\BufferName{knotFromStrands} 372 | \startbuffer[\BufferName] 373 | path p[]; 374 | p1 := (dir(90)*4/3cm) {dir(0)} .. tension 3/2 375 | .. (dir(90 + 120)*4/3cm){dir(90 + 30)} .. tension 3/2 376 | .. (dir(90 - 120)*4/3cm){dir(-90 - 30)} .. tension 3/2 377 | .. cycle; 378 | p2 := (fullcircle scaled 3cm) shifted (0, -3/2cm); 379 | p3 := (fullcircle scaled 4cm); 380 | addStrandToKnot (theknot) (p1 shifted (4cm, -4cm), 1/5cm, "l", 381 | "-1,1,-1,1,-1,1,-1,1,-1"); 382 | addStrandToKnot (theknot) (p2 shifted (4cm, -4cm), 1/6cm, "s", 383 | ""); 384 | addStrandToKnot (theknot) (p3 shifted (4cm, -4cm), 1/7cm, "e", 385 | "-1,1"); 386 | draw knotFromStrands (theknot); 387 | \stopbuffer 388 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 389 | 390 | \subsection{Other 3D contraptions} 391 | Some macros can be used to shade 3D polygons. Currently only flat surfaces are supported 392 | 393 | \subsubsection{flatSurface\emph{\#@}(\emph{surface outline path, normal vector, hatch angle})} 394 | This macro returns a \type{picture} of a flat surface with the specified \type{surface outline path} with the given \type{normal vector}, illuminated from the direction determined by \type{lightDirection} and with hatches aligned at the andle \type{hatch angle}. If \type{\#@} is \type{".hatches"} then the surface is shaded with hatches, if it’s \type{".stipples"}, then the surface is shaded with stipples. 395 | 396 | \def\BufferName{flatSurface} 397 | \startbuffer[\BufferName] 398 | path p[]; 399 | p1 := unitsquare xscaled 1cm yscaled 2cm; 400 | p2 := p1 shifted (1cm, 0); 401 | draw flatSurface.hatches(p1, (-1,0,1), 45); 402 | draw flatSurface.hatches(p2, (1,0,1), 45); 403 | draw p1; draw p2; 404 | \stopbuffer 405 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 406 | 407 | \section{Other macros} 408 | Some macros that are not directly related to drawing are listed below 409 | 410 | \subsection{refractionPath (\emph{initial ray, shape, refraction coefficient})} 411 | This macro returns a \type{path} that represent refraction of some \type{ray} (any variable of type \type{path}, point next to last in a given path is considered a source of a \quotation{ray}, and last point determines its direction) through some \type{shape} with given \type{refraction coefficient}. When appropriate, the \quotation{ray} is fully internally reflected. 412 | 413 | Setting \type{refraction coefficient} to 0 results in reflection instead of refraction in all cases. 414 | 415 | \def\BufferName{refractionPath} 416 | \startbuffer[\BufferName] 417 | path r, p; 418 | p := fullcircle scaled 2.1cm; 419 | draw p; 420 | for i:= 1cm step -1/4cm until -1cm: 421 | r := (-4cm, i) -- (-1cm, i); 422 | draw refractionPath(r, p, 1.5); 423 | endfor; 424 | \stopbuffer 425 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 426 | 427 | 428 | \subsection{lens (\emph{(left radius, right radius), thickness, diameter, units})} 429 | This macro returns a \type{path} that represent a section of a lens with given radii of curvature (positive value for convex, negative --- for concave), thickness (i. e. distance benween sides' centers) and diameter (i. e. height) in given arbitrary units. 430 | 431 | \def\BufferName{lens} 432 | \startbuffer[\BufferName] 433 | draw lens((5, 10), 1/2, 2, cm); 434 | draw lens((-10, -5), 1/4, 2, cm) shifted (2cm, 0); 435 | draw lens((infinity, 7), 1/4, 2, cm) shifted (4cm, 0); 436 | \stopbuffer 437 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 438 | 439 | \section{Auxilary macros} 440 | Some macros that not related to physical problems at all are listed below. 441 | 442 | \subsection{\emph{picture} maskedWith \emph{path}} 443 | This macro masks a part of a \type{picture} with closed \type{path}. In fact this is inversion of metapost’s built-in \type{clip} but, in contrast to the latter, it does not modify original image. Note that it requires that counter-clockwise \type{path} to work properly. 444 | 445 | \subsection{\emph{path} firstIntersectionTimes \emph{path}} 446 | This macro is similar to metapost’s \type{intersectiontimes} but it returns intersection times with smallest time on first path. 447 | 448 | \subsection{pathSubdivide \emph{path, n}} 449 | This macro returns original \type{path} with \type{n}-times more points. 450 | 451 | \subsection{drawmidarrow (\emph{path})} 452 | Draws \type{path} with arrows in the middles of segments with length no less than \type{midArrowLimit} (another global variable, 1cm by default). 453 | 454 | \subsection{markAngle (\emph{point a, point o, point b})(\emph{text})} 455 | This macro marks an angle \type{aob} (counter-clockwise) with some \type{text} 456 | 457 | \def\BufferName{markAngle} 458 | \startbuffer[\BufferName] 459 | pair a, o, b; 460 | for i:= 30 step 60 until 390: 461 | o := (10cm*(i/360), 0); 462 | a := dir(i/2)*4/3cm shifted o; 463 | b := dir(i)*4/3cm shifted o; 464 | draw (a--o--b); 465 | markAngle(a, o, b)(btex $\alpha$ etex); 466 | endfor; 467 | \stopbuffer 468 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 469 | 470 | 471 | \section{Some examples} 472 | 473 | \subsection{Gregory-Maksutov type telescope} 474 | Lines 3--11 define parameters of lenses and mirrors\footnote{Taken from here http://www.google.ru/patents/US2701983}. Lines 12--16 generate lenses. On line 20 shape of prism is defined. Line 22 cuts part of the rear mirror. Line 26 describes mirror part of the front lens. On lines 31--33 all the glass parts are drawn. On lines 34--36 all the mirror ones. On lines 39--44 rays are traced through all system in order specified in loop on line 41. Lines 49--56 are about the telescope frame. 475 | 476 | \def\BufferName{GMtt} 477 | \startbuffer[\BufferName] 478 | path p[], q[], axis[], f[]; pair o; 479 | u := 6mm; 480 | r1 := -36.979; r2 := -r1; t1 := 0.7; n1 := 1.517; d1 := 5; 481 | l1 := 8.182; 482 | r3 := -11.657; r4 := r3; t2 := 0.2; n2 := n1; d2 := 3/2; 483 | l2 := 0.4; 484 | r5 := -30.433; r6 := 9.598; t3 := 0.39; n3 := 1.621; d3 := d2; 485 | l3 := 0.828; 486 | r7 := -35.512; r8 := infinity; t4 := 0.7; n4 := 0; d4 := d1; 487 | l4 := 5.272; 488 | ll0 := 0; 489 | for i := 1 upto 4: 490 | ll[i] := ll[i-1] + t[i] + l[i]; 491 | p[i] := lens ((r[i*2 - 1], r[i*2]), t[i], d[i], u) 492 | shifted (ll[i-1]*u, 0); 493 | endfor; 494 | axis1 := (0, 0) -- (ll4*u, 0); 495 | axis2 := reverse(axis1); 496 | ll5 := ll4 - 1/2l4; 497 | p5 := ((-1,-1) -- (1,1) -- (-1,1) -- cycle) 498 | scaled (1/2d2*u) shifted (ll5*u, 0); 499 | p6 := (subpath 500 | (ypart((axis1 shifted (0, 1/2d2*u)) firstIntersectionTimes p4), 501 | ypart((axis2 shifted (0, 1/2d2*u)) firstIntersectionTimes p4)) 502 | of p4) -- cycle; 503 | p7 := (subpath 504 | (ypart((axis2 shifted (0, 3/4d2*u)) firstIntersectionTimes p1), 505 | ypart((axis2 shifted (0, -3/4d2*u)) firstIntersectionTimes p1)) 506 | of p1); 507 | p7 := p7 -- (reverse(p7) shifted ((-1/3t1)*u, 0)) -- cycle; 508 | for i := 1, 2, 3, 5: 509 | draw p[i] withpen thickpen; draw solid (p[i], 45, 1); 510 | endfor; 511 | draw solid (p7, -45, 0); 512 | draw p6 withpen thickpen; draw solid (p6, -45, 0); 513 | draw p6 yscaled -1 withpen thickpen; 514 | draw solid (p6 yscaled -1, -45, 0); 515 | n7 := 0; n5 := n1; 516 | for i := 0, 1: 517 | q[i] := (-3/2u, -2u + i*4u) -- (16u, -2u + i*4u); 518 | for j = 1, 4, 7, 2, 3, 5: 519 | q[i] := refractionPath(q[i], p[j], n[j]); 520 | endfor; 521 | endfor; 522 | o := whatever[point length(q0) of q0, point length(q0)-1 of q0] 523 | = whatever[point length(q1) of q1, point length(q1)-1 of q1]; 524 | for i := 0, 1: drawmidarrow (q[i] -- o) withpen thinpen; endfor; 525 | draw eye(-91) shifted o shifted (0, u); 526 | f1 := (-1/4u, 1/2d1*u) -- ((ll3 + t4)*u, 1/2d1*u) 527 | -- ((ll3 + t4)*u, 1/2d2*u); 528 | f2 := (ll1*u - 1/8u, 1/2d2*u) -- (ll5*u - 1/2d2*u, 1/2d2*u) 529 | -- (ll5*u - 1/2d2*u, ypart(o)); 530 | f3 := (ll1*u - 1/8u, -1/2d2*u) -- (ll5*u + 1/2d2*u, -1/2d2*u) 531 | -- (ll5*u + 1/2d2*u, ypart(o)); 532 | draw f1 withpen fatpen; draw f1 yscaled -1 withpen fatpen; 533 | draw f2 withpen fatpen; draw f3 withpen fatpen; 534 | \stopbuffer 535 | \typebuffer[\BufferName][keeptogether=no] \processMPbuffer[\BufferName] 536 | 537 | 538 | \subsection{L’Hôpital’s Pulley Problem} 539 | Line 3 describe initial setup. Line 4 is problem’s solution. Lines 8–11 set all the points where they belong. Lines 12–16 are needed to decide where to put the pulley. 540 | 541 | \def\BufferName{PulleyProblem} 542 | \startbuffer[\BufferName] 543 | pair p[], o[]; 544 | numeric a, d[], l[], x[], y[]; 545 | l0 := 6; l1 := 4; l2 := 4; 546 | x1 := (l1**2 + abs(l1)*((sqrt(8)*l0)++l1))/4l0; 547 | y1 := l1+-+x1; 548 | y2 := l2 - ((l0-x1)++y1); 549 | d1 := 2/3cm; d2 := 4/3cm; d3 := 5/6d1; 550 | p1 := (0, 0); 551 | p2 := (l0*cm, 0); 552 | p3 := (x1*cm, -y1*cm); 553 | p4 := p3 shifted (0, -y2*cm); 554 | o1 := (unitvector(p4-p3) rotated 90 scaled 1/2d3); 555 | o2 := (unitvector(p3-p2) rotated 90 scaled 1/2d3); 556 | p5 := whatever [p3 shifted o1, p4 shifted o1] 557 | = whatever [p3 shifted o2, p2 shifted o2]; 558 | a := angle(p1-p3); 559 | draw solidSurface(11/10[p1,p2] -- 11/10[p2, p1]); 560 | draw pulley (d1, a - 90) shifted p5; 561 | draw image( 562 | draw p1 -- p3 -- p2 withpen thickpen; 563 | draw p3 -- p4 withpen thickpen; 564 | ) maskedWith (pulleyOutline shifted p5); 565 | draw sphere.c(d2) shifted p4 shifted (0, -1/2d2); 566 | dotlabel.llft(btex $A$ etex, p1); 567 | dotlabel.lrt(btex $B$ etex, p2); 568 | dotlabel.ulft(btex $C$ etex, p4); 569 | label.llft(btex $l$ etex, 1/2[p1, p3]); 570 | markAngle(p3, p1, p2)(btex $\alpha$ etex); 571 | \stopbuffer 572 | \typebuffer[\BufferName][keeptogether=no] \processMPbuffer[\BufferName] 573 | 574 | \subsection{Hooke’s law} 575 | 576 | \def\BufferName{HookesLaw} 577 | \startbuffer[\BufferName] 578 | numeric l[],d, h; 579 | pair p[], q[]; 580 | l0 := 3/2cm; l1 := 1cm; 581 | d := 1cm; h := 7/8cm; 582 | p1 := (0, 0); p2 := (0, -l0); 583 | p3 := (d, 0); p4 := (d, -l0-l1); 584 | p5 := (2d, 0); p6 := (2d, -l0-2l1); p7 := (2d, -l0-2l1-h); 585 | draw solidSurface((2d + 1/2cm, 0)--(-1/2cm, 0)); 586 | draw spring(p1, p2, 20); 587 | draw spring(p3, p4, 20); 588 | draw weight.h(h) shifted p4; 589 | draw spring(p5, p6, 20); 590 | draw weight.h(h) shifted p6; 591 | draw weight.h(h) shifted p7; 592 | q1 := (0, ypart(p2)); 593 | q2 := (0, ypart(p4)); 594 | q3 := (0, ypart(p6)); 595 | draw p2 -- q1 withpen thinpen; 596 | draw p4 -- q2 withpen thinpen; 597 | draw p6 -- q3 withpen thinpen; 598 | drawdblarrow q1--q2 withpen thinpen; 599 | drawdblarrow q2--q3 withpen thinpen; 600 | label.lft (btex $x$ etex, 1/2[q1, q2]); 601 | label.lft (btex $x$ etex, 1/2[q2, q3]); 602 | \stopbuffer 603 | \typebuffer[\BufferName][keeptogether=no] \processMPbuffer[\BufferName] 604 | 605 | \subsection{Weight on a cart} 606 | 607 | \def\BufferName{Weight} 608 | \startbuffer[\BufferName] 609 | numeric l, w, r, h; 610 | l := 4cm; 611 | w := 1/4cm; 612 | r := 2/3cm; 613 | h := 1cm; 614 | draw solidSurface((-1/5l, 0) -- (6/5l, 0)); 615 | draw woodBlock (l, w) shifted (0, r); 616 | draw wheel (r, 0) shifted (r, 1/2r); 617 | draw wheel (r, 0) shifted (l-r, 1/2r); 618 | draw weight.s(h) shifted (1/2l, r + w); 619 | \stopbuffer 620 | \typebuffer[\BufferName] \processMPbuffer[\BufferName] 621 | 622 | \subsection{Some knots} 623 | 624 | \def\BufferName{Knots} 625 | \startbuffer[\BufferName] 626 | path p[]; 627 | p1 := (dir(90)*4/3cm) {dir(0)} .. tension 3/2 628 | .. (dir(90 + 120)*4/3cm){dir(90 + 30)} .. tension 3/2 629 | .. (dir(90 - 120)*4/3cm){dir(-90 - 30)} .. tension 3/2 630 | .. cycle; 631 | p1 := p1 scaled 6/5; 632 | addStrandToKnot (primeOne) (p1, 1/4cm, "l", "1, -1, 1"); 633 | draw knotFromStrands (primeOne); 634 | p2 := (0, 2cm) .. (1/2cm, 3/2cm) .. (-1/2cm, 0) 635 | .. (1/2cm, -2/3cm) .. (4/3cm, 0) .. (0, 17/12cm) 636 | .. (-4/3cm, 0) .. (-1/2cm, -2/3cm) .. (1/2cm, 0) 637 | .. (-1/2cm, 3/2cm) .. cycle; 638 | p2 := p2 scaled 6/5; 639 | addStrandToKnot (primeTwo) (p2, 1/4cm, "l", "1, -1, 1, -1, 1"); 640 | draw knotFromStrands (primeTwo) shifted (4cm, 0); 641 | p3 := (dir(0)*3/2cm) .. (dir(1*72)*2/3cm) 642 | .. (dir(2*72)*3/2cm) .. (dir(3*72)*2/3cm) 643 | .. (dir(4*72)*3/2cm) .. (dir(0)*2/3cm) 644 | .. (dir(1*72)*3/2cm) .. (dir(2*72)*2/3cm) 645 | .. (dir(3*72)*3/2cm) .. (dir(4*72)*2/3cm) 646 | .. cycle; 647 | p3 := (p3 rotated (72/4)) scaled 6/5; 648 | addStrandToKnot (primeThree) (p3, 1/4cm, "l", "-1, 1, -1, 1, -1"); 649 | draw knotFromStrands (primeThree) shifted (8cm, 0); 650 | \stopbuffer 651 | \typebuffer[\BufferName][keeptogether=no] \processMPbuffer[\BufferName] 652 | 653 | \stopdocument 654 | -------------------------------------------------------------------------------- /LICENSE.md: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | 3 | Version 3, 29 June 2007 4 | 5 | Copyright © 2007 Free Software Foundation, Inc. 6 | 7 | Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for software and other kinds of works. 11 | 12 | The licenses for most software and other practical works are designed to take away your freedom to share and change the works. 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But first, please read . 226 | -------------------------------------------------------------------------------- /fiziko.tex: -------------------------------------------------------------------------------- 1 | \documentclass{ltxdoc} 2 | 3 | \usepackage{luamplib, listings, bxtexlogo, ccicons} 4 | \everymplib{verbatimtex \leavevmode etex; input fiziko.mp; beginfig(1);} 5 | \everyendmplib{endfig;} 6 | 7 | \lstset{ 8 | language=MetaPost, 9 | numbers=left, 10 | numberstyle=\tiny, 11 | basicstyle=\scriptsize 12 | } 13 | 14 | \author{Sergey Slyusarev} 15 | \title{``fiziko'' v. 0.2.1 package for \METAPOST} 16 | 17 | \begin{document} 18 | \maketitle 19 | 20 | \begin{abstract} 21 | This document describes a bunch of macros provided by ``fiziko'' library for \METAPOST. 22 | \end{abstract} 23 | 24 | \begin{centering} 25 | 26 | This document is distributed under CC-BY-SA 4.0 license 27 | 28 | \ccbysa 29 | 30 | https://github.com/jemmybutton/fiziko 31 | 32 | \end{centering} 33 | 34 | \section{Introduction} 35 | This \METAPOST\ library was initially written to automate some elements of black and white illustrations for a physics textbook. First and foremost it provides functions to draw things like lines of variable width, shaded spheres and tubes of different kinds, which can be used to produce images of a variety of objects. The library also contains functions to draw some objects constructed from these primitives. 36 | 37 | \section{Usage} 38 | Simply include this in the beginning of your \METAPOST\ document: 39 | 40 | \begin{lstlisting} 41 | input fiziko.mp 42 | \end{lstlisting} 43 | 44 | \section{Global variables} 45 | A few global variables control different aspects of the behavior of the provided macros. Not all possible values are meaningful and some will definitely result in ugly pictures or errors. 46 | 47 | \subsection{minStrokeWidth} 48 | This variable controls minimal thickness of lines that are used for shading. Below this value lines are not getting thinner, but become dashed instead, maintaining roughly the same amount of ink per unit length as a thinner line would take. Default value is one fifth of a point. There are several things that depend on this value, so it's convenient to change it using a macro: 49 | 50 | \begin{lstlisting} 51 | defineMinStrokeWidth(1/2pt); 52 | \end{lstlisting} 53 | 54 | \subsection{lightDirection} 55 | This variable controls direction from which light falls on shaded objects. It's of \texttt{pair} type and is set in radians. Default direction is top-left: 56 | \begin{lstlisting} 57 | lightDirection := (-1/8pi, 1/8pi); 58 | \end{lstlisting} 59 | 60 | 61 | \subsection{invertedLight} 62 | This variable determines whether the light is inverted. This comes in handy when you need to have your shaded objects white on black. It's of \texttt{boolean} type. Default value is false: 63 | 64 | \begin{lstlisting} 65 | draw sphere.s(1cm); 66 | invertedLight := true; 67 | fill ((unitsquare shifted (-1/2,-1/2)) scaled 3/2cm) shifted (3/2cm, 0) withcolor black; 68 | draw sphere.s(1cm) shifted (3/2cm, 0) withcolor white; 69 | \end{lstlisting} 70 | 71 | \begin{mplibcode} 72 | draw sphere.c(1cm); 73 | invertedLight := true; 74 | fill ((unitsquare shifted (-1/2,-1/2)) scaled 3/2cm) shifted (3/2cm, 0) withcolor black; 75 | draw sphere.c(1cm) shifted (3/2cm, 0) withcolor white; 76 | invertedLight := false; 77 | \end{mplibcode} 78 | 79 | \section{``Lower level'' macros} 80 | Currently, algorithms are quite stupid and will produce decent results only in certain simple circumstances. 81 | 82 | \subsection{offsetPath (\emph{path})(\emph{offset function})} 83 | This macro returns offset path (of type \texttt{path}) to a current path with a distance from the original path controlled by some arbitrary function; typically, it is a function of path length, set as either \texttt{offsetPathTime} or \texttt{offsetPathLength}. Former is simply \texttt{time} on current path and changes from 0 to \texttt{length(path)}, and latter changes from 0 to 1 over the path \texttt{arctime} (as a function of \texttt{arclength}). 84 | 85 | \begin{lstlisting} 86 | path p, q; 87 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 88 | q := offsetPath(p)(1cm*sin(offsetPathLength*pi)); 89 | draw p; 90 | draw q dashed evenly; 91 | \end{lstlisting} 92 | 93 | \begin{mplibcode} 94 | path p, q; 95 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 96 | q := offsetPath(p)(1cm*sin(offsetPathLength*pi)); 97 | draw p; 98 | draw q dashed evenly; 99 | \end{mplibcode} 100 | 101 | \subsection{brush (\emph{path})(\emph{offset function})} 102 | This macro returns a \texttt{picture} of a line of variable width along given path, which is controlled by some arbitrary function, analogous to \texttt{offsetPath}. If line is getting thinner than \texttt{minStrokeWith}, it is drawn dashed. 103 | 104 | \begin{lstlisting} 105 | path p; 106 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 107 | draw brush (p)(2minStrokeWidth*sin(offsetPathLength*pi)); 108 | \end{lstlisting} 109 | 110 | \begin{mplibcode} 111 | path p; 112 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 113 | draw brush (p)(2minStrokeWidth*sin(offsetPathLength*pi)); 114 | \end{mplibcode} 115 | 116 | \subsection{sphere.c (\emph{diameter})} 117 | This macro returns a \texttt{picture} of a sphere with specified diameter shaded with concentric strokes. Strokes are arranged to fit those of \texttt{tube.l}. 118 | 119 | \begin{lstlisting} 120 | for i := 1 step 1 until 6: 121 | draw sphere.c(i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 122 | endfor; 123 | \end{lstlisting} 124 | 125 | \begin{mplibcode} 126 | for i := 1 step 1 until 6: 127 | draw sphere.c(i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 128 | endfor; 129 | \end{mplibcode} 130 | 131 | \subsection{sphere.s (\emph{diameter})} 132 | This macro returns a \texttt{picture} of a sphere with specified diameter shaded with stipples. 133 | 134 | \begin{lstlisting} 135 | for i := 1 step 1 until 6: 136 | draw sphere.s(i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 137 | endfor; 138 | \end{lstlisting} 139 | 140 | \begin{mplibcode} 141 | for i := 1 step 1 until 6: 142 | draw sphere.s(i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 143 | endfor; 144 | \end{mplibcode} 145 | 146 | \subsection{sphereLat (\emph{diameter, angle})} 147 | This macro returns a \texttt{picture} of a shaded sphere with specified diameter. Unlike \texttt{sphere.c} macro, this one draws latitudinal strokes around axis rotated at specified \texttt{angle}. 148 | 149 | \begin{lstlisting} 150 | for i := 1 step 1 until 6: 151 | draw sphereLat(i*1/4cm, -90 + i*30) 152 | shifted (1/2cm*(i*(i+1))/2, 0); 153 | endfor; 154 | \end{lstlisting} 155 | 156 | \begin{mplibcode} 157 | for i := 1 step 1 until 6: 158 | draw sphereLat(i*1/4cm, -90 + i*30) 159 | shifted (1/2cm*(i*(i+1))/2, 0); 160 | endfor; 161 | \end{mplibcode} 162 | 163 | \subsection{tube.l (\emph{path})(\emph{offset function})} 164 | This macro returns a \texttt{picture} of a shaded ``tube'' of a variable width along a given path, which is controlled by some arbitrary function, analogous to \texttt{offsetPath}. ``Tube'' drawn by this macro is shaded be longitudal strokes. Once tube is generated, you can call \texttt{tubeOutline} path global variable, if you need one. 165 | 166 | \begin{lstlisting} 167 | path p; 168 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 169 | draw tube.l (p)(1/2cm*sin(offsetPathLength*pi)); 170 | \end{lstlisting} 171 | 172 | \begin{mplibcode} 173 | path p; 174 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 175 | draw tube.l (p)(1/2cm*sin(offsetPathLength*pi)); 176 | \end{mplibcode} 177 | 178 | \subsection{tube.t (\emph{path})(\emph{offset function})} 179 | This macro returns a \texttt{picture} of a shaded ``tube'' of variable width along given path, which is controlled by some arbitrary function, analogous to \texttt{offsetPath}. ``Tube'' drawn by this macro is shaded be transverse strokes. Once tube is generated, you can call \texttt{tubeOutline} path global variable, if you need one. 180 | 181 | \begin{lstlisting} 182 | path p; 183 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 184 | draw tube.t (p)(1/2cm*sin(offsetPathLength*pi)); 185 | \end{lstlisting} 186 | 187 | \begin{mplibcode} 188 | path p; 189 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 190 | draw tube.t (p)(1/2cm*sin(offsetPathLength*pi)); 191 | \end{mplibcode} 192 | 193 | \subsection{tube.s (\emph{path})(\emph{offset function})} 194 | This macro returns a \texttt{picture} of a shaded ``tube'' of variable width along given path, which is controlled by some arbitrary function, analogous to \texttt{offsetPath}. ``Tube'' drawn by this macro is shaded with stipples. Once tube is generated, you can call \texttt{tubeOutline} path global variable, if you need one. 195 | 196 | \begin{lstlisting} 197 | path p; 198 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 199 | draw tube.s (p)(1/2cm*sin(offsetPathLength*pi)); 200 | \end{lstlisting} 201 | 202 | \begin{mplibcode} 203 | path p; 204 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 205 | draw tube.s (p)(1/2cm*sin(offsetPathLength*pi)); 206 | \end{mplibcode} 207 | 208 | \subsection{tube.e (\emph{path})(\emph{offset function})} 209 | This macro returns the outline of a tube as a path. 210 | 211 | \section{``Higher level'' macros} 212 | Using macros described in the previous section it is possible to construct more complex images. Macros for drawing some often used images are present in this package. 213 | 214 | \subsection{eye (\emph{angle})} 215 | This macro returns a \texttt{picture} of an eye pointed at the direction \texttt{angle} (in degrees). Eye size is controlled by a global variable \texttt{eyescale}, which has default value of \texttt{eyescale := 1/2cm;}. 216 | 217 | \begin{lstlisting} 218 | save eyescale; 219 | for i := 1 step 1 until 6: 220 | eyescale := 1/6cm*i; 221 | draw eye(i*60) shifted (1/2cm*(i*(i+1))/2, 0); 222 | endfor; 223 | \end{lstlisting} 224 | 225 | \begin{mplibcode} 226 | save eyescale; 227 | for i := 1 step 1 until 6: 228 | eyescale := 1/6cm*i; 229 | draw eye(i*60) shifted (1/2cm*(i*(i+1))/2, 0); 230 | endfor; 231 | \end{mplibcode} 232 | 233 | \subsection{pulley (\emph{diameter, angle})} 234 | This macro returns a \texttt{picture} of a pulley with specified \texttt{diameter} and its support pointed at the direction \texttt{angle} (in degrees). Note that pulley's support protrudes from its center by \texttt{pulleySupportSize*diameter} and by default \texttt{pulleySupportSize} = 3/2. Once pulley is generated, you can call \texttt{pulleyOutline} path global variable, if you need one. 235 | 236 | \begin{lstlisting} 237 | draw (-1/8cm, 0)--(12cm, 0); 238 | for i := 1 step 1 until 6: 239 | r := 1/7cm*i; 240 | draw image( 241 | draw pulley(2r, 0) shifted (0, -4/3r); 242 | draw (r, -4/3r) -- (r, -2cm); 243 | drawarrow (-r, -4/3r) -- (-r, -2cm); 244 | ) shifted (1/2cm*(i*(i+1))/2, 0); 245 | endfor; 246 | \end{lstlisting} 247 | 248 | \noindent\begin{mplibcode} 249 | draw (-1/8cm, 0)--(12cm, 0); 250 | for i := 1 step 1 until 6: 251 | r := 1/7cm*i; 252 | draw image( 253 | draw pulley(2r, 0) shifted (0, -4/3r); 254 | draw (r, -4/3r) -- (r, -2cm); 255 | drawarrow (-r, -4/3r) -- (-r, -2cm); 256 | ) shifted (1/2cm*(i*(i+1))/2, 0); 257 | endfor; 258 | \end{mplibcode} 259 | 260 | \subsection{pulleyWheel (\emph{diameter})} 261 | This macro returns a \texttt{picture} of a pulley wheel with specified \texttt{diameter}. 262 | 263 | \begin{lstlisting} 264 | for i := 1 step 1 until 6: 265 | r := 1/7cm*i; 266 | draw image( 267 | draw pulleyWheel(2r); 268 | draw (r, 0) -- (r, 1cm); 269 | drawarrow (-r, 0) -- (-r, 1cm); 270 | ) shifted (1/2cm*(i*(i+1))/2, 0); 271 | endfor; 272 | \end{lstlisting} 273 | 274 | \begin{mplibcode} 275 | for i := 1 step 1 until 6: 276 | r := 1/7cm*i; 277 | draw image( 278 | draw pulleyWheel(2r); 279 | draw (r, 0) -- (r, 1cm); 280 | drawarrow (-r, 0) -- (-r, 1cm); 281 | ) shifted (1/2cm*(i*(i+1))/2, 0); 282 | endfor; 283 | \end{mplibcode} 284 | 285 | \subsection{wheel (\emph{diameter, angle})} 286 | This macro returns a \texttt{picture} of a wheel with specified \texttt{diameter} and its support pointed at the direction \texttt{angle} (in degrees). 287 | 288 | \begin{lstlisting} 289 | draw (-1/8cm, 0)--(12cm, 0); 290 | for i := 1 step 1 until 6: 291 | r := 1/7cm*i; 292 | draw wheel(2r, 0) shifted (0, -r) shifted (1/2cm*(i*(i+1))/2, 0); 293 | endfor; 294 | \end{lstlisting} 295 | 296 | 297 | \noindent\begin{mplibcode} 298 | draw (-1/8cm, 0)--(12cm, 0); 299 | for i := 1 step 1 until 6: 300 | r := 1/7cm*i; 301 | draw wheel(2r, 0) shifted (0, -r) shifted (1/2cm*(i*(i+1))/2, 0); 302 | endfor; 303 | \end{mplibcode} 304 | 305 | 306 | \subsection{weight.s (\emph{height})} 307 | This macro returns a \texttt{picture} of a weight of a specific \texttt{height} that is standing on the point \texttt{(0, 0)}. 308 | 309 | \begin{lstlisting} 310 | for i := 1 step 1 until 6: 311 | draw weight.s(1/4cm + i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 312 | endfor; 313 | draw (-1/8cm, 0)--(12cm, 0); 314 | \end{lstlisting} 315 | 316 | \noindent\begin{mplibcode} 317 | for i := 1 step 1 until 6: 318 | draw weight.s(1/4cm + i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 319 | endfor; 320 | draw (-1/8cm, 0)--(12cm, 0); 321 | \end{mplibcode} 322 | 323 | \subsection{weight.h (\emph{height})} 324 | This macro returns a \texttt{picture} of a weight of a specific \texttt{height} that is is hanging from the point \texttt{(0, 0)}. 325 | 326 | \begin{lstlisting} 327 | for i := 1 step 1 until 6: 328 | draw weight.h(1/4cm + i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 329 | endfor; 330 | draw (12cm, 0)--(-1/8cm, 0); 331 | \end{lstlisting} 332 | 333 | \noindent\begin{mplibcode} 334 | for i := 1 step 1 until 6: 335 | draw weight.h(1/4cm + i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0); 336 | endfor; 337 | draw (12cm, 0)--(-1/8cm, 0); 338 | \end{mplibcode} 339 | 340 | 341 | \subsection{spring (\emph{point a, point b, number of steps})} 342 | This macro returns a \texttt{picture} of a spring stretched between points \texttt{a} and \texttt{b} (of type \texttt{pair}), with specified \texttt{number of steps}. Spring width is controlled by global variable \texttt{springwidth} with the default value \texttt{springwidth := 1/8cm;}. 343 | 344 | \begin{lstlisting} 345 | pair a, b; 346 | a := (0, 0); 347 | for i := 1 step 1 until 6: 348 | springwidth := 1/16cm + i*1/48cm; 349 | b := (i*1/3cm, - i*1/5cm); 350 | draw spring (a, b, 10) shifted (2/5cm*(i*(i+1))/2, 0); 351 | endfor; 352 | \end{lstlisting} 353 | 354 | \begin{mplibcode} 355 | pair a, b; 356 | a := (0, 0); 357 | for i := 1 step 1 until 6: 358 | springwidth := 1/16cm + i*1/48cm; 359 | b := (i*1/3cm, - i*1/5cm); 360 | draw spring (a, b, 10) shifted (2/5cm*(i*(i+1))/2, 0); 361 | endfor; 362 | \end{mplibcode} 363 | 364 | \subsection{solidSurface (\emph{path})} 365 | This macro returns a \texttt{picture} of a solid surface on the right side of a given \texttt{path}. 366 | 367 | \begin{lstlisting} 368 | path p; 369 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 370 | draw solidSurface(p); 371 | \end{lstlisting} 372 | 373 | \begin{mplibcode} 374 | path p; 375 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 376 | draw solidSurface(p); 377 | \end{mplibcode} 378 | 379 | \subsection{solid (\emph{path, angle, type})} 380 | Fills given \texttt{path} with strokes of specific type at a given \texttt{angle}. \texttt{type} can be 0 (``solid'' strokes) and 1 (``glass'' strokes). 381 | 382 | \begin{lstlisting} 383 | path p[]; 384 | p1 := unitsquare scaled 2cm; 385 | p2 := p1 shifted (4cm, 0); 386 | draw solid(p1, 45, 0); 387 | draw solid(p2, -45, 1); 388 | \end{lstlisting} 389 | 390 | \begin{mplibcode} 391 | path p[]; 392 | p1 := unitsquare scaled 2cm; 393 | p2 := p1 shifted (4cm, 0); 394 | draw solid(p1, 45, 0); 395 | draw solid(p2, -45, 1); 396 | \end{mplibcode} 397 | 398 | \subsection{woodBlock (\emph{width, height})} 399 | Returns a \texttt{picture} of a rectangular block of wood with its bottom-left corner in the origin. 400 | 401 | \begin{lstlisting} 402 | draw woodBlock(10cm, 1/2cm); 403 | \end{lstlisting} 404 | 405 | \begin{mplibcode} 406 | draw woodBlock(10cm, 1/2cm); 407 | \end{mplibcode} 408 | 409 | \subsection{woodenThing (\emph{path, angle})} 410 | Returns a \texttt{picture} of a wood texture at a given \texttt{angle} fitted into a given \texttt{path}. 411 | 412 | \begin{lstlisting} 413 | path p, q; 414 | p := dir(-60) scaled 1/2 -- dir(90) scaled 2/3 -- dir (-120) scaled 3/5 -- cycle; 415 | for i := 1 step 1 until 6: 416 | q := (p scaled 3/2cm) rotated (i*60); 417 | draw woodenThing (q, i*60) shifted (2cm*i, 0); 418 | endfor; 419 | \end{lstlisting} 420 | 421 | \begin{mplibcode} 422 | path p, q; 423 | p := dir(-60) scaled 1/2 -- dir(90) scaled 2/3 -- dir (-120) scaled 3/5 -- cycle; 424 | for i := 1 step 1 until 6: 425 | q := (p scaled 3/2cm) rotated (i*60); 426 | draw woodenThing (q, i*60) shifted (2cm*i, 0); 427 | endfor; 428 | \end{mplibcode} 429 | 430 | \subsection{woodenSurface (\emph{path})} 431 | 432 | Returns a \texttt{picture} similar to that of a solid surface on the right side of a given \texttt{path}, but with wood texture . 433 | 434 | \begin{lstlisting} 435 | path p; 436 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 437 | draw woodenSurface(p); 438 | \end{lstlisting} 439 | 440 | \begin{mplibcode} 441 | path p; 442 | p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0); 443 | draw woodenSurface(p); 444 | \end{mplibcode} 445 | 446 | \subsection{globe (\emph{radius, longitude, latitude})} 447 | This macro returns a \texttt{picture} of the globe of specified \texttt{radius} centered at specific \texttt{longitude} and \texttt{latitude}; 448 | 449 | \begin{lstlisting} 450 | for i := 1 step 1 until 6: 451 | draw globe(i*1/4cm, i*60, -90 + i*30) 452 | shifted (1/2cm*(i*(i+1))/2, 0); 453 | endfor; 454 | \end{lstlisting} 455 | 456 | \begin{mplibcode} 457 | for i := 1 step 1 until 6: 458 | draw globe(i*1/4cm, i*60, -90 + i*30) 459 | shifted (1/2cm*(i*(i+1))/2, 0); 460 | endfor; 461 | \end{mplibcode} 462 | 463 | \subsection{Knots} 464 | There are two macros to handle knot drawing: \texttt{addStrandToKnot} and \texttt{knot\-From\-Strands}. Currently the algorithm is not especially stable. 465 | 466 | % \subsubsection{initKnot (\emph{knotName})} 467 | % This macro creates an empty knot with no strands named \texttt{knotName} and returns nothing. Useful if a knot is redefined with the same name repeatedly. 468 | 469 | \subsubsection{addStrandToKnot (\emph{knotName}) (\emph{path, ropeWidth, ropeType, intersectionOrder})} 470 | This macro adds a strand to knot named \texttt{knotName} and returns nothing. Strand follows the given \texttt{path} and has a given \texttt{ropeWidth}. \texttt{ropeType} can be \texttt{"l"}, \texttt{"t"} (as in \texttt{tube.l} and \texttt{tube.t}) or \texttt{"e"} (for an unshaded strand). \texttt{intersectionOrder} is a string of comma separated numbers which represent a ``layer'' to which intersections along the strand go. 471 | 472 | \subsubsection{knotFromStrands (\emph{knotName})} 473 | This macro returns a picture of a knot with a given \texttt{knotName}. 474 | 475 | \begin{lstlisting} 476 | path p[]; 477 | p1 := (dir(90)*4/3cm) {dir(0)} .. tension 3/2 478 | .. (dir(90 + 120)*4/3cm){dir(90 + 30)} .. tension 3/2 479 | .. (dir(90 - 120)*4/3cm){dir(-90 - 30)} .. tension 3/2 480 | .. cycle; 481 | p2 := (fullcircle scaled 3cm) shifted (0, -3/2cm); 482 | p3 := (fullcircle scaled 4cm); 483 | addStrandToKnot (theknot) (p1 shifted (4cm, -4cm), 1/5cm, "l", 484 | "-1,1,-1,1,-1,1,-1,1,-1"); 485 | addStrandToKnot (theknot) (p2 shifted (4cm, -4cm), 1/6cm, "s", 486 | ""); 487 | addStrandToKnot (theknot) (p3 shifted (4cm, -4cm), 1/7cm, "e", 488 | "-1,1"); 489 | draw knotFromStrands (theknot); 490 | \end{lstlisting} 491 | 492 | \begin{mplibcode} 493 | path p[]; 494 | p1 := (dir(90)*4/3cm) {dir(0)} .. tension 3/2 495 | .. (dir(90 + 120)*4/3cm){dir(90 + 30)} .. tension 3/2 496 | .. (dir(90 - 120)*4/3cm){dir(-90 - 30)} .. tension 3/2 497 | .. cycle; 498 | p2 := (fullcircle scaled 3cm) shifted (0, -3/2cm); 499 | p3 := (fullcircle scaled 4cm); 500 | addStrandToKnot (theknot) (p1 shifted (4cm, -4cm), 1/5cm, "l", 501 | "-1,1,-1,1,-1,1,-1,1,-1"); 502 | addStrandToKnot (theknot) (p2 shifted (4cm, -4cm), 1/6cm, "s", 503 | ""); 504 | addStrandToKnot (theknot) (p3 shifted (4cm, -4cm), 1/7cm, "e", 505 | "-1,1"); 506 | draw knotFromStrands (theknot); 507 | \end{mplibcode} 508 | 509 | \subsection{Other 3D contraptions} 510 | Some macros can be used to shade 3D polygons. Currently only flat surfaces re supported 511 | 512 | \subsubsection{flatSurface\emph{\#@}(\emph{surface outline path, normal vector, hatch angle})} 513 | This macro returns a \texttt{picture} of a flat surface with the specified \texttt{surface outline path} with the given \texttt{normal vector}, illuminated from the direction determined by \texttt{lightDirection} and with hatches aligned at the andle \texttt{hatch angle}. If \texttt{\#@} is \texttt{".hatches"} then the surface is shaded with hatches, if it's \texttt{".stipples"}, then the surface is shaded with stipples. 514 | 515 | \begin{mplibcode} 516 | path p[]; 517 | p1 := unitsquare xscaled 1cm yscaled 2cm; 518 | p2 := p1 shifted (1cm, 0); 519 | draw flatSurface.hatches(p1, (-1,0,1), 45); 520 | draw flatSurface.hatches(p2, (1,0,1), 45); 521 | draw p1; draw p2; 522 | \end{mplibcode} 523 | 524 | \section{Other macros} 525 | Some macros that are not directly related to drawing are listed below 526 | 527 | \subsection{refractionPath (\emph{initial ray, shape, refraction coefficient})} 528 | This macro returns a \texttt{path} that represent refraction of some \texttt{ray} (any variable of type \texttt{path}, point next to last in a given path is considered a source of a ``ray'', and last point determines its direction) through some \texttt{shape} with given \texttt{refraction coefficient}. When appropriate, the ``ray'' is fully internally reflected. 529 | 530 | Setting \texttt{refraction coefficient} to 0 results in reflection instead of refraction in all cases. 531 | 532 | \begin{lstlisting} 533 | path r, p; 534 | p := fullcircle scaled 2.1cm; 535 | draw p; 536 | for i:= 1cm step -1/4cm until -1cm: 537 | r := (-4cm, i) -- (-1cm, i); 538 | draw refractionPath(r, p, 1.5); 539 | endfor; 540 | \end{lstlisting} 541 | 542 | \begin{mplibcode} 543 | path r, p; 544 | p := fullcircle scaled 2.1cm; 545 | draw p; 546 | for i:= 1cm step -1/4cm until -1cm: 547 | r := (-4cm, i) -- (-1cm, i); 548 | draw refractionPath(r, p, 1.5); 549 | endfor; 550 | \end{mplibcode} 551 | 552 | 553 | \subsection{lens (\emph{(left radius, right radius), thickness, diameter, units})} 554 | This macro returns a \texttt{path} that represent a section of a lens with given radii of curvature (positive value for convex, negative --- for concave), thickness (i. e. distance benween sides' centers) and diameter (i. e. height) in given arbitrary units. 555 | 556 | \begin{lstlisting} 557 | draw lens((5, 10), 1/2, 2, cm); 558 | draw lens((-10, -5), 1/4, 2, cm) shifted (2cm, 0); 559 | draw lens((infinity, 7), 1/4, 2, cm) shifted (4cm, 0); 560 | \end{lstlisting} 561 | 562 | \begin{mplibcode} 563 | draw lens((5, 10), 1/2, 2, cm); 564 | draw lens((-10, -5), 1/4, 2, cm) shifted (2cm, 0); 565 | draw lens((infinity, 7), 1/4, 2, cm) shifted (4cm, 0); 566 | \end{mplibcode} 567 | 568 | \section{Auxilary macros} 569 | Some macros that not related to physical problems at all are listed below. 570 | 571 | \subsection{\emph{picture} maskedWith \emph{path}} 572 | This macro masks a part of a \texttt{picture} with closed \texttt{path}. In fact this is inversion of \METAPOST's built-in \texttt{clip} but, in contrast to the latter, it does not modify original image. Note that it requires that counter-clockwise \texttt{path} to work properly. 573 | 574 | \subsection{\emph{path} firstIntersectionTimes \emph{path}} 575 | This macro is similar to \METAPOST's \texttt{intersectiontimes} but it returns intersection times with smallest time on first path. 576 | 577 | \subsection{pathSubdivide \emph{path, n}} 578 | This macro returns original \texttt{path} with \texttt{n}-times more points. 579 | 580 | \subsection{drawmidarrow (\emph{path})} 581 | Draws \texttt{path} with arrows in the middles of segments with length no less than \texttt{midArrowLimit} (another global variable, 1cm by default). 582 | 583 | \subsection{markAngle (\emph{point a, point o, point b})(\emph{text})} 584 | This macro marks an angle \texttt{aob} (counter-clockwise) with some \texttt{text} 585 | 586 | \begin{lstlisting} 587 | pair a, o, b; 588 | for i:= 30 step 60 until 390: 589 | o := (10cm*(i/360), 0); 590 | a := dir(i/2)*4/3cm shifted o; 591 | b := dir(i)*4/3cm shifted o; 592 | draw (a--o--b); 593 | markAngle(a, o, b)(btex $\alpha$ etex); 594 | endfor; 595 | \end{lstlisting} 596 | 597 | \begin{mplibcode} 598 | pair a, o, b; 599 | for i:= 30 step 60 until 390: 600 | o := (10cm*(i/360), 0); 601 | a := dir(i/2)*4/3cm shifted o; 602 | b := dir(i)*4/3cm shifted o; 603 | draw (a--o--b); 604 | markAngle(a, o, b)(btex $\alpha$ etex); 605 | endfor; 606 | \end{mplibcode} 607 | 608 | 609 | \section{Some examples} 610 | 611 | \subsection{Gregory-Maksutov type telescope} 612 | Lines 3--11 define parameters of lenses and mirrors\footnote{Taken from here http://www.google.ru/patents/US2701983}. Lines 12--16 generate lenses. On line 20 shape of prism is defined. Line 22 cuts part of the rear mirror. Line 26 describes mirror part of the front lens. On lines 31--33 all the glass parts are drawn. On lines 34--36 all the mirror ones. On lines 39--44 rays are traced through all system in order specified in loop on line 41. Lines 49--56 are about the telescope frame. 613 | \begin{lstlisting} 614 | path p[], q[], axis[], f[]; pair o; 615 | u := 6mm; 616 | r1 := -36.979; r2 := -r1; t1 := 0.7; n1 := 1.517; d1 := 5; 617 | l1 := 8.182; 618 | r3 := -11.657; r4 := r3; t2 := 0.2; n2 := n1; d2 := 3/2; 619 | l2 := 0.4; 620 | r5 := -30.433; r6 := 9.598; t3 := 0.39; n3 := 1.621; d3 := d2; 621 | l3 := 0.828; 622 | r7 := -35.512; r8 := infinity; t4 := 0.7; n4 := 0; d4 := d1; 623 | l4 := 5.272; 624 | ll0 := 0; 625 | for i := 1 upto 4: 626 | ll[i] := ll[i-1] + t[i] + l[i]; 627 | p[i] := lens ((r[i*2 - 1], r[i*2]), t[i], d[i], u) 628 | shifted (ll[i-1]*u, 0); 629 | endfor; 630 | axis1 := (0, 0) -- (ll4*u, 0); 631 | axis2 := reverse(axis1); 632 | ll5 := ll4 - 1/2l4; 633 | p5 := ((-1,-1) -- (1,1) -- (-1,1) -- cycle) 634 | scaled (1/2d2*u) shifted (ll5*u, 0); 635 | p6 := (subpath 636 | (ypart((axis1 shifted (0, 1/2d2*u)) firstIntersectionTimes p4), 637 | ypart((axis2 shifted (0, 1/2d2*u)) firstIntersectionTimes p4)) 638 | of p4) -- cycle; 639 | p7 := (subpath 640 | (ypart((axis2 shifted (0, 3/4d2*u)) firstIntersectionTimes p1), 641 | ypart((axis2 shifted (0, -3/4d2*u)) firstIntersectionTimes p1)) 642 | of p1); 643 | p7 := p7 -- (reverse(p7) shifted ((-1/3t1)*u, 0)) -- cycle; 644 | for i := 1, 2, 3, 5: 645 | draw p[i] withpen thickpen; draw solid (p[i], 45, 1); 646 | endfor; 647 | draw solid (p7, -45, 0); 648 | draw p6 withpen thickpen; draw solid (p6, -45, 0); 649 | draw p6 yscaled -1 withpen thickpen; 650 | draw solid (p6 yscaled -1, -45, 0); 651 | n7 := 0; n5 := n1; 652 | for i := 0, 1: 653 | q[i] := (-3/2u, -2u + i*4u) -- (16u, -2u + i*4u); 654 | for j = 1, 4, 7, 2, 3, 5: 655 | q[i] := refractionPath(q[i], p[j], n[j]); 656 | endfor; 657 | endfor; 658 | o := whatever[point length(q0) of q0, point length(q0)-1 of q0] 659 | = whatever[point length(q1) of q1, point length(q1)-1 of q1]; 660 | for i := 0, 1: drawmidarrow (q[i] -- o) withpen thinpen; endfor; 661 | draw eye(-91) shifted o shifted (0, u); 662 | f1 := (-1/4u, 1/2d1*u) -- ((ll3 + t4)*u, 1/2d1*u) 663 | -- ((ll3 + t4)*u, 1/2d2*u); 664 | f2 := (ll1*u - 1/8u, 1/2d2*u) -- (ll5*u - 1/2d2*u, 1/2d2*u) 665 | -- (ll5*u - 1/2d2*u, ypart(o)); 666 | f3 := (ll1*u - 1/8u, -1/2d2*u) -- (ll5*u + 1/2d2*u, -1/2d2*u) 667 | -- (ll5*u + 1/2d2*u, ypart(o)); 668 | draw f1 withpen fatpen; draw f1 yscaled -1 withpen fatpen; 669 | draw f2 withpen fatpen; draw f3 withpen fatpen; 670 | \end{lstlisting} 671 | 672 | \begin{mplibcode} 673 | path p[], q[], axis[], f[]; pair o; 674 | u := 6mm; 675 | r1 := -36.979; r2 := -r1; t1 := 0.7; n1 := 1.517; d1 := 5; 676 | l1 := 8.182; 677 | r3 := -11.657; r4 := r3; t2 := 0.2; n2 := n1; d2 := 3/2; 678 | l2 := 0.4; 679 | r5 := -30.433; r6 := 9.598; t3 := 0.39; n3 := 1.621; d3 := d2; 680 | l3 := 0.828; 681 | r7 := -35.512; r8 := infinity; t4 := 0.7; n4 := 0; d4 := d1; 682 | l4 := 5.272; 683 | ll0 := 0; 684 | for i := 1 upto 4: 685 | ll[i] := ll[i-1] + t[i] + l[i]; 686 | p[i] := lens ((r[i*2 - 1], r[i*2]), t[i], d[i], u) 687 | shifted (ll[i-1]*u, 0); 688 | endfor; 689 | axis1 := (0, 0) -- (ll4*u, 0); 690 | axis2 := reverse(axis1); 691 | ll5 := ll4 - 1/2l4; 692 | p5 := ((-1,-1) -- (1,1) -- (-1,1) -- cycle) 693 | scaled (1/2d2*u) shifted (ll5*u, 0); 694 | p6 := (subpath 695 | (ypart((axis1 shifted (0, 1/2d2*u)) firstIntersectionTimes p4), 696 | ypart((axis2 shifted (0, 1/2d2*u)) firstIntersectionTimes p4)) 697 | of p4) -- cycle; 698 | p7 := (subpath 699 | (ypart((axis2 shifted (0, 3/4d2*u)) firstIntersectionTimes p1), 700 | ypart((axis2 shifted (0, -3/4d2*u)) firstIntersectionTimes p1)) 701 | of p1); 702 | p7 := p7 -- (reverse(p7) shifted ((-1/3t1)*u, 0)) -- cycle; 703 | for i := 1, 2, 3, 5: 704 | draw p[i] withpen thickpen; draw solid (p[i], 45, 1); 705 | endfor; 706 | draw solid (p7, -45, 0); 707 | draw p6 withpen thickpen; draw solid (p6, -45, 0); 708 | draw p6 yscaled -1 withpen thickpen; 709 | draw solid (p6 yscaled -1, -45, 0); 710 | n7 := 0; n5 := n1; 711 | for i := 0, 1: 712 | q[i] := (-3/2u, -2u + i*4u) -- (16u, -2u + i*4u); 713 | for j = 1, 4, 7, 2, 3, 5: 714 | q[i] := refractionPath(q[i], p[j], n[j]); 715 | endfor; 716 | endfor; 717 | o := whatever[point length(q0) of q0, point length(q0)-1 of q0] 718 | = whatever[point length(q1) of q1, point length(q1)-1 of q1]; 719 | for i := 0, 1: drawmidarrow (q[i] -- o) withpen thinpen; endfor; 720 | draw eye(-91) shifted o shifted (0, u); 721 | f1 := (-1/4u, 1/2d1*u) -- ((ll3 + t4)*u, 1/2d1*u) 722 | -- ((ll3 + t4)*u, 1/2d2*u); 723 | f2 := (ll1*u - 1/8u, 1/2d2*u) -- (ll5*u - 1/2d2*u, 1/2d2*u) 724 | -- (ll5*u - 1/2d2*u, ypart(o)); 725 | f3 := (ll1*u - 1/8u, -1/2d2*u) -- (ll5*u + 1/2d2*u, -1/2d2*u) 726 | -- (ll5*u + 1/2d2*u, ypart(o)); 727 | draw f1 withpen fatpen; draw f1 yscaled -1 withpen fatpen; 728 | draw f2 withpen fatpen; draw f3 withpen fatpen; 729 | \end{mplibcode} 730 | 731 | \subsection{L'H\^{o}pital's Pulley Problem} 732 | Line 3 describe initial setup. Line 4 is problem's solution. Lines 8--11 set all the points where they belong. Lines 12--16 are needed to decide where to put the pulley. 733 | 734 | \begin{lstlisting} 735 | pair p[], o[]; 736 | numeric a, d[], l[], x[], y[]; 737 | l0 := 6; l1 := 4; l2 := 4; 738 | x1 := (l1**2 + abs(l1)*((sqrt(8)*l0)++l1))/4l0; 739 | y1 := l1+-+x1; 740 | y2 := l2 - ((l0-x1)++y1); 741 | d1 := 2/3cm; d2 := 4/3cm; d3 := 5/6d1; 742 | p1 := (0, 0); 743 | p2 := (l0*cm, 0); 744 | p3 := (x1*cm, -y1*cm); 745 | p4 := p3 shifted (0, -y2*cm); 746 | o1 := (unitvector(p4-p3) rotated 90 scaled 1/2d3); 747 | o2 := (unitvector(p3-p2) rotated 90 scaled 1/2d3); 748 | p5 := whatever [p3 shifted o1, p4 shifted o1] 749 | = whatever [p3 shifted o2, p2 shifted o2]; 750 | a := angle(p1-p3); 751 | draw solidSurface(11/10[p1,p2] -- 11/10[p2, p1]); 752 | draw pulley (d1, a - 90) shifted p5; 753 | draw image( 754 | draw p1 -- p3 -- p2 withpen thickpen; 755 | draw p3 -- p4 withpen thickpen; 756 | ) maskedWith (pulleyOutline shifted p5); 757 | draw sphere.c(d2) shifted p4 shifted (0, -1/2d2); 758 | dotlabel.llft(btex $A$ etex, p1); 759 | dotlabel.lrt(btex $B$ etex, p2); 760 | dotlabel.ulft(btex $C$ etex, p4); 761 | label.llft(btex $l$ etex, 1/2[p1, p3]); 762 | markAngle(p3, p1, p2)(btex $\alpha$ etex); 763 | \end{lstlisting} 764 | 765 | \begin{mplibcode} 766 | pair p[], o[]; 767 | numeric a, d[], l[], x[], y[]; 768 | l0 := 6; l1 := 4; l2 := 4; 769 | x1 := (l1**2 + abs(l1)*((sqrt(8)*l0)++l1))/4l0; 770 | y1 := l1+-+x1; 771 | y2 := l2 - ((l0-x1)++y1); 772 | d1 := 2/3cm; d2 := 4/3cm; d3 := 5/6d1; 773 | p1 := (0, 0); 774 | p2 := (l0*cm, 0); 775 | p3 := (x1*cm, -y1*cm); 776 | p4 := p3 shifted (0, -y2*cm); 777 | o1 := (unitvector(p4-p3) rotated 90 scaled 1/2d3); 778 | o2 := (unitvector(p3-p2) rotated 90 scaled 1/2d3); 779 | p5 := whatever [p3 shifted o1, p4 shifted o1] 780 | = whatever [p3 shifted o2, p2 shifted o2]; 781 | a := angle(p1-p3); 782 | draw solidSurface(11/10[p1,p2] -- 11/10[p2, p1]); 783 | draw pulley (d1, a - 90) shifted p5; 784 | draw image( 785 | draw p1 -- p3 -- p2 withpen thickpen; 786 | draw p3 -- p4 withpen thickpen; 787 | ) maskedWith (pulleyOutline shifted p5); 788 | draw sphere.c(d2) shifted p4 shifted (0, -1/2d2); 789 | dotlabel.llft(btex $A$ etex, p1); 790 | dotlabel.lrt(btex $B$ etex, p2); 791 | dotlabel.ulft(btex $C$ etex, p4); 792 | label.llft(btex $l$ etex, 1/2[p1, p3]); 793 | markAngle(p3, p1, p2)(btex $\alpha$ etex); 794 | \end{mplibcode} 795 | 796 | \subsection{Hooke's law} 797 | 798 | \begin{lstlisting} 799 | numeric l[],d, h; 800 | pair p[], q[]; 801 | l0 := 3/2cm; l1 := 1cm; 802 | d := 1cm; h := 7/8cm; 803 | p1 := (0, 0); p2 := (0, -l0); 804 | p3 := (d, 0); p4 := (d, -l0-l1); 805 | p5 := (2d, 0); p6 := (2d, -l0-2l1); p7 := (2d, -l0-2l1-h); 806 | draw solidSurface((2d + 1/2cm, 0)--(-1/2cm, 0)); 807 | draw spring(p1, p2, 20); 808 | draw spring(p3, p4, 20); 809 | draw weight.h(h) shifted p4; 810 | draw spring(p5, p6, 20); 811 | draw weight.h(h) shifted p6; 812 | draw weight.h(h) shifted p7; 813 | q1 := (0, ypart(p2)); 814 | q2 := (0, ypart(p4)); 815 | q3 := (0, ypart(p6)); 816 | draw p2 -- q1 withpen thinpen; 817 | draw p4 -- q2 withpen thinpen; 818 | draw p6 -- q3 withpen thinpen; 819 | drawdblarrow q1--q2 withpen thinpen; 820 | drawdblarrow q2--q3 withpen thinpen; 821 | label.lft (btex $x$ etex, 1/2[q1, q2]); 822 | label.lft (btex $x$ etex, 1/2[q2, q3]); 823 | \end{lstlisting} 824 | 825 | \begin{mplibcode} 826 | numeric l[],d, h; 827 | pair p[], q[]; 828 | l0 := 3/2cm; l1 := 1cm; 829 | d := 1cm; h := 7/8cm; 830 | p1 := (0, 0); p2 := (0, -l0); 831 | p3 := (d, 0); p4 := (d, -l0-l1); 832 | p5 := (2d, 0); p6 := (2d, -l0-2l1); p7 := (2d, -l0-2l1-h); 833 | draw solidSurface((2d + 1/2cm, 0)--(-1/2cm, 0)); 834 | draw spring(p1, p2, 20); 835 | draw spring(p3, p4, 20); 836 | draw weight.h(h) shifted p4; 837 | draw spring(p5, p6, 20); 838 | draw weight.h(h) shifted p6; 839 | draw weight.h(h) shifted p7; 840 | q1 := (0, ypart(p2)); 841 | q2 := (0, ypart(p4)); 842 | q3 := (0, ypart(p6)); 843 | draw p2 -- q1 withpen thinpen; 844 | draw p4 -- q2 withpen thinpen; 845 | draw p6 -- q3 withpen thinpen; 846 | drawdblarrow q1--q2 withpen thinpen; 847 | drawdblarrow q2--q3 withpen thinpen; 848 | label.lft (btex $x$ etex, 1/2[q1, q2]); 849 | label.lft (btex $x$ etex, 1/2[q2, q3]); 850 | \end{mplibcode} 851 | 852 | \subsection{Weight on a cart} 853 | 854 | \begin{lstlisting} 855 | numeric l, w, r, h; 856 | l := 4cm; 857 | w := 1/4cm; 858 | r := 2/3cm; 859 | h := 1cm; 860 | draw solidSurface((-1/5l, 0) -- (6/5l, 0)); 861 | draw woodBlock (l, w) shifted (0, r); 862 | draw wheel (r, 0) shifted (r, 1/2r); 863 | draw wheel (r, 0) shifted (l-r, 1/2r); 864 | draw weight.s(h) shifted (1/2l, r + w); 865 | \end{lstlisting} 866 | 867 | \begin{mplibcode} 868 | numeric l, w, r, h; 869 | l := 4cm; 870 | w := 1/4cm; 871 | r := 2/3cm; 872 | h := 1cm; 873 | draw solidSurface((-1/5l, 0) -- (6/5l, 0)); 874 | draw woodBlock (l, w) shifted (0, r); 875 | draw wheel (r, 0) shifted (r, 1/2r); 876 | draw wheel (r, 0) shifted (l-r, 1/2r); 877 | draw weight.s(h) shifted (1/2l, r + w); 878 | \end{mplibcode} 879 | 880 | \subsection{Some knots} 881 | 882 | \begin{lstlisting} 883 | path p[]; 884 | p1 := (dir(90)*4/3cm) {dir(0)} .. tension 3/2 885 | .. (dir(90 + 120)*4/3cm){dir(90 + 30)} .. tension 3/2 886 | .. (dir(90 - 120)*4/3cm){dir(-90 - 30)} .. tension 3/2 887 | .. cycle; 888 | p1 := p1 scaled 6/5; 889 | addStrandToKnot (primeOne) (p1, 1/4cm, "l", "1, -1, 1"); 890 | draw knotFromStrands (primeOne); 891 | p2 := (0, 2cm) .. (1/2cm, 3/2cm) .. (-1/2cm, 0) 892 | .. (1/2cm, -2/3cm) .. (4/3cm, 0) .. (0, 17/12cm) 893 | .. (-4/3cm, 0) .. (-1/2cm, -2/3cm) .. (1/2cm, 0) 894 | .. (-1/2cm, 3/2cm) .. cycle; 895 | p2 := p2 scaled 6/5; 896 | addStrandToKnot (primeTwo) (p2, 1/4cm, "l", "1, -1, 1, -1, 1"); 897 | draw knotFromStrands (primeTwo) shifted (4cm, 0); 898 | p3 := (dir(0)*3/2cm) .. (dir(1*72)*2/3cm) 899 | .. (dir(2*72)*3/2cm) .. (dir(3*72)*2/3cm) 900 | .. (dir(4*72)*3/2cm) .. (dir(0)*2/3cm) 901 | .. (dir(1*72)*3/2cm) .. (dir(2*72)*2/3cm) 902 | .. (dir(3*72)*3/2cm) .. (dir(4*72)*2/3cm) 903 | .. cycle; 904 | p3 := (p3 rotated (72/4)) scaled 6/5; 905 | addStrandToKnot (primeThree) (p3, 1/4cm, "l", "-1, 1, -1, 1, -1"); 906 | draw knotFromStrands (primeThree) shifted (8cm, 0); 907 | \end{lstlisting} 908 | 909 | \begin{mplibcode} 910 | path p[]; 911 | p1 := (dir(90)*4/3cm) {dir(0)} .. tension 3/2 912 | .. (dir(90 + 120)*4/3cm){dir(90 + 30)} .. tension 3/2 913 | .. (dir(90 - 120)*4/3cm){dir(-90 - 30)} .. tension 3/2 914 | .. cycle; 915 | p1 := p1 scaled 6/5; 916 | addStrandToKnot (primeOne) (p1, 1/4cm, "l", "1, -1, 1"); 917 | draw knotFromStrands (primeOne); 918 | p2 := (0, 2cm) .. (1/2cm, 3/2cm) .. (-1/2cm, 0) 919 | .. (1/2cm, -2/3cm) .. (4/3cm, 0) .. (0, 17/12cm) 920 | .. (-4/3cm, 0) .. (-1/2cm, -2/3cm) .. (1/2cm, 0) 921 | .. (-1/2cm, 3/2cm) .. cycle; 922 | p2 := p2 scaled 6/5; 923 | addStrandToKnot (primeTwo) (p2, 1/4cm, "s", "1, -1, 1, -1, 1"); 924 | draw knotFromStrands (primeTwo) shifted (4cm, -2cm); 925 | p3 := (dir(0)*3/2cm) .. (dir(1*72)*2/3cm) 926 | .. (dir(2*72)*3/2cm) .. (dir(3*72)*2/3cm) 927 | .. (dir(4*72)*3/2cm) .. (dir(0)*2/3cm) 928 | .. (dir(1*72)*3/2cm) .. (dir(2*72)*2/3cm) 929 | .. (dir(3*72)*3/2cm) .. (dir(4*72)*2/3cm) 930 | .. cycle; 931 | p3 := (p3 rotated (72/4)) scaled 6/5; 932 | addStrandToKnot (primeThree) (p3, 1/4cm, "e", "-1, 1, -1, 1, -1"); 933 | draw knotFromStrands (primeThree) shifted (8cm, 0); 934 | \end{mplibcode} 935 | 936 | 937 | \end{document} -------------------------------------------------------------------------------- /fiziko.mp: -------------------------------------------------------------------------------- 1 | % fiziko 0.2.1 2 | % MetaPost library for physics textbook illustrations 3 | % Copyright 2023 Sergey Slyusarev 4 | % 5 | % This program is free software: you can redistribute it and/or modify 6 | % it under the terms of the GNU General Public License as published by 7 | % the Free Software Foundation, either version 3 of the License, or 8 | % (at your option) any later version. 9 | % 10 | % This program is distributed in the hope that it will be useful, 11 | % but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | % GNU General Public License for more details. 14 | % 15 | % You should have received a copy of the GNU General Public License 16 | % along with this program. If not, see . 17 | 18 | % https://github.com/jemmybutton/fiziko 19 | 20 | % 21 | % Here we define some things of general interest 22 | % 23 | 24 | pi := 3.1415926; 25 | radian := 180/pi; 26 | 27 | vardef sin primary x = (sind(x*radian)) enddef; 28 | 29 | vardef cos primary x = (cosd(x*radian)) enddef; 30 | 31 | vardef log (expr n, b) = 32 | save rv; 33 | numeric rv; 34 | if n > 0: 35 | rv := (mlog(n)/mlog(b)); 36 | else: 37 | rv := 0; 38 | fi; 39 | rv 40 | enddef; 41 | 42 | vardef arcsind primary x = angle((1+-+x,x)) enddef; 43 | 44 | vardef arccosd primary x = angle((x,1+-+x)) enddef; 45 | 46 | vardef arcsin primary x = ((arcsind(x))/radian) enddef; 47 | 48 | vardef arccos primary x = ((arccosd(x))/radian) enddef; 49 | 50 | vardef angleRad primary x = angle(x)/radian enddef; 51 | 52 | vardef dirRad primary x = dir(x*radian) enddef; 53 | 54 | % used here and there. 55 | 56 | vardef sign (expr x)= 57 | if x > 0: 1 fi 58 | if x < 0: -1 fi 59 | if x = 0: 1 fi 60 | enddef; 61 | 62 | % This is inverted `clip` 63 | 64 | primarydef i maskedWith p = 65 | begingroup 66 | save q, invertedmask, resultimage, breakpoint; 67 | pair q[]; 68 | path invertedmask; 69 | picture resultimage; 70 | resultimage := i; 71 | q1 := ulcorner(i) shifted (-1, 1); 72 | q3 := lrcorner(i) shifted (1, -1); 73 | q2 := (xpart(q3), ypart(q1)); 74 | q4 := (xpart(q1), ypart(q3)); 75 | breakpoint := ypart((ulcorner(p)--llcorner(p)) firstIntersectionTimes p); 76 | invertedmask := (subpath (breakpoint, length(p) + breakpoint) of p) -- q1 -- q2 -- q3 -- q4 -- q1 -- cycle; 77 | clip resultimage to invertedmask; 78 | resultimage 79 | endgroup 80 | enddef; 81 | 82 | % 83 | % Since metapost is somewhat unpredictable in determining where paths intersect, here's macro 84 | % that returns first intersection times with first path (ray) priority. 85 | % Actually, it is so in most cases, but sometimes second path can take precedence, 86 | % so the macro just checks whether reversing 'q' changes something 87 | % 88 | 89 | primarydef p firstIntersectionTimes q = 90 | begingroup 91 | save t; 92 | pair t[]; 93 | t1 := p intersectiontimes q; 94 | t2 := p intersectiontimes reverse(q); 95 | if xpart(t1) < xpart(t2): 96 | t3 := t1; 97 | else: 98 | t3 := (xpart(t2), length(q) - ypart(t2)); 99 | fi; 100 | if xpart(t1) < 0: t3 := t2; fi; 101 | t3 102 | endgroup 103 | enddef; 104 | 105 | % This checks if point a is inside of closed path p 106 | 107 | primarydef a isInside p = 108 | begingroup 109 | save ang, v, i, rv, pp; 110 | boolean rv; 111 | pair pp[]; 112 | ang := 0; 113 | for i := 0 step 1/4 until (length(p)): 114 | pp1 := (point i of p) - a; 115 | pp2 := (point i + 1/4 of p) - a; 116 | if (pp1 <> (0, 0)) and (pp2 <> (0, 0)): 117 | v := angle(pp1) - angle(pp2); 118 | if v > 180: v := v - 360; fi; if v < -180: v := v + 360; fi; 119 | ang := ang + v; 120 | fi; 121 | endfor; 122 | if abs(ang) > 355: 123 | rv := true; 124 | else: 125 | rv := false; 126 | fi; 127 | rv 128 | endgroup 129 | enddef; 130 | 131 | % rotation in radians 132 | 133 | primarydef somethingToRotate radRotated radAngle = 134 | somethingToRotate rotated ((radAngle/pi)*180) 135 | enddef; 136 | 137 | % 138 | % some 3D stuff 139 | % 140 | 141 | % this one's from byrne.mp 142 | 143 | primarydef colorone dotprodXYZ colortwo = 144 | begingroup 145 | save xp, yp, zp; 146 | numeric xp[], yp[], zp[]; 147 | xp1 := (redpart colorone); 148 | yp1 := (greenpart colorone); 149 | zp1 := (bluepart colorone); 150 | xp2 := (redpart colortwo); 151 | yp2 := (greenpart colortwo); 152 | zp2 := (bluepart colortwo); 153 | xp1*xp2 + yp1*yp2 + zp1*zp2 154 | endgroup 155 | enddef; 156 | 157 | % 158 | % sometimes it's useful to put some arrows along the path. this macro puts them 159 | % in the middles of the segments that have length no less than midArrowLimit; 160 | % 161 | 162 | midArrowLimit := 1cm; 163 | 164 | def drawmidarrow (expr p) text t = 165 | begingroup 166 | save i, j, q; 167 | path q; 168 | j := 0; 169 | for i := 1 upto length(p): 170 | if arclength(subpath(i-1, i) of p) >= midArrowLimit: 171 | q := subpath(j, i - 1/2) of p; 172 | j := i - 1/2; 173 | draw q t; 174 | filldraw arrowhead q t; 175 | fi; 176 | endfor; 177 | draw subpath(j, length(p)) of p t; 178 | endgroup 179 | enddef; 180 | 181 | % This macro marks angles, unsurprisingly 182 | 183 | def markAngle (expr a, o, b) (text t) = 184 | begingroup 185 | save p, an, d; 186 | numeric an[], d[]; 187 | pair p; 188 | an1 := angle(a-o); 189 | an2 := angle(b-o) - an1; 190 | if (an2 < 0): an2 := an2 + 360; fi; 191 | an3 := an1 + 1/2an2; 192 | p := center(t); 193 | d1 := abs(ulcorner(t)-lrcorner(t)); 194 | if (an2 < 90) and (an2 > 0): 195 | d2 := max(1/3cm, (d1/(abs(sind(an2))*1/3cm))*1/3cm); 196 | else: 197 | d2 := 1/3cm; 198 | fi; 199 | draw subpath (0, 8an2/360) of fullcircle scaled 2d2 rotated an1 shifted o withpen thinpen; 200 | draw (t) shifted -p shifted o shifted (dir(an3)*(d2 + d1)); 201 | endgroup 202 | enddef; 203 | 204 | % 205 | % Here we define some auxilary global variables 206 | % 207 | 208 | % Offset path algorithm can subdivide original path in order to be more precise 209 | offsetPathSteps := 4; 210 | 211 | % The following macro sets all the values related to minimal stroke width at once. 212 | % It can be used to easily redefine all of them. 213 | def defineMinStrokeWidth (expr msw) = 214 | % We don't want to display strokes that are too thin to print. Default value 215 | % is subject to change when needed. 216 | minStrokeWidth := msw; 217 | maxShadingStrokeWidth := 3/2minStrokeWidth; 218 | 219 | % At some point it's useless to display even dashes 220 | minDashStrokeWidth := 1/3minStrokeWidth; 221 | 222 | % this value corresponds to particular dashing algorithm and is subject to change whenever this algorithm changes 223 | minDashStrokeLength := 6minStrokeWidth; 224 | 225 | dashStrokeWidthStep := (minStrokeWidth - minDashStrokeWidth)/16; 226 | 227 | % all the shading algorithms need to know how close lines should be packed 228 | shadingDensity := 3maxShadingStrokeWidth; 229 | 230 | stippleSize := 3/2minStrokeWidth; 231 | minStippleStep := 1/2stippleSize; 232 | stippleShadingDensity := 3minStippleStep; 233 | minStippleStrokeWidth := 1/20stippleSize; 234 | 235 | % here are some pens 236 | pen thinpen, thickpen, fatpen, stipplepen; 237 | 238 | thinpen := pencircle scaled minStrokeWidth; 239 | thickpen := pencircle scaled 3minStrokeWidth; 240 | fatpen := pencircle scaled 6minStrokeWidth; 241 | stipplepen := pencircle scaled stippleSize; 242 | enddef; 243 | 244 | defineMinStrokeWidth(1/5pt); 245 | 246 | % here we set global light direction 247 | 248 | def defineLightDirection (expr ldx, ldy) = 249 | pair lightDirection; 250 | color lightDirectionVectorXYZ; 251 | lightDirection := (ldx, ldy); 252 | lightDirectionVectorXYZ := (0, 0, 1); 253 | lightDirectionVectorXYZ := rotateXYZaround.x(lightDirectionVectorXYZ, ldy); 254 | lightDirectionVectorXYZ := rotateXYZaround.y(lightDirectionVectorXYZ, ldx); 255 | enddef; 256 | 257 | vardef rotateXYZaround@# (expr p, a) = 258 | save partProj, rv; 259 | pair partProj; 260 | color rv; 261 | if str @# = "x": 262 | partProj := (greenpart(p), bluepart(p)) radRotated -a; 263 | rv := (redpart(p), xpart(partProj), ypart(partProj)); 264 | elseif str @# = "y": 265 | partProj := (redpart(p), bluepart(p)) radRotated -a; 266 | rv := (xpart(partProj), greenpart(p), ypart(partProj)); 267 | elseif str @# = "z": 268 | partProj := (redpart(p), greenpart(p)) radRotated -a; 269 | rv := (xpart(partProj), ypart(partProj), bluepart(p)); 270 | else: 271 | errmessage("What axis is " & str @# & "?"); 272 | fi; 273 | rv 274 | enddef; 275 | 276 | defineLightDirection(-1/8pi, 1/8pi); 277 | 278 | boolean shadowsEnabled; 279 | shadowsEnabled := false; 280 | 281 | % 282 | % To simplify further calculations we need subdivided original path 283 | % 284 | 285 | vardef pathSubdivideBase (expr p, subdivideStep, i) = 286 | save returnPath, sp; 287 | path returnPath, sp; 288 | returnPath := point i of p; 289 | if i 0): 328 | offsetPathLength := arclength(subpath (0, i) of p)/arclength(p); 329 | else: 330 | offsetPathLength := 0; 331 | fi; 332 | returnPath := (arclength(subpath (0, i) of p), offsetFunction); 333 | if (i < length(p)): 334 | % this thing is glitchy, but should be more accurate 335 | %if (arclength(subpath (0, i) of p) < arclength(subpath (0, i + 1/4) of p)): 336 | % offsetPathTime := i + 1/4; 337 | % offsetPathLength := arclength(subpath (0, i + 1/4) of p)/arclength(p); 338 | % instantDirection := unitvector((arclength(subpath (0, i + 1/4) of p), offsetFunction) - point 0 of returnPath); 339 | % offsetPathTime := i + 1; 340 | % offsetPathLength := arclength(subpath (0, i + 1) of p)/arclength(p); 341 | % nextDirection := (arclength(subpath (0, i + 1) of p), offsetFunction); 342 | % offsetPathTime := i + 3/4; 343 | % offsetPathLength := arclength(subpath (0, i + 3/4) of p)/arclength(p); 344 | % nextDirection := unitvector(nextDirection - (arclength(subpath (0, i + 3/4) of p), offsetFunction)); 345 | % returnPath := returnPath{instantDirection} .. {nextDirection}offsetPathTemplate(p, i + 1)(offsetFunction); 346 | % returnPath := returnPath -- offsetPathTemplate(p, i + 1)(offsetFunction); 347 | %else: 348 | returnPath := returnPath -- offsetPathTemplate(p, i + 1)(offsetFunction); 349 | %fi; 350 | fi; 351 | returnPath 352 | enddef; 353 | 354 | % 355 | % This macro creates offset path p based on previously built template q, instead of function itself 356 | % It is loosely based on something called Tiller-Hanson heuristic as described here: 357 | % http://math.stackexchange.com/questions/465782/control-points-of-offset-bezier-curve 358 | % 359 | 360 | vardef offsetPathGenerate (expr p, q, i) = 361 | save returnPath, c, d, a, pl, ps; 362 | path returnPath, pl[]; 363 | pair c[], d[]; 364 | numeric a[]; 365 | c1 := precontrol i of p; 366 | c2 := point i of p; 367 | c3 := postcontrol i of p; 368 | if abs(c1-c2) = 0: 369 | c1 := c2 shifted (c2-c3); 370 | fi; 371 | if abs(c3-c2) = 0: 372 | c3 := c2 shifted (c2-c1); 373 | fi; 374 | if (abs(c1-c2) > 0) and (abs(c2-c3) > 0): 375 | d1 := unitvector(c1-c2) rotated -90; 376 | d2 := unitvector(c2-c3) rotated -90; 377 | pl1 := (unitvector(c2-c1)--unitvector(c1-c2)) 378 | scaled arclength(subpath (i - 1/2, i + 1/2) of p) 379 | shifted (point i of p shifted (d1 scaled ypart(point i of q))); 380 | pl2 := (unitvector(c2-c3)--unitvector(c3-c2)) 381 | scaled arclength(subpath (i - 1/2, i + 1/2) of p) 382 | shifted (point i of p shifted (d2 scaled ypart(point i of q))); 383 | if (abs(angle(d1) - angle(d2)) > 2) and (xpart(pl1 intersectiontimes pl2) > 0): 384 | c4 := pl1 intersectionpoint pl2; 385 | else: 386 | c4 := c2 shifted (d1 scaled ypart(point i of q)); 387 | fi; 388 | returnPath := c4; 389 | else: 390 | returnPath := c2 shifted (unitvector( (point i-1 of p) - (point i+1 of p) rotated -90) scaled ypart (point i of q)); 391 | fi; 392 | if i < length(p): 393 | path ps; 394 | ps := subpath (i, i + 1) of p; 395 | c1 := point 0 of ps; 396 | c2 := postcontrol 0 of ps; 397 | c3 := precontrol 1 of ps; 398 | c4 := point 1 of ps; 399 | c5 := point 0 of returnPath; 400 | if (abs(c3-c4)>0) 401 | and (abs(c1-c2)>0) 402 | and (abs(c1-c4)>0) 403 | and (abs(direction i of q) > 0): 404 | c6 := c4 shifted (unitvector(c4 - c3) rotated 90 scaled ypart(point i + 1 of q)); 405 | %if abs(direction i of q) > 0: 406 | a1 := angle(direction i of q); 407 | %else: 408 | % a1 := angle((point (i + 1/10) of q) - (point (i - 1/10) of q)); 409 | %fi; 410 | %if abs(direction i + 1 of q) > 0: 411 | a2 := angle(direction i + 1 of q); 412 | %else: 413 | % a2 := angle((point (i + 1 + 1/10) of q) - (point (i + 1 - 1/10) of q)); 414 | %fi; 415 | c7 := (c2 - c1) scaled (abs(c5-c6)/abs(c1-c4)) rotated a1 shifted c5; 416 | c8 := (c3 - c4) scaled (abs(c5-c6)/abs(c1-c4)) rotated a2 shifted c6; 417 | returnPath := returnPath .. controls c7 and c8 .. offsetPathGenerate (p, q, i + 1); 418 | else: 419 | returnPath := returnPath -- offsetPathGenerate (p, q, i + 1); 420 | fi; 421 | fi; 422 | returnPath 423 | enddef; 424 | 425 | % 426 | % Frontend for offsetPathGenerate and offsetPathTemplate 427 | % 428 | 429 | vardef offsetPath (expr p)(text offsetFunction) = 430 | offsetPathGenerate (p, offsetPathTemplate(p, 0)(offsetFunction), 0) 431 | enddef; 432 | 433 | % 434 | % Brush macro. It draws line with brush of variable width. 435 | % For parts thicker than minStrokeWidth it uses offsetPath functions' 436 | % results, for thiner parts it draws dashed lines of fixed width 437 | % 438 | 439 | def brushGenerate (expr p, q, i) = 440 | begingroup 441 | save w, brushPath, bt, t; 442 | numeric w[], t[]; 443 | path brushPath[], bt; 444 | bt := q; 445 | w0 := (ypart(urcorner(bt))); 446 | w1 := (ypart(lrcorner(bt))); 447 | t := cutPathTime(bt, minStrokeWidth); 448 | if ((w0 > minStrokeWidth) 449 | and (w1 < minStrokeWidth) 450 | and (t > 0) 451 | and (t < length(p)) 452 | and (arclength(p) > minDashStrokeLength) 453 | and (i < 10)): 454 | brushGenerate (subpath (0, t) of p, subpath (0, t) of q, i + 1); 455 | brushGenerate (subpath (t, length(p)) of p, subpath (t, length(q)) of q, i + 1); 456 | elseif (arclength(p) > 0): 457 | if (w0 > 99/100minStrokeWidth) 458 | and (w1 > 99/100minStrokeWidth): 459 | brushPath1 := offsetPathGenerate (p, q yscaled 1/2, 0); 460 | brushPath2 := offsetPathGenerate (p, q yscaled -1/2, 0); 461 | fill brushPath1 -- reverse(brushPath2) -- cycle; 462 | elseif (w0 < 101/100minStrokeWidth) and (w1 < 101/100minStrokeWidth): 463 | thinBrushGenerate (p, q, 0) 464 | fi; 465 | fi; 466 | endgroup 467 | enddef; 468 | 469 | % 470 | % macro for thin lines which are actually dashed 471 | % 472 | 473 | vardef thinBrushGenerate@#(expr p, q, i) = 474 | begingroup 475 | save w, brushPath, bt, t, h, minLength, minWidth, dashPatternImage; 476 | numeric w[], t[]; 477 | path brushPath[], bt; 478 | picture dashPatternImage; 479 | if (str @# = "") or (str @# = "hatches"): 480 | minLength := minDashStrokeLength; 481 | minWidth := minDashStrokeWidth; 482 | elseif str @# = "stipples": 483 | minLength := minStippleStep; 484 | minWidth := minStippleStrokeWidth; 485 | fi; 486 | bt := q; 487 | w0 := ypart(urcorner(bt)); 488 | w1 := ypart(lrcorner(bt)); 489 | if (w0 > minWidth + 1/100): 490 | if (w1 > minWidth - 1/100): 491 | w2 := floor((1/2(w0 + w1) - minWidth)/dashStrokeWidthStep)*dashStrokeWidthStep + minWidth; 492 | else: 493 | w2 := minWidth; 494 | fi; 495 | t := cutPathTime(bt, w2); 496 | brushPath1 := subpath (0, t) of p; 497 | brushPath2 := subpath (t, length(p)) of p; 498 | if (((w0 - w1) >= dashStrokeWidthStep) and (i < 15)) 499 | and ((arclength(brushPath1) > minLength) 500 | or (arclength(brushPath2) > minLength)) 501 | and (t > 1/100) and (t < length(p) - 1/100): 502 | thinBrushGenerate@#(brushPath1, subpath (0, t) of q, i + 1); 503 | thinBrushGenerate@#(brushPath2, subpath (t, length(q)) of q, i + 1); 504 | else: 505 | if (str @# = "") or (str @# = "hatches"): 506 | if (w2 > minStrokeWidth): 507 | w2 := minStrokeWidth; 508 | fi; 509 | if (w2 >= minWidth) and (arclength(p) > 0): 510 | if (w2 < minStrokeWidth) and (arclength(p) > minLength): 511 | draw p withpen thinpen dashed thinBrushPattern(w2, arclength(p)); 512 | else: 513 | draw p withpen thinpen; 514 | fi; 515 | fi; 516 | elseif str @# = "stipples": 517 | begingroup 518 | interim linecap := rounded; 519 | save stippleSizeVar; 520 | stippleSizeVar := stippleSize; 521 | save stippleSize; 522 | w2 := 1/3w2; 523 | if (w2 >= minWidth) and (arclength(p) > 0): 524 | stippleSize := stippleSizeVar * (0.9 + uniformdeviate(0.3)); 525 | dashPatternImage := stipplesBrushPattern(w2, arclength(p)); 526 | if urcorner(dashPatternImage) <> (0,0): 527 | brushPath1 := offsetPathGenerate (p, (q yscaled 0) shifted (0, 1/3stippleShadingDensity), 0); 528 | draw brushPath1 withpen (pencircle scaled stippleSize) dashed dashPatternImage; 529 | fi; 530 | stippleSize := stippleSizeVar * (0.9 + uniformdeviate(0.3)); 531 | dashPatternImage := stipplesBrushPattern(w2, arclength(p)); 532 | if urcorner(dashPatternImage) <> (0,0): 533 | brushPath2 := offsetPathGenerate (p, (q yscaled 0) shifted (0, -1/3stippleShadingDensity), 0); 534 | draw brushPath2 withpen (pencircle scaled stippleSize) dashed dashPatternImage; 535 | fi; 536 | stippleSize := stippleSizeVar * (0.9 + uniformdeviate(0.3)); 537 | dashPatternImage := stipplesBrushPattern(w2, arclength(p)); 538 | if urcorner(dashPatternImage) <> (0,0): 539 | draw p withpen (pencircle scaled stippleSize) dashed dashPatternImage; 540 | fi; 541 | fi; 542 | endgroup 543 | fi; 544 | fi; 545 | fi; 546 | endgroup 547 | enddef; 548 | 549 | % 550 | % this macro returns path as a shaded edge 551 | % 552 | 553 | vardef shadedEdge (expr p) = 554 | image( 555 | brushGenerate (p, 556 | offsetPathTemplate (p, 0) ( 557 | 1/2minStrokeWidth + 2*minStrokeWidth 558 | * normalVectorToLightness( 559 | sphereAnglesToNormalVector( 560 | (angleRad(point offsetPathTime of p), arcsin(1/2)) 561 | ), 0, point offsetPathTime of p 562 | ) 563 | ), 0); 564 | ) 565 | enddef; 566 | 567 | % 568 | % Whenever we have brush thinner than minStrokeWidth we call this dash pattern macro 569 | % 570 | 571 | vardef thinBrushPattern (expr w, l) = 572 | save d; 573 | numeric d[]; 574 | d0 := w; 575 | if d0 > minStrokeWidth: d0 := minStrokeWidth; fi; 576 | % d1 is a result of some arbitrary function of line width 577 | % we do not use simple linear function because minimal dash length 578 | % also shouldn't be less than minStrokeWidth. 579 | % After we get d1 other measurements are calculated, 580 | % so filled area per unit length remains adequate and dashes are aligned 581 | % with segments 582 | % d1*mSW = (d1*w + d2*w) -> d2=d1(mSW-w)/w 583 | d1 := (1/2minDashStrokeLength) + (((d0/minStrokeWidth)**(5/2))*1/2minDashStrokeLength); 584 | d1 := d1 + 1/2uniformdeviate(d1); 585 | d2 := (minStrokeWidth - d0)*(d1/d0); 586 | d3 := round(l/(d2 + d1)); 587 | if (d3 < 1): d3 := 1; fi; 588 | d4 := (l/d3)/(d2 + d1); 589 | d1 := d1*d4; 590 | d2 := d2*d4; 591 | if (uniformdeviate(2) > 1): 592 | dashpattern (on d1/2 off d2 on d1/2) 593 | else: 594 | dashpattern (off d2/2 on d1 off d2/2) 595 | fi 596 | enddef; 597 | 598 | 599 | % 600 | % Stipples are also dashes 601 | % 602 | 603 | vardef stipplesBrushPattern (expr w, l) = 604 | save d, n, rn, rv, ss; 605 | ss := 1/1000; 606 | numeric d[]; 607 | picture rv; 608 | %if w > stippleSize: 609 | % d0 := minStippleStep; 610 | %else: 611 | n := (w*l)/(stippleSize**2); 612 | rn := floor(n); 613 | if rn > 0: 614 | d0 := l/rn; 615 | fi; 616 | %fi; 617 | if rn > 0: 618 | d1 := uniformdeviate(d0); 619 | d2 := d0-d1; 620 | if rn >=3: 621 | d3 := uniformdeviate(d0); 622 | d4 := d0-d3; 623 | %if uniformdeviate(2) > 1: 624 | % d5 := uniformdeviate(d0); 625 | % d6 := d0-d5; 626 | % rv := dashpattern (off d1 on ss off (d2+d5)-ss on ss off (d4+d6)-ss on ss off d3-ss); 627 | %else: 628 | rv := dashpattern (off d1 on ss off (d2+d3)-ss on ss off d4-ss); 629 | %fi; 630 | else: 631 | rv := dashpattern (off d1 on ss off d2-ss); 632 | fi; 633 | else: 634 | if uniformdeviate(1) < n: 635 | rv := dashpattern (off uniformdeviate(l-ss) on ss off l); 636 | else: 637 | rv := image(); 638 | fi; 639 | fi; 640 | rv 641 | enddef; 642 | 643 | % 644 | % macro that actually draws line of variable width 645 | % 646 | 647 | vardef brush (expr p) (text offsetFunction) = 648 | image( 649 | brushGenerate (p, offsetPathTemplate(p, 0)(offsetFunction), 0); 650 | ) 651 | enddef; 652 | 653 | % 654 | % same, but only for thin brushes 655 | % 656 | 657 | vardef thinBrush@#(expr p) (text offsetFunction) = 658 | image( 659 | thinBrushGenerate@#(p, offsetPathTemplate(p, 0)(offsetFunction), 0); 660 | ) 661 | enddef; 662 | 663 | % 664 | % This macro generates tube between paths p and q, of variable width d 665 | % Tube is subdivided into segments in such a way that within every segment 666 | % we need 2**n lines to generate even fill 667 | % 668 | 669 | vardef tubeGenerate@#(expr p, q, d, i) = 670 | save w, bw, k, t, tubeWidth, sp, currentPath, currentTubePath, currentDepth, lineDensity; 671 | numeric w[], bw[], t, currentDepth; 672 | path tubeWidth, sp, currentPath, currentTubePath; 673 | tubeWidth := d yscaled 2; 674 | if (str @# = "") or (str @# = "hatches"): 675 | lineDensity := shadingDensity; 676 | elseif (str @# = "stipples"): 677 | lineDensity := stippleShadingDensity; 678 | fi; 679 | w0 := (ypart(urcorner(tubeWidth))) - 1/1000; 680 | w1 := (ypart(lrcorner(tubeWidth))) + 1/1000; 681 | w2 := ceiling(log(w0/lineDensity, 2)); 682 | w3 := ceiling(log(w1/lineDensity, 2)); 683 | if ((w2 > w3) and (i<20)): 684 | t := cutPathTime(tubeWidth, lineDensity*(2**(w2-1))); 685 | tubeGenerate@#(subpath (0, t) of p, subpath (0, t) of q, subpath (0, t) of d, i + 1); 686 | tubeGenerate@#(subpath (t, length(p)) of p, subpath (t, length(q)) of q, subpath (t, length(d)) of d, i + 1); 687 | else: 688 | if (arclength(p) > 0) and (arclength(q) > 0): 689 | bw1 := 2**w2; 690 | currentTubePath := interpath (1/2, q, p); 691 | for k := 0 upto bw1: 692 | currentPath := interpath (k/bw1, q, p); 693 | angleOnTube := arcsin(((k/bw1)*2) - 1); 694 | currentDepth := -abs((1-sin(angleOnTube + 1/2pi))*w0); 695 | if shadowsEnabled: 696 | currentPath := shadowCut(currentPath, currentDepth); 697 | fi; 698 | if (str @# = "") or (str @# = "hatches"): 699 | brushGenerate (currentPath, 700 | offsetPathTemplate(currentPath, 0)( 701 | maxShadingStrokeWidth 702 | if odd (k): * (abs(ypart(point offsetPathTime of tubeWidth)/bw1) - 1/2lineDensity) fi 703 | * normalVectorToLightness( 704 | tubeAnglesToNormalVector(( 705 | angleOnTube, 706 | angleRad(direction offsetPathTime of currentTubePath), 707 | angleRad(direction offsetPathTime of (tubeWidth yscaled 1/2)) 708 | )), currentDepth, point offsetPathTime of currentPath) 709 | ), 0); 710 | elseif (str @# = "stipples"): 711 | begingroup 712 | save stippleShadingDensity; 713 | if w2 > 0: 714 | stippleShadingDensity := 2w0/(2**w2); % When the distance between the lines changes, wtipples should spread further apart 715 | else: 716 | stippleShadingDensity := w0; 717 | fi; 718 | thinBrushGenerate.@#(currentPath, 719 | offsetPathTemplate(currentPath, 0)( 720 | stippleSize 721 | if odd (k): * (abs(ypart(point offsetPathTime of tubeWidth)/bw1) - 1/2lineDensity) fi 722 | * normalVectorToLightness( 723 | tubeAnglesToNormalVector(( 724 | angleOnTube, 725 | angleRad(direction offsetPathTime of currentTubePath), 726 | angleRad(direction offsetPathTime of (tubeWidth yscaled 1/2)) 727 | )), currentDepth, point offsetPathTime of currentPath) 728 | ), 0); 729 | endgroup 730 | fi; 731 | endfor; 732 | fi; 733 | fi; 734 | enddef; 735 | 736 | % 737 | % This macro is analogous to tubeGenerate, but draws transverse strokes 738 | % result is somewhat suboptimal for now, but in simple cases it works ok 739 | % 740 | 741 | def tubeGenerateAlt (expr p, q, d) = 742 | begingroup 743 | save spth, lpth, currentPath, pos, t, pthdir, corr, o, l, i, j, k, tubeAngle, pathAngle, scorr, dt; 744 | numeric l[]; 745 | path spth, lpth, currentPath; 746 | pos := 0; 747 | j := 0; 748 | forever: 749 | dt := (xpart(point pos of d) + 1/2shadingDensity); 750 | scorr := cosd(angle(direction xpart(d intersectiontimes ((dt, ypart(lrcorner(d))) -- (dt, ypart(urcorner(d))))) of d)); 751 | t1 := arctime ((arclength(subpath(0, pos) of p)) + shadingDensity/scorr) of p; 752 | t2 := arctime ((arclength(subpath(0, pos) of q)) + shadingDensity/scorr) of q; 753 | if (arclength(subpath(pos, t1) of p) < arclength(subpath(pos, t1) of q)): 754 | pthdir := -1; 755 | t3 := t1; 756 | else: 757 | pthdir := 1; 758 | t3 := t2; 759 | fi; 760 | corr := round(arclength(subpath(pos, t3) of if pthdir = 1: p else: q fi)/(shadingDensity/scorr)); 761 | if (corr < 1): corr := 1; fi; 762 | corr := (arclength(subpath(pos, t3) of if pthdir = 1: p else: q fi) - (corr*(shadingDensity/scorr)))/corr; 763 | t3 := arctime (arclength(subpath(0, t3) of if pthdir = 1: q else: p fi) - 1/3corr) of if pthdir = 1: q else: p fi; 764 | spth := subpath(pos, t3) of if pthdir = 1: q else: p fi; 765 | lpth := subpath(pos, t3) of if pthdir = 1: p else: q fi; 766 | tubeAngle := angleRad(direction 1/2[pos, t3] of d); 767 | pathAngle := angleRad(direction 1/2 of interpath (1/2, spth, lpth)); 768 | pos := t3; 769 | l1 := round(arclength(lpth)/(shadingDensity/scorr)); 770 | if (l1 < 1): l1 := 1; fi; 771 | l2 := arclength(lpth)/(l1*(shadingDensity/scorr)); 772 | for i := 0 upto l1 - 1: 773 | j := j + 1; 774 | k := i*(arclength(lpth)/l1); 775 | currentPath := point (arctime k of lpth) of spth -- point (arctime k of lpth) of lpth; 776 | currentPath := offsetPathSubdivide(currentPath); 777 | brushGenerate ( 778 | currentPath, 779 | offsetPathTemplate(currentPath, 0)( 780 | maxShadingStrokeWidth 781 | * orderFade(offsetPathLength[1/l1, l2], j) 782 | * normalVectorToLightness( 783 | tubeAnglesToNormalVector(( 784 | arcsin(pthdir*((offsetPathLength*2)-1)), 785 | pathAngle, 786 | tubeAngle) 787 | ), -2(1/2arclength(currentPath))+sqrt(1 - (2offsetPathLength - 1)**2)*(1/2arclength(currentPath)), point offsetPathTime of currentPath) 788 | ) 789 | , 0); 790 | endfor; 791 | exitif pos >= length(p); 792 | endfor; 793 | endgroup 794 | enddef; 795 | 796 | % 797 | % This macro converts some measurements of point on tube to absolute angle. 798 | % Since there are three such measurements, macro gets them as as a single 799 | % argument of "color" type, in case it would eventually appear as a result 800 | % of some other macro. 801 | % 802 | % redpart is the angle on the tube's circumference 803 | % greenpart is the angle of the tube path 804 | % bluepart is the angle of the tube's outline 805 | % 806 | 807 | vardef tubeAnglesToNormalVector (expr p) = 808 | save normalVector; 809 | color normalVector; 810 | normalVector := (0, 0, 1); 811 | normalVector := rotateXYZaround.y(normalVector, -bluepart(p)); 812 | normalVector := rotateXYZaround.x(normalVector, redpart(p)); 813 | normalVector := rotateXYZaround.z(normalVector, -greenpart(p)); 814 | normalVector 815 | enddef; 816 | 817 | % 818 | % frontend to simplify tube drawing. tubeOutline variable changes on every call 819 | % of the function and can be used afterwards. 820 | % 821 | 822 | path tubeOutline; 823 | boolean drawTubeEnds; 824 | drawTubeEnds := true; 825 | 826 | vardef tube@#(expr p)(text offsetFunction)= 827 | save q, respic; 828 | path q[]; 829 | picture respic; 830 | q0 := offsetPathSubdivide(p); 831 | q1 := offsetPathTemplate(q0, 0)(offsetFunction); 832 | q2 := offsetPathGenerate (q0, q1, 0); 833 | q3 := offsetPathGenerate (q0, q1 yscaled -1, 0); 834 | tubeOutline := q3--reverse(q2)--cycle; 835 | if str @# = "e": 836 | if not drawTubeEnds: 837 | image( 838 | draw q2 withpen thinpen; 839 | draw q3 withpen thinpen; 840 | ) 841 | else: 842 | tubeOutline 843 | fi 844 | else: 845 | image( 846 | if str @# = "l": 847 | respic := image(tubeGenerate (q2, q3, q1, 0);); 848 | elseif str @# = "s": 849 | respic := image(tubeGenerate.stipples(q2, q3, q1, 0);) 850 | elseif str @# = "t": 851 | respic := image(tubeGenerateAlt (q2, q3, q1);); 852 | fi; 853 | if (cycle p) or (not drawTubeEnds): 854 | draw q2 withpen thinpen; 855 | draw q3 withpen thinpen; 856 | else: 857 | draw q2--reverse(q3)--cycle withpen thinpen; 858 | fi; 859 | clip respic to (q2--reverse(q3)--cycle); 860 | draw respic; 861 | ) 862 | fi 863 | enddef; 864 | 865 | % 866 | % Sphere can be used as a cap for a tube, so it has same 2**n lines. 867 | % 868 | 869 | vardef sphere@#(expr d) = 870 | save currentCircle, origCircle, currentRadius, currentDepth, order, circleThickness, lineDensity, shadingPicture; 871 | path currentCircle, origCircle; 872 | numeric currentRadius, currentDepth, order; 873 | picture shadingPicture; 874 | if (str @# = "") or (str @# = "c"): 875 | lineDensity := shadingDensity; 876 | elseif (str @# = "s"): 877 | lineDensity := stippleShadingDensity; 878 | fi; 879 | origCircle := fullcircle; 880 | order := 2**ceiling(log((1/2d)/lineDensity, 2)); 881 | image( 882 | draw fullcircle scaled d withpen thinpen; 883 | shadingPicture := image( 884 | for i := 1 upto order: 885 | currentRadius := i/order; 886 | currentCircle := origCircle scaled (currentRadius*d) rotated uniformdeviate (1/4pi); 887 | if odd(i): 888 | circleThickness := maxShadingStrokeWidth * ((abs(d - (lineDensity*order)))/order); 889 | else: 890 | circleThickness := maxShadingStrokeWidth; 891 | fi; 892 | currentDepth:= -(1-sqrt(1-currentRadius**2))*(1/2d); 893 | if shadowsEnabled: 894 | currentCircle := shadowCut(currentCircle, currentDepth); 895 | fi; 896 | if (str @# = "") or (str @# = "c"): 897 | brushGenerate (currentCircle, 898 | offsetPathTemplate (currentCircle, 0) ( 899 | circleThickness 900 | * normalVectorToLightness( 901 | sphereAnglesToNormalVector( 902 | (angleRad(point offsetPathTime of currentCircle), arcsin(currentRadius)) 903 | ), currentDepth, point offsetPathTime of currentCircle 904 | ) 905 | ), 0); 906 | elseif (str @# = "s"): 907 | begingroup 908 | save stippleShadingDensity; 909 | if order > 0: 910 | stippleShadingDensity := d/order; % When the distance between the lines changes, wtipples should spread further ap 911 | else: 912 | stippleShadingDensity := 1/2d; 913 | fi; 914 | thinBrushGenerate.stipples(currentCircle, 915 | offsetPathTemplate (currentCircle, 0) ( 916 | circleThickness 917 | * normalVectorToLightness( 918 | sphereAnglesToNormalVector( 919 | (angleRad(point offsetPathTime of currentCircle), arcsin(currentRadius)) 920 | ), currentDepth, point offsetPathTime of currentCircle 921 | ) 922 | ), 0); 923 | endgroup 924 | fi; 925 | endfor; 926 | ); 927 | clip shadingPicture to (fullcircle scaled d); 928 | draw shadingPicture; 929 | ) 930 | enddef; 931 | 932 | % 933 | % Alternative sphere macro. It's all about latitudinal strokes. 934 | % The idea is: when we have a sphere with evenly distributed parallel strokes 935 | % we know how their density rises towards edge in a projection, 936 | % so all we need to do is to fade lines correspondingly 937 | % 938 | 939 | vardef sphereLat (expr d, lat) = 940 | save p, a, x, y, sphlat, latrad, n, c, currentPath, nline, tlat; 941 | path p[], currentPath, currentArc; 942 | sphlat := 0; 943 | nline := 0; 944 | latrad := (2pi*lat/360); 945 | n := ceiling((pi*1/2d)/shadingDensity); 946 | if (cosd(lat) <> 0): tlat := (sind(lat)/cosd(lat)); fi; 947 | image( 948 | draw fullcircle scaled d withpen thinpen; 949 | p0 := fullcircle rotated 90; 950 | for nline := 1 upto n-1: 951 | sphlat := nline*(pi/n); 952 | if (sphlat + latrad < pi) and (sphlat + latrad > 0): 953 | if (cosd(lat) <> 0): 954 | if (sin(sphlat) <> 0): 955 | x := tlat*(cos(sphlat)/sin(sphlat)); 956 | else: 957 | x := 0; 958 | fi; 959 | else: 960 | if ((sphlat > 1/2pi) and (lat > 0)) or ((sphlat < 1/2pi) and (lat < 0)): 961 | x := -2; 962 | else: 963 | x := 2; 964 | fi; 965 | fi; 966 | if (abs(x) <= 1): 967 | y := arcsin(x); 968 | p1 := subpath(6 + 8y/2pi, 2 - 8y/2pi) of p0; 969 | else: 970 | p1 := p0; 971 | fi; 972 | if (x > -1) and (arclength(p1) > 0): 973 | currentPath := (p1 scaled (d*sin(sphlat)) yscaled sind(lat)) shifted (0, 1/2d*cos(sphlat)*cosd(lat)); 974 | currentPath := offsetPathSubdivide(currentPath); 975 | brushGenerate(currentPath, 976 | offsetPathTemplate(currentPath, 0)( 977 | maxShadingStrokeWidth * orderFade( 978 | sqrt(1 - 979 | abs( 980 | ypart(point offsetPathTime of currentPath)/(1/2d), 981 | 1 - abs( 982 | 1 - abs( 983 | xpart(point offsetPathTime of currentPath) 984 | /(1/2d) 985 | ) 986 | )**abs(sind(lat)) 987 | )**2) 988 | , nline) 989 | * normalVectorToLightness( 990 | sphereAnglesToNormalVector(( 991 | ( 992 | if (abs(point offsetPathTime of currentPath) > 0): 993 | angleRad(point offsetPathTime of currentPath) 994 | else: 995 | 0 996 | fi 997 | ), arcsin(2abs(point offsetPathTime of currentPath)/(d+1))) 998 | ), 0, point offsetPathTime of currentPath) 999 | ), 0); 1000 | fi; 1001 | fi; 1002 | endfor; 1003 | ) 1004 | enddef; 1005 | 1006 | vardef orderFade (expr v, n)= 1007 | save o; 1008 | if (v > 1/256): 1009 | o := 2**ceiling(log(1/v, 2)); 1010 | if ((n mod 1/2o) = 0): 1011 | if ((n mod o) = 0): 1012 | 1 1013 | else: 1014 | (v*o) - 1 1015 | fi 1016 | else: 1017 | 0 1018 | fi 1019 | else: 1020 | 0 1021 | fi 1022 | enddef; 1023 | 1024 | % 1025 | % This one converts point location on sphere to normal vector 1026 | % 1027 | 1028 | vardef sphereAnglesToNormalVector (expr p) = 1029 | save normalVector; 1030 | color normalVector; 1031 | normalVector := (0, 0, 1); 1032 | normalVector := rotateXYZaround.y(normalVector, ypart(p)); 1033 | normalVector := rotateXYZaround.z(normalVector, -xpart(p)); 1034 | normalVector 1035 | enddef; 1036 | 1037 | % 1038 | % Once we get two angles at some point of some surface, we can compute light intensity there. 1039 | % 1040 | 1041 | % In case you need to have your shaded objects white-on-black, 1042 | % you can just switch invertedLight invertedLight to 'true' 1043 | 1044 | boolean invertedLight; 1045 | invertedLight := false; 1046 | 1047 | vardef normalVectorToLightness (expr normalVector, d, q) = 1048 | save returnValue, shiftedShadowPath; 1049 | path shiftedShadowPath; 1050 | if shadowsEnabled: 1051 | for i := 0 step 1 until numberOfShadows: 1052 | shiftedShadowPath := shadowPath[i] shifted 1053 | ((redpart(lightDirectionVectorXYZ), greenpart(lightDirectionVectorXYZ)) 1054 | scaled ((d-shadowDepth[i])*bluepart(lightDirectionVectorXYZ))); 1055 | if q isInside shiftedShadowPath: 1056 | returnValue := 1; 1057 | fi; 1058 | endfor; 1059 | fi; 1060 | if not known returnValue: 1061 | returnValue := 1 - (normalVector dotprodXYZ lightDirectionVectorXYZ); 1062 | returnValue := lightnessPP(returnValue); 1063 | fi; 1064 | if returnValue > 1: 1065 | returnValue := 1; 1066 | fi; 1067 | if returnValue < 0: 1068 | returnValue := 0; 1069 | fi; 1070 | if invertedLight: 1071 | returnValue := 1 - returnValue; 1072 | fi; 1073 | returnValue 1074 | enddef; 1075 | 1076 | vardef lightnessPP (expr v) = 1077 | v 1078 | enddef; 1079 | 1080 | % Shadows are global 1081 | 1082 | path shadowPath[]; 1083 | numeric shadowDepth[]; 1084 | 1085 | % Shadows either require high path resolution, or some points 1086 | % on a path in just the right place for shadows. 1087 | % This macro adds such points. 1088 | 1089 | vardef shadowCut (expr pathToCut, currentDepth)= 1090 | save shiftedShadowPath, pathShadowIntersection, pathShadowCut, currentPath; 1091 | path shiftedShadowPath, currentPath; 1092 | pair pathShadowIntersection; 1093 | numeric pathShadowCut; 1094 | currentPath := pathToCut; 1095 | for j := 0 step 1 until numberOfShadows: 1096 | shiftedShadowPath := shadowPath[j] shifted 1097 | ((redpart(lightDirectionVectorXYZ), greenpart(lightDirectionVectorXYZ)) 1098 | scaled ((currentDepth - shadowDepth[j])*bluepart(lightDirectionVectorXYZ))); 1099 | forever: 1100 | pathShadowIntersection := shiftedShadowPath firstIntersectionTimes currentPath; 1101 | pathShadowCut := ypart(pathShadowIntersection); 1102 | if (pathShadowCut > 1/10) and (pathShadowCut < length(currentPath) - 1/10): 1103 | currentPath := (subpath (0, pathShadowCut - 1/20) of currentPath) .. (subpath (pathShadowCut + 1/20, length(currentPath)) of currentPath); 1104 | fi; 1105 | shiftedShadowPath := subpath (xpart(pathShadowIntersection) + 1/5, length(shiftedShadowPath)) of shiftedShadowPath; 1106 | exitif (pathShadowCut = -1); 1107 | endfor; 1108 | endfor; 1109 | currentPath 1110 | enddef; 1111 | 1112 | % 1113 | % Several macros rely on cutting offset path template at given height. 1114 | % Taking cutting points closer to the middle gives better results, and that's 1115 | % just what this macro tries to do. 1116 | % 1117 | 1118 | vardef cutPathTime (expr p, h) = 1119 | save cutTime, d; 1120 | numeric cutTime[], d[]; 1121 | d1 := xpart(urcorner(p)); 1122 | d2 := xpart(ulcorner(p)); 1123 | if (d2 < d1): 1124 | d3 := 1/2(d1 + d2); 1125 | cutTime1 := ypart(((d3, h) -- (d1, h)) firstIntersectionTimes p); 1126 | cutTime2 := ypart(((d3, h) -- (d2, h)) firstIntersectionTimes p); 1127 | d4 := xpart (point cutTime1 of p); 1128 | d5 := xpart (point cutTime2 of p); 1129 | if abs(d4-d3) < abs(d5-d3): 1130 | cutTime3 := cutTime1 1131 | else: 1132 | cutTime3 := cutTime2 1133 | fi; 1134 | else: 1135 | cutTime3 := -1; 1136 | fi; 1137 | cutTime3 1138 | enddef; 1139 | 1140 | % 1141 | % This macro calculates ray angle after refraction. It takes raw angles (one of ray — p and one of surface — q) 1142 | % and refraction indices ratio. Whether ray comes from opticaly denser material is determined by direction of q 1143 | % relative to that of p 1144 | % 1145 | 1146 | vardef refractionAngle (expr p, q, n) = 1147 | save a; 1148 | numeric a[]; 1149 | a0 := p - q; 1150 | if (sin(a0) < 0): 1151 | a1 := cos(a0 + pi) * n; 1152 | a2 := pi; 1153 | else: 1154 | a1 := cos(a0) / n; 1155 | a2 := 0; 1156 | fi; 1157 | if abs(a1) <= 1: 1158 | a3 := arccos(a1) + q + a2; 1159 | else: 1160 | a3 := -1000; 1161 | fi; 1162 | a3 1163 | enddef; 1164 | 1165 | % 1166 | % Same thing for reflection angle, just in case 1167 | % 1168 | 1169 | vardef reflectionAngle (expr p, q) = 1170 | (2pi - p + 2q) 1171 | enddef; 1172 | 1173 | % 1174 | % This macro returns path of ray 'sa' (which can actually be any path, but only ray from next to last to last point 1175 | % will count) refracted with coef. n through some shape p; if ray can't be refracted and, therefore, totally reflected, 1176 | % it will contunue as reflected from that point. i is total number of refractions to compute; 1177 | % 1178 | 1179 | vardef refractionPathR (expr sa, p, n, i, mn) = 1180 | save ray, resultRay, d, s, a, iT; 1181 | path ray, resultRay; 1182 | pair s, iT; 1183 | numeric d[], a; 1184 | s := point (length(sa) - 1) of sa; 1185 | a := angleRad((point (length(sa)) of sa)-(point (length(sa) - 1) of sa)); 1186 | ray := (s shifted (-dirRad(a) scaled 2)) -- s -- (s shifted (dirRad(a) scaled (abs(llcorner(p)-(urcorner(p))) + abs(s-(center(p)))))); 1187 | if (i > 0): ray := subpath (1 + 1/1000, 2) of ray; fi; 1188 | iT := ray firstIntersectionTimes p; 1189 | d1 := xpart(iT); 1190 | d2 := ypart(iT); 1191 | d3 := a; 1192 | d4 := angleRad(direction d2 of p); 1193 | if (n > 0): 1194 | d5 := refractionAngle(d3, d4, n); 1195 | if (d5 < -100) and (d2 >= 0): 1196 | d5 := reflectionAngle(d3, d4); 1197 | fi; 1198 | else: 1199 | d5 := reflectionAngle(d3, d4); 1200 | fi; 1201 | if (d1 >= 0) and (i < mn) and (d5 > -100): 1202 | resultRay := (subpath (0, length(sa) - 1) of sa) -- refractionPathR(point d2 of p -- (point d2 of p shifted dirRad(d5)), p, n, i + 1, mn); 1203 | else: 1204 | if (d5 > -100) or (d1 < 0): 1205 | resultRay := subpath (0, 1/2) of ray; 1206 | else: 1207 | resultRay := subpath (0, d1) of ray; 1208 | fi; 1209 | fi; 1210 | resultRay 1211 | enddef; 1212 | 1213 | vardef refractionPath (expr sa, p, n) = 1214 | refractionPathR(sa, p, n, 0, 10) 1215 | enddef; 1216 | 1217 | % 1218 | % These macros are for isolines. cLine draws continuous line and is called by isoLines. 1219 | % For now they are only used to draw wood texture, but can be used elsewhere 1220 | % 1221 | 1222 | % 1223 | % isoLines goes through i by j matrix of nodes (xy), looking for a square, that has some of its 1224 | % angles below zero and some - above, when found, it calls cLine, that tries to build segment of 1225 | % isoline, that happen to go through abovementioned square. Thickness of line is 1226 | % controlled by values in v array. 1227 | % All squares with lines already drawn through are ignored. 1228 | % 1229 | 1230 | vardef isoLines (suffix xy)(expr cs, l, s) = 1231 | save xxyy, i, j, c, v, sqB, iL, lvl, isNotMasked; 1232 | numeric c[], v[], sqB, sqbM; 1233 | boolean isNotMasked, xxyy[][]; 1234 | isNotMasked := true; 1235 | lvl := l; 1236 | path iL; 1237 | image( 1238 | for i := 0 step 1 until xpart(cs) - 1: 1239 | for j := 0 step 1 until ypart(cs) - 1: 1240 | if (boolean isoLinesMask[i][j]): 1241 | isNotMasked := isoLinesMask[i][j]; 1242 | fi; 1243 | if isNotMasked: 1244 | if (unknown xxyy[i][j]): 1245 | c1 := xy[i][j]+lvl; 1246 | c2 := xy[i][j+1]+lvl; 1247 | c3 := xy[i+1][j]+lvl; 1248 | c4 := xy[i+1][j+1]+lvl; 1249 | sqB := 0; 1250 | sqBm := 0; 1251 | if (abs(sign(c1)+sign(c2)+sign(c3)+sign(c4)) < 4): 1252 | iL := cLine (xy)((i, j), (0, 0), 0, cs) scaled s; 1253 | brushGenerate (reverse(iL), 1254 | offsetPathTemplate(iL, 0)( 1255 | 1/16minStrokeWidth 1256 | /(1/64 + 2( 1257 | if (offsetPathTime < length(iL) - 1): 1258 | (offsetPathTime - floor(offsetPathTime)) 1259 | [v[floor(sqB + offsetPathTime)], 1260 | v[ceiling(sqB + offsetPathTime)]] 1261 | else: 1262 | 1 1263 | fi 1264 | )) 1265 | ) 1266 | , 0); 1267 | fi; 1268 | fi; 1269 | fi; 1270 | endfor; 1271 | endfor; 1272 | draw (0,0); 1273 | ) 1274 | enddef; 1275 | 1276 | % cLine tries to generate continouos segment of an isoline 1277 | 1278 | vardef cLine (suffix xy)(expr ij, dr, st, cs) = 1279 | save p, d, dd, n, i, j, k, outputPath, sqS, cp, dp, nd, isNotMasked; 1280 | pair p[], d[], dd[], cp[], dp[]; 1281 | path outputPath; 1282 | boolean isNotMasked; 1283 | isNotMasked := true; 1284 | i := xpart(ij); 1285 | j := ypart(ij); 1286 | sqS := 0; 1287 | if (boolean isoLinesMask[i][j]): 1288 | isNotMasked := isoLinesMask[i][j]; 1289 | fi; 1290 | if (i >= 0) and (i <= xpart(cs)-1) and (j >= 0) and (j <= ypart(cs)-1): 1291 | n := 0; 1292 | c1 := xy[i][j] + lvl; d1:= (i, j); 1293 | c2 := xy[i][j+1] + lvl; d2:= (i, j+1); 1294 | c3 := xy[i+1][j] + lvl; d3:= (i+1, j); 1295 | c4 := xy[i+1][j+1] + lvl; d4:= (i+1, j+1); 1296 | cp1 := (1, 2); dp1 := (-1, 0); 1297 | cp2 := (1, 3); dp2 := (0, -1); 1298 | cp3 := (2, 4); dp3 := (0, 1); 1299 | cp4 := (3, 4); dp4 := (1, 0); 1300 | for k := 1 upto 4: 1301 | c5 := c[xpart(cp[k])]; d5 := d[xpart(cp[k])]; 1302 | c6 := c[ypart(cp[k])]; d6 := d[ypart(cp[k])]; 1303 | if (sign(c5)) <> (sign(c6)): 1304 | n := n + 1; 1305 | p[n] := (abs(-c5/(c6-c5)))[d5, d6]; 1306 | dd[n] := dp[k]; 1307 | fi; 1308 | endfor; 1309 | sqS := max(c1, c2, c3, c4) - min(c1, c2, c3, c4); 1310 | if (unknown xxyy[i][j]) and isNotMasked: 1311 | xxyy[i][j] := true; 1312 | if (boolean isoLinesMask[i][j]): 1313 | isoLinesMask[i][j] := false; 1314 | fi; 1315 | if (dr = (0, 0)): 1316 | outputPath := cLine (xy)(ij shifted dd2, dd2, st + 1,cs) -- p1 -- p2 -- cLine (xy)(ij shifted dd1, dd1, st - 1,cs); 1317 | else: 1318 | nd := 0; 1319 | if (unknown(xxyy[i + xpart(dd1)][j + ypart(dd1)])): 1320 | nd := 1; 1321 | elseif (unknown(xxyy[i + xpart(dd2)][j + ypart(dd2)])): 1322 | nd := 2; 1323 | fi; 1324 | if nd > 0: 1325 | outputPath := cLine (xy)(ij shifted dd[nd], dd[nd], st + sign(st),cs); 1326 | p3 := p[nd]; 1327 | if (st > 0): 1328 | outputPath := outputPath -- p3; 1329 | else: 1330 | outputPath := p3 -- outputPath; 1331 | fi; 1332 | else: 1333 | outputPath := 1/2[p1, p2]; 1334 | fi; 1335 | fi; 1336 | else: 1337 | outputPath := 1/2[p1, p2]; 1338 | fi; 1339 | else: 1340 | outputPath := (i, j); 1341 | xxyy[i][j] := true; 1342 | if (boolean isoLinesMask[i][j]): 1343 | isoLinesMask[i][j] := false; 1344 | fi; 1345 | fi; 1346 | if (st < sqB): sqB := st; fi; 1347 | if (st > sqBm): sqBm := st; fi; 1348 | v[st] := sqS; 1349 | outputPath 1350 | enddef; 1351 | 1352 | % 1353 | % 1354 | % 1355 | % In following section are gathered all the things for some commonly used 1356 | % real life objects 1357 | % 1358 | % 1359 | % 1360 | 1361 | % 1362 | % Though there's a decent library to deal with geography for mp already 1363 | % (http://melusine.eu.org/lab/bmp/a_mp-geo), here's some basic globe-drawing 1364 | % routine for simple cases, note that latitude starts from the pole, 1365 | % not from the equator (for convenience sake) 1366 | % Below some landmasses are defined 1367 | % 1368 | 1369 | path landmass[]; 1370 | landmass1 := (206, 122.33)--(211.07, 116)--(213.3, 109.94)--(218.57, 106.03)--(218.38, 97.36)--(220.28, 91.28)--(229.75, 78.07)--(221.41, 78.29)--(220.78, 76.52)--(218.07, 74.48)--(213.8, 66.08)--(213.38, 62.04)--(222.31, 77.1)--(233.88, 72.27)--(237.79, 68.59)--(234.88, 64.69)--(229.83, 65.57)--(228.98, 64.73)--(227.37, 59.82)--(250.57, 68.12)--(254.63, 80.83)--(257.07, 80.93)--(257.38, 80.52)--(258.64, 75.5)--(266.4, 68.48)--(269.56, 67.49)--(271.88, 70.43)--(272.67, 74.49)--(275.36, 72.94)--(276.87, 78.6)--(276.68, 79.04)--(276.11, 79.28)--(276.3, 80.22)--(276.75, 79.96)--(276.56, 82.38)--(277.05, 82.04)--(280.5, 86.44)--(277.25, 85.56)--(276.55, 88.03)--(279.47, 92.77)--(283.29, 92.25)--(282.68, 90.91)--(283.74, 90.4)--(282.53, 89.58)--(283.03, 88.6)--(278.44, 80.08)--(279.15, 76.64)--(281.08, 78.25)--(282.29, 80.21)--(285.35, 79.72)--(288, 77.83)--(284.21, 71.22)--(287.94, 68.57)--(288, 68.6)--(288.74, 69.82)--(300.09, 61.89)--(300.86, 59.94)--(299.36, 59.63)--(297.64, 55.13)--(301.24, 52.55)--(296.1, 51.5)--(300.45, 49.51)--(299.83, 50.75)--(299.84, 50.82)--(299.44, 51.42)--(303.59, 50.57)--(302.72, 51.9)--(302.96, 52.12)--(304.97, 52.87)--(304.12, 55.13)--(307.89, 53.38)--(306.37, 50.11)--(308.65, 47.92)--(315.01, 45.12)--(319.69, 40.31)--(320.43, 44.25)--(321.66, 44.31)--(323.19, 41.66)--(320.37, 35.59)--(318.47, 37.21)--(315.99, 36.32)--(313.68, 35.16)--(320.43, 31.11)--(332.73, 30.38)--(338.5, 28.24)--(340.91, 28.61)--(334.92, 32.27)--(335, 39.2)--(340.58, 35.32)--(341.69, 32.15)--(340.43, 31.93)--(344.49, 29.68)--(352.49, 28.33)--(355.9, 25.35)--(358.67, 24.01)--(366.1, 25.61)--(368.78, 23.99)--(319.11, 17.34)--(309.82, 19)--(308.23, 18.4)--(307.69, 16.74)--(297.49, 16.63)--(290.61, 13.26)--(285.38, 13.37)--(284.06, 12.79)--(258.59, 16.61)--(260.79, 18.13)--(254.13, 18.01)--(253.53, 17.04)--(252.25, 17.02)--(252.44, 18.56)--(253.69, 19.64)--(251.71, 20.89)--(249.66, 16.97)--(245.54, 19.39)--(236.64, 19.73)--(239.08, 21)--(237.57, 21.46)--(232.4, 21.62)--(232.29, 21.34)--(225.16, 22.27)--(221.46, 21.23)--(218.52, 25.09)--(216.81, 24.69)--(214.76, 24.93)--(214.95, 25.52)--(213.66, 25.25)--(211.67, 23.33)--(215.44, 23.49)--(217.75, 21.65)--(200.52, 19.57)--(194.37, 21.1)--(186.19, 26.3)--(183.33, 30.4)--(187.61, 31.42)--(191.44, 33.88)--(194.61, 33.54)--(197.17, 30.74)--(196.08, 28.46)--(196.04, 27.66)--(203.54, 24.58)--(203.45, 24.88)--(200.38, 27.18)--(200.91, 27.54)--(200.05, 29.69)--(199.62, 29.91)--(201.03, 30.25)--(207.36, 29.93)--(205.2, 31.05)--(199.88, 30.97)--(199.94, 31.44)--(200.26, 32.2)--(202.19, 31.76)--(202.85, 32.2)--(199.62, 32.83)--(199.15, 34.61)--(189.46, 35.87)--(189.93, 35.46)--(191.12, 35.08)--(190.83, 34.56)--(188.1, 33.45)--(186.87, 34.75)--(187.11, 36.02)--(176.39, 40.19)--(176.65, 41.24)--(173.41, 42.02)--(176.82, 43.77)--(169.68, 46.56)--(169.15, 53.05)--(171.1, 53.62)--(173.12, 53.39)--(178.7, 51.26)--(183.17, 46.73)--(186.38, 46.75)--(192.72, 49.52)--(191.46, 52.64)--(193.74, 52.83)--(196.74, 50.32)--(190.71, 44.65)--(191.74, 44.4)--(198.11, 50.06)--(198.89, 52.03)--(200.95, 53.75)--(202.49, 51.99)--(201.15, 49.3)--(204.15, 49.28)--(206.54, 53.44)--(214.39, 53.25)--(211.18, 58.75)--(198.36, 57.7)--(197.88, 59.47)--(188.5, 55.87)--(189.63, 53.18)--(189.49, 52.79)--(173.31, 54.75)--(168.56, 58.21)--(161.34, 69.75)--(160.58, 75.18)--(161.25, 77.58)--(162.08, 79.09)--(163.71, 80.23)--(165.04, 82.46)--(168.88, 84.86)--(182.72, 83.77)--(184.88, 85.79)--(187.22, 85.99)--(186.79, 90.34)--(190.56, 95.97)--(190.23, 105.47)--(193.05, 115.74)--(196.18, 121.46)--(196.92, 124.65)--(206, 122.33)--(206, 122.33); 1371 | landmass2 := (111.44, 45.06)--(113.41, 44.75)--(111.77, 46)--(111.77, 46.07)--(118.69, 43.98)--(118.13, 42.88)--(116.49, 43.6)--(114.48, 42.7)--(114.1, 43.65)--(114.04, 41.9)--(113.28, 42.04)--(108.57, 42.18)--(114.57, 39.81)--(120.91, 38.84)--(119.04, 41.38)--(119.53, 41.59)--(122.9, 42.64)--(121.94, 42.77)--(121.82, 43.31)--(124.3, 42.48)--(125.29, 42.37)--(125.59, 41.84)--(125.41, 41.3)--(124.75, 41.38)--(122.58, 40.38)--(122.97, 39.95)--(121.71, 40.06)--(123.02, 38.38)--(121.65, 38.53)--(120.78, 35.69)--(116.8, 33.48)--(114.09, 29.59)--(110.59, 31.42)--(108.79, 28.81)--(104.18, 27.54)--(99.54, 29.42)--(100.85, 30.15)--(100.61, 31.83)--(100.51, 34.6)--(98.7, 35.56)--(99.11, 36.37)--(99.33, 38.41)--(96.3, 36.78)--(85.98, 32.83)--(83.79, 29.73)--(86.02, 28)--(87.63, 26.53)--(92.02, 23.6)--(94.53, 23.9)--(94.57, 23.59)--(95.6, 23.75)--(96.08, 21.63)--(96.05, 20.47)--(99.61, 19.73)--(103.5, 21.33)--(105.9, 22.76)--(103.75, 23.87)--(104.54, 24.37)--(101.78, 25.83)--(112.52, 27.74)--(113.4, 27.33)--(113.39, 27.23)--(110.6, 24.25)--(110.62, 24.18)--(111.27, 23.6)--(116.34, 23.81)--(117.17, 23.3)--(110.5, 21.34)--(111.78, 20.87)--(110.82, 20.4)--(111.3, 20.21)--(109.74, 19.84)--(110.11, 19.43)--(102.09, 17.29)--(97.38, 16.64)--(92.88, 17.67)--(92.21, 18.01)--(91.83, 17.28)--(89.16, 18.82)--(92.76, 20.05)--(93.22, 20.96)--(92.06, 21.98)--(91.69, 22.39)--(88.11, 21.59)--(87.79, 20.91)--(86.11, 20.22)--(86.94, 19.77)--(84.28, 18.1)--(84.81, 17.32)--(85.92, 16.37)--(82.62, 16.82)--(82.26, 18.46)--(82.22, 20.63)--(80.29, 21.42)--(73.81, 21.72)--(73.19, 21.56)--(73.02, 21.15)--(75.97, 21.21)--(75.92, 20.34)--(77.6, 20.64)--(73.05, 17.2)--(70.79, 18.11)--(67.81, 17.27)--(64.31, 17.23)--(54.27, 15.93)--(52.31, 18.03)--(60.06, 17.29)--(60.43, 18.73)--(59.79, 19.06)--(65.44, 20.05)--(71.86, 20.7)--(72.16, 20.95)--(69.43, 21.73)--(70.4, 21.96)--(70.06, 22.49)--(69.48, 22.4)--(63.3, 21.97)--(48.4, 19.77)--(41.64, 20.99)--(22.72, 18.59)--(11.06, 21.67)--(16.58, 23.75)--(14.57, 23.75)--(10.29, 24.54)--(17.36, 25.3)--(17.42, 26.18)--(12.61, 29.54)--(15.96, 29.89)--(15.52, 31.43)--(20.94, 31.31)--(13.31, 35.43)--(16.05, 35.66)--(19.1, 35.11)--(18.12, 34.75)--(27.83, 28.87)--(28.89, 30.18)--(33.87, 29.92)--(33.36, 30.35)--(38.31, 30.44)--(42.27, 33.16)--(42.87, 32.94)--(47.84, 35.37)--(50.85, 39.13)--(53.79, 42.3)--(54.39, 50.26)--(64.16, 61.59)--(63.13, 61.47)--(62.78, 61.95)--(64.93, 63.33)--(66.24, 65.62)--(67.78, 65.49)--(65.67, 61.75)--(65.09, 58.99)--(66.42, 61.44)--(68.81, 63.42)--(72.94, 69.36)--(81.5, 74.4)--(83.61, 73.92)--(85.99, 75.53)--(90.7, 76.75)--(93.55, 80.26)--(95.61, 82.43)--(96.7, 82.3)--(98.47, 82.54)--(101.05, 86.23)--(98.22, 93.14)--(100.55, 101.04)--(102.97, 105.27)--(107.45, 108.16)--(104.04, 132.27)--(104.08, 133.7)--(103.49, 134.62)--(102.5, 136.82)--(104.04, 136.98)--(103.44, 141.15)--(104.17, 143.63)--(108.08, 144.9)--(110.27, 145.35)--(111.35, 145.04)--(113.34, 144.63)--(109.31, 140.79)--(112.69, 137.21)--(111.47, 135.36)--(113.17, 133.67)--(113.34, 130.92)--(116.56, 129.1)--(119.97, 124.37)--(128.41, 119.87)--(133.19, 114.17)--(136.37, 113.08)--(138.56, 109.76)--(141.63, 100.78)--(139.94, 93.61)--(133.56, 91.17)--(129.89, 90.92)--(128.12, 89.29)--(123.75, 83.93)--(119.97, 83.01)--(117.24, 81.38)--(117.85, 80.79)--(116.9, 80.06)--(117.65, 79.02)--(114.24, 79.23)--(110.12, 78.93)--(108.35, 77.69)--(102.27, 80.15)--(102.6, 80.45)--(101.42, 81.66)--(96.3, 80.94)--(95.6, 75.16)--(91.88, 73.8)--(89.69, 73.89)--(91.19, 69.61)--(91.08, 68.3)--(87.73, 69.96)--(81.32, 69.32)--(81.63, 61.96)--(88.41, 60.66)--(88.78, 61.23)--(92.41, 60.31)--(95.93, 65.23)--(96.7, 65.47)--(97.12, 65.14)--(97.12, 59.81)--(100.34, 56.62)--(103.22, 54.85)--(104.21, 50.99)--(106.28, 48.84)--(108.51, 48.83)--(108.23, 48.05)--(111.68, 45.41); 1372 | landmass3 := (309.58, 101.89)--(307.85, 104.82)--(304.23, 104.36)--(301.98, 106.89)--(301.81, 107.2)--(301.39, 106.32)--(297.9, 109.91)--(292.61, 112.27)--(292.42, 116.24)--(291.76, 116.34)--(293.22, 123.3)--(295.54, 125.57)--(300.79, 123.84)--(313.31, 124.74)--(314.35, 125.13)--(314.72, 125.92)--(316.53, 125.74)--(318.45, 127.71)--(324.06, 128.78)--(326.88, 127.94)--(328.82, 125.64)--(331.64, 120.19)--(331.26, 115.24)--(328.34, 111.83)--(327.46, 109.78)--(327.32, 109.75)--(323.91, 106.24)--(320.57, 100.41)--(318.09, 106.52)--(315.29, 105.19)--(314.65, 104.27)--(314.4, 103.64)--(314.38, 101.88)--(314.02, 100.8)--(310.93, 100.72)--(310, 101.21)--(309.58, 101.89); 1373 | landmass4 := (360, 173.94)--(347.31, 173.02)--(337.83, 170.31)--(340.03, 168.66)--(345.63, 168.61)--(346.01, 167.92)--(341.09, 166.89)--(341.61, 165.5)--(343.88, 164.64)--(343.24, 163.51)--(349.37, 161.91)--(322.58, 157.73)--(323.11, 157.14)--(263.4, 156.39)--(263.26, 156.59)--(263.82, 157.03)--(245.18, 163.09)--(245.85, 157.68)--(234.93, 156.8)--(226.52, 156.65)--(194.69, 160.02)--(194.23, 160.12)--(182.27, 160.22)--(175.88, 161.21)--(175.09, 160.92)--(174.87, 161.24)--(171.99, 160.65)--(165.8, 161.33)--(163.91, 162.6)--(161.68, 163.73)--(141.54, 169.39)--(118.58, 172.13)--(116.78, 171.69)--(102.46, 169.67)--(94.78, 168.49)--(97.74, 167.88)--(101.28, 166.75)--(117.86, 164.33)--(118.52, 163.02)--(117.24, 161.46)--(117.41, 160.81)--(114.93, 158.64)--(113.38, 158.53)--(113.67, 158.17)--(112.94, 157.45)--(115.93, 156.83)--(115.81, 156.34)--(116.18, 155.88)--(116.84, 155.67)--(119.7, 154.63)--(119.77, 154.11)--(121.16, 153.99)--(121.76, 153.53)--(116.74, 154)--(113.84, 154.79)--(110.65, 157.28)--(111.18, 157.79)--(111.19, 159.12)--(104.73, 163.13)--(104.3, 163)--(90.27, 162.69)--(86.46, 162.59)--(74.77, 162.74)--(78.14, 164.63)--(64.48, 164.84)--(65.31, 164.46)--(50.04, 164.22)--(50.29, 164.61)--(32.44, 165.76)--(29.52, 166.6)--(27.21, 166.74)--(27.17, 166.97)--(22.41, 166.97)--(23.06, 168.33)--(21.43, 168.63)--(29.78, 169.97)--(27.58, 170.36)--(29.1, 170.81)--(23.15, 171.94)--(24.93, 172.46)--(17.69, 173.06)--(13.37, 172.69)--(3.71, 172.63)--(13.68, 173.98)--(0, 174.21); 1374 | landmass5 := (124.62, 19.08)--(123.98, 19.56)--(126.36, 20.09)--(127.24, 20.59)--(124.98, 23.19)--(130.77, 29.28)--(135.8, 28.99)--(137.84, 25.04)--(141.86, 24.34)--(146.13, 22.18)--(157, 19.51)--(155.91, 17.98)--(155.55, 16.8)--(159.25, 15.48)--(158.44, 14.93)--(159.9, 14.05)--(157.97, 12.46)--(159.52, 10.77)--(159.19, 10.3)--(167.06, 8.42)--(159.95, 8.2)--(156.76, 8.73)--(153.02, 7.87)--(131.44, 7.07)--(130.82, 7.37)--(127.12, 7.44)--(116.94, 8.32)--(111.03, 9.65)--(105.32, 11.75)--(107.03, 12.86)--(108.98, 13.43)--(112.23, 14.12)--(119.83, 14.46)--(121.54, 15.67)--(120.54, 15.91)--(122.91, 16.69)--(121.82, 17.23)--(124.62, 19.08); 1375 | landmass6 := (307.49, 56.47)--(307.06, 57.11)--(308.22, 57.5)--(310.39, 56.79)--(310.75, 57.43)--(312.59, 56.96)--(313.38, 56.17)--(316.84, 55.24)--(317.14, 55.51)--(319.46, 54.34)--(320.21, 51.88)--(320.32, 48.77)--(319.72, 48.29)--(319.35, 47.51)--(322.01, 46.93)--(323.56, 45.58)--(319.79, 44.82)--(319.05, 44.6)--(318.2, 46.06)--(317.67, 48.01)--(318.7, 48.63)--(315.73, 52.34)--(311.83, 54.71)--(307.49, 56.47); 1376 | landmass7 := (172.44, 33.8)--(171.76, 34.44)--(174.73, 35.22)--(173.52, 37.33)--(172.83, 38.17)--(172.56, 39.98)--(179.32, 38.52)--(178.63, 37.06)--(175.74, 33.85)--(176.19, 30.59)--(172.04, 32.2)--(171.52, 33.36)--(172.44, 33.8); 1377 | landmass8 := (222.04, 111.1)--(224.53, 115.35)--(228.6, 106.45)--(226.81, 103.35)--(222.04, 111.1); 1378 | 1379 | % 1380 | % This macro draws contures for a landmass on globe centered on lon,lat 1381 | % 1382 | 1383 | vardef drawLandMass (expr p, lon, lat) = 1384 | save i, j, k, l, horizon, currentPoint, horizonTimes, outHorizon, inHorizon, visibleContours, pathNumber, horizonArc, arcTimes, resultPath; 1385 | path resultPath, visibleContours[], horizon, horizonArc; 1386 | pair currentPoint, horizonTimes[]; 1387 | numeric pathNumber, outHorizon, arcTimes[]; 1388 | horizon := fullcircle scaled 2; 1389 | pathNumber := 0; 1390 | outHorizon := -1; 1391 | inHorizon := -1; 1392 | 1393 | % In the following loop visible segments of landmass and points of 1394 | % horizon-crossing are calculated 1395 | % visibleContours are just what they are called and horizonTimes are 1396 | % times on horizon circle where visible segment should cross it 1397 | for i := 0 upto length(p): 1398 | currentPoint := pointOnGlobe (point i of p, lon, lat); 1399 | if (horizonOnGlobe (point i of p, lon, lat) < 0): 1400 | if (unknown visibleContours[pathNumber]): 1401 | visibleContours[pathNumber] := currentPoint; 1402 | if (i > 0): 1403 | outHorizon := xpart(horizon intersectiontimes ((0,0) -- (findHorizonPoint (subpath(i-1, i) of p, lon, lat, 0) scaled 5))); 1404 | if (outHorizon < inHorizon): outHorizon := outHorizon + 8; fi; 1405 | horizonTimes[pathNumber - 1] := (inHorizon, outHorizon); 1406 | fi; 1407 | else: 1408 | visibleContours[pathNumber] := visibleContours[pathNumber] -- currentPoint; 1409 | fi; 1410 | else: 1411 | if (known visibleContours[pathNumber]): 1412 | pathNumber := pathNumber + 1; 1413 | inHorizon := xpart(horizon intersectiontimes ((0,0) -- (findHorizonPoint (subpath(i, i-1) of p, lon, lat, 0) scaled 5))); 1414 | fi; 1415 | fi; 1416 | endfor; 1417 | if (unknown visibleContours0): 1418 | resultPath := (1,0); 1419 | else: 1420 | if (unknown visibleContours[pathNumber]): pathNumber := pathNumber - 1; fi; 1421 | if (unknown horizonTimes[-1]): 1422 | if (pathNumber > 0): 1423 | visibleContours0 := visibleContours[pathNumber] -- visibleContours0; 1424 | fi; 1425 | pathNumber := pathNumber - 1; 1426 | else: 1427 | if (ypart(horizonTimes[-1]) < inHorizon): 1428 | horizonTimes[pathNumber] := (inHorizon, ypart(horizonTimes[-1]) + 8); 1429 | else: 1430 | horizonTimes[pathNumber] := (inHorizon, ypart(horizonTimes[-1])); 1431 | fi; 1432 | fi; 1433 | % In these loops horizon arcs directions should be handled 1434 | % The idea is that when we have path with no self-intersections arcs should 1435 | % not cross one another, these conflicts are resolved here 1436 | % It's important to note, that horizon-time detecting algorithm is 1437 | % not absolutely precise for now, so at times in will work incorrect. 1438 | for i := 0 upto pathNumber - 1: 1439 | for j := i + 1 upto pathNumber: 1440 | l := 0; 1441 | for k := -8, 0, 8: 1442 | if (xpart(horizonTimes[j]) > xpart(horizonTimes[i]) + k) and (xpart(horizonTimes[j]) < ypart(horizonTimes[i]) + k): l := l + 1; fi; 1443 | if (xpart(horizonTimes[i]) > xpart(horizonTimes[j]) + k) and (xpart(horizonTimes[i]) < ypart(horizonTimes[j]) + k): l := l + 1; fi; 1444 | endfor; 1445 | if (l > 1): horizonTimes[j] := (xpart(horizonTimes[j]) + 8, ypart(horizonTimes[j])); fi; 1446 | endfor; 1447 | endfor; 1448 | 1449 | % In the following loop previously calculated segments of a landmass and 1450 | % arcs of the horizon are sewed together in order 1451 | resultPath := visibleContours0 1452 | for i := 1 upto pathNumber + 1: 1453 | if (known horizonTimes[i-1]): -- (subpath horizonTimes[i-1] of horizon) fi 1454 | if (i <= pathNumber): -- visibleContours[i] fi 1455 | endfor 1456 | fi; 1457 | resultPath -- cycle 1458 | enddef; 1459 | 1460 | % This thing just converts coordinates on globe rotated by lon, lat to screen coordinates 1461 | 1462 | vardef pointOnGlobe (expr p, lon, lat) = 1463 | (cosd(lon + xpart(p)) * sind(ypart(p)), 1464 | cosd(ypart(p)) * cosd(lat) 1465 | + sind(lon + xpart(p)) * sind(ypart(p)) * sind(lat)) 1466 | enddef; 1467 | 1468 | % This one is needed to check if point on globe is in view 1469 | 1470 | vardef horizonOnGlobe (expr p, lon, lat) = 1471 | (sind(lon + xpart(p)) * cosd(lat) * sind(ypart(p))) - (cosd(ypart(p)) * sind(lat)) 1472 | enddef; 1473 | 1474 | % This macro calculates horizon crossing point with given precision (recursion depth). 1475 | % Likely, this could be done analytically, though. 1476 | 1477 | vardef findHorizonPoint (expr p, lon, lat, i) = 1478 | save selecthalf, returnpoint; 1479 | pair selecthalf, returnpoint; 1480 | if (horizonOnGlobe (point 1/2 of p, lon, lat) < 0): 1481 | selecthalf := (0, 1/2); 1482 | else: 1483 | selecthalf := (1/2, 1); 1484 | fi; 1485 | if (i < 5): 1486 | returnpoint := findHorizonPoint (subpath selecthalf of p, lon, lat, i + 1) 1487 | else: 1488 | returnpoint := pointOnGlobe (point 1/2 of p, lon, lat); 1489 | fi; 1490 | returnpoint 1491 | enddef; 1492 | 1493 | vardef globe (expr s, lon, lat) = 1494 | save i, p, lm; 1495 | picture p[]; 1496 | path lm; 1497 | begingroup 1498 | save lightnessPP; 1499 | vardef lightnessPP (expr v) = 1500 | 1/2v 1501 | enddef; 1502 | p1 := image(draw sphereLat(2s, lat)); 1503 | vardef lightnessPP (expr v) = 1504 | if (abs(cos(sphlat)) > 7/8 + uniformdeviate (1/20)): 1505 | 1/4v 1506 | else: 1507 | 1/3v + 2/3 1508 | fi 1509 | enddef; 1510 | p2 := image(draw sphereLat(2s, lat)); 1511 | endgroup; 1512 | image( 1513 | draw fullcircle scaled 2s withpen thinpen; 1514 | for i := 1 upto 8: 1515 | lm := drawLandMass(landmass[i], lon + 90, lat) scaled s; 1516 | p3 := p2; 1517 | clip p3 to lm; 1518 | draw p3; 1519 | thinBrushGenerate (lm, 1520 | offsetPathTemplate (lm, 0) ( 1521 | 2/3minStrokeWidth + 1/3minStrokeWidth 1522 | * normalVectorToLightness( 1523 | sphereAnglesToNormalVector( 1524 | (angleRad(point offsetPathTime of lm), arcsin(abs(point offsetPathTime of lm)/2s)) 1525 | ), 0, point offsetPathTime of lm 1526 | ) 1527 | ), 0); 1528 | p1 := p1 maskedWith lm; 1529 | endfor; 1530 | draw p1; 1531 | ) 1532 | enddef; 1533 | 1534 | % 1535 | % This macro draws an eye pointed in the direction a (in degrees) 1536 | % Eye is opened at random angle and pupil is scaled randomly by design 1537 | % Scaling below some level, dependent on minStrokeWidth, simplifies image 1538 | % 1539 | 1540 | eyescale := 1/2cm; 1541 | 1542 | vardef eye (expr a) = 1543 | save s, eyelids, pupil, eyeball, eyelash, loopstep, p, o; 1544 | path eyelids[], pupil[], eyelash; 1545 | pair p[]; 1546 | picture eyeball; 1547 | numeric s, loopstep; 1548 | o := 10 + (15/(1 + 2**(3/2normaldeviate))); 1549 | s := eyescale; 1550 | p1 := (-3/4s, 0); 1551 | pupil1 := ((subpath (-2, 2) of fullcircle xscaled 3/5) .. (subpath (3, 5) of fullcircle xscaled 2/5) .. cycle) scaled 3/5s; 1552 | pupil2 := fullcircle scaled (1/3s + uniformdeviate(1/5s)) xscaled 1/3; 1553 | p2 := ((p1 -- ((1/2s, 0) rotatedabout (p1, o - 5))) intersectionpoint (subpath (0, 4) of pupil1)); 1554 | eyelids1 := (p1 shifted (0, -1/16s)){dir(1/3o)} .. {dir(0)}p2; 1555 | eyelids2 := p1 {dir(-1/3o)} .. {dir(0)}((1/6s, 0) rotatedabout (p1, -2/3o - 5)); 1556 | eyelids2 := subpath(xpart(eyelids2 intersectiontimes eyelids1), length(eyelids2)) of eyelids2; 1557 | eyelids3 := (p1){dir(2/3o)} .. tension 3/2 .. {dir(o-1/3o)}p2 rotatedabout (p1, 1/3o + 7); 1558 | eyelids3 := subpath (1/8, length(eyelids3)) of eyelids3; 1559 | eyelids4 := (p1 shifted (0, -1/16s)) .. {dir(1/4o - 2/3o)}((1/6s, -1/6s) rotatedabout (p1, -2/3o - 5)); 1560 | eyelids4 := subpath (1/2, length(eyelids4)) of eyelids4; 1561 | loopstep := length(eyelids1)/20; 1562 | if (arclength(subpath(0, loopstep) of eyelids1) < 5minStrokeWidth): 1563 | loopstep := arctime (5minStrokeWidth) of eyelids1; 1564 | fi; 1565 | eyeball := image( 1566 | if (5loopstep <= 1): 1567 | draw pupil1 withpen thinpen; 1568 | fill pupil2; 1569 | for i := 0 step 5loopstep until length pupil1: 1570 | draw brush ((point i of pupil1) -- (point i + 6 of pupil2 scaled 5/6 yscaled 1/2))(cos(offsetPathLength*1/2pi)*2minStrokeWidth); 1571 | endfor; 1572 | else: 1573 | fill pupil1; 1574 | fi; 1575 | ); 1576 | clip eyeball to (eyelids1{(1, 0)} .. (s, 0) .. {-1, 0}reverse(eyelids2) -- cycle); 1577 | eyeball := eyeball maskedWith ((fullcircle scaled (1/4s) xscaled 1/2 rotated 2 shifted (1/12s, 0) rotatedabout (p1, 1/3o + 2))); 1578 | image( 1579 | draw brush (eyelids1 .. tension 2.5 .. reverse (eyelids3))((1-offsetPathLength)*2minStrokeWidth); 1580 | draw brush (eyelids2)((offsetPathLength)*2minStrokeWidth); 1581 | draw brush (eyelids4)(sin(offsetPathLength*pi)*minStrokeWidth); 1582 | draw eyeball; 1583 | for i := length(eyelids1) step -loopstep until 0: 1584 | eyelash := (point i of eyelids1) {dir(angle(direction i of eyelids1) - 60 + 50*(i/length(eyelids1)))} 1585 | .. (point i of eyelids1) shifted (1/16s + (i/length(eyelids1))*1/4s, (i/length(eyelids1))*1/5s); 1586 | if (arclength(eyelash) > 2/3minDashStrokeLength): 1587 | draw brush (eyelash shifted ((-1/32s, uniformdeviate(1/12s)) scaled ((length(eyelids1)-i)/length(eyelids1))) )(minStrokeWidth + (1-offsetPathLength)*minStrokeWidth); 1588 | fi; 1589 | endfor; 1590 | for i := length(eyelids2) step -3/2loopstep until 0: 1591 | eyelash := (point i of eyelids2) {dir(angle(direction i of eyelids2) + 20 - 40*(i/length(eyelids2)))} 1592 | .. (point i of eyelids2) shifted (1/16s + (i/length(eyelids2))**2*1/7s, 1/16s - (i/length(eyelids2))*1/5s); 1593 | if (arclength(eyelash) > minDashStrokeLength): 1594 | draw brush (eyelash shifted (-1/32s, -uniformdeviate(1/24s)))(minStrokeWidth + (1-offsetPathLength)*minStrokeWidth); 1595 | fi; 1596 | endfor; 1597 | ) if cosd(a) < 0: yscaled -1 rotated (a) else: rotated a fi 1598 | enddef; 1599 | 1600 | % 1601 | % This macro draws solid surface 1602 | % 1603 | 1604 | numeric solidSurfaceThickness; 1605 | solidSurfaceThickness := 1/4cm; 1606 | 1607 | vardef solidSurface (expr p) = 1608 | save q, s, d, stripes; 1609 | path q, s; 1610 | picture stripes; 1611 | q := offsetPath(p) (-solidSurfaceThickness); 1612 | s := p -- reverse(q) -- cycle; 1613 | image( 1614 | draw solid (s, 45, 0); 1615 | draw p withpen thinpen; 1616 | ) 1617 | enddef; 1618 | 1619 | vardef solid (expr p, a, t) = 1620 | save stripes, stripeskind, d, i, j, c, strokeVariation; 1621 | picture stripes, stripeskind; 1622 | pair c; 1623 | stripes := image( 1624 | d1 := abs(ulcorner(p rotated (90 - a)) - urcorner(p rotated (90 - a))); 1625 | d2 := abs(ulcorner(p rotated (90 - a)) - llcorner(p rotated (90 - a))); 1626 | stripeskind := dashpattern (on 1mm); 1627 | c := 1/2[ulcorner(p rotated (90 - a)), lrcorner(p rotated (90 - a))] rotated (a - 90); 1628 | for i:= 0 step (3/2shadingDensity)/d1 until 1: 1629 | if (t = 1): 1630 | strokeVariation := uniformdeviate(1)-1/2; 1631 | j := round(i*d1/(3/2shadingDensity)); 1632 | if (j mod 4) = 0: 1633 | stripeskind := dashpattern (on (8-strokeVariation)*shadingDensity off (4+strokeVariation)*shadingDensity); 1634 | fi; 1635 | if ((j mod 4) = 1) or ((j mod 4) = 3): 1636 | stripeskind := dashpattern (off 1shadingDensity on (6-strokeVariation)*shadingDensity off (5+strokeVariation)*shadingDensity); 1637 | fi; 1638 | if (j mod 4) = 2: 1639 | stripeskind := dashpattern (on 0 off 12shadingDensity); 1640 | fi; 1641 | fi; 1642 | draw ((dir(a) scaled 1/2(d2-uniformdeviate(3shadingDensity))) -- (dir(a + 180) scaled 1/2d2)) shifted c shifted i[dir(a + 90) scaled 1/2d1, dir(a -90) scaled 1/2d1] withpen thinpen 1643 | dashed stripeskind; 1644 | endfor; 1645 | ); 1646 | clip stripes to p; 1647 | stripes 1648 | enddef; 1649 | 1650 | % 1651 | % Returns a picture of shaded gradient inside shape p at an angle a 1652 | % 1653 | 1654 | vardef gradientShade (expr p, a) = 1655 | save stripes, stripeshd, d, i, j, s; 1656 | picture stripes; 1657 | path s; 1658 | stripes := image( 1659 | d1 := abs(ulcorner(p rotated (90 - a)) - urcorner(p rotated (90 - a))); 1660 | d2 := abs(ulcorner(p rotated (90 - a)) - llcorner(p rotated (90 - a))); 1661 | for i:= 0 step (shadingDensity)/d1 until 1: 1662 | s := ((dir(a) scaled 1/2d2) -- (dir(a + 180) scaled 1/2d2)) shifted 1/2[ulcorner(p), lrcorner(p)] shifted i[dir(a + 90) scaled 1/2d1, dir(a -90) scaled 1/2d1]; 1663 | stripeshd := 1/4 + 3/4i; 1664 | draw brush(s)(minStrokeWidth*stripeshd); 1665 | endfor; 1666 | ); 1667 | clip stripes to p; 1668 | stripes 1669 | enddef; 1670 | 1671 | % 1672 | % This one draws a spring between points p and q with n steps 1673 | % if stretched more than possible, displayed as a straight line 1674 | % if compressed too much, displayed as having less steps 1675 | % 1676 | 1677 | springwidth := 1/8cm; 1678 | 1679 | vardef spring (expr p, q, n) = 1680 | save sp, ss, t, x, springstep, springcoef, springsegment; 1681 | transform t; 1682 | path ss[]; 1683 | pair sp; 1684 | picture springsegment; 1685 | springstep := (arclength(p--q) - 2springwidth)/(n+1); 1686 | if (springstep < 6minStrokeWidth): springstep := arclength(p--q)/round(arclength(p--q)/6minStrokeWidth); fi; 1687 | if (springstep < (springwidth*pi)): 1688 | springcoef := (1-(springstep/(springwidth*pi))); 1689 | else: 1690 | springcoef := 0; 1691 | fi; 1692 | image( 1693 | for i := 0 step 30 until 360: 1694 | sp := ((cosd(i - 90), sind(i - 90)) scaled springwidth xscaled 1/4 yscaled springcoef) shifted (springstep*(i/360) - 1/2springstep, 0); 1695 | if (i = 0): 1696 | ss1 := sp; 1697 | else: 1698 | ss1 := ss1 -- sp; 1699 | fi; 1700 | endfor; 1701 | ss2 := subpath (0, 6) of ss1; 1702 | ss3 := subpath (6, 12) of ss1; 1703 | ss4 := subpath (0, ypart(ss2 shifted (-3minStrokeWidth, 0) intersectiontimes ss3)) of ss3; 1704 | x := ypart(ss2 shifted (3minStrokeWidth, 0) intersectiontimes ss3); 1705 | if (x > 0): 1706 | ss5 := subpath (x, length(ss3)) of ss3; 1707 | else: 1708 | ss5 := point length(ss3) of ss3; 1709 | fi; 1710 | if (xpart(llcorner(ss4)) - 3minStrokeWidth < xpart(urcorner(ss2 shifted (-springstep, 0)))): 1711 | x := ypart((subpath (3, 6) of ss2 shifted (-springstep + 3minStrokeWidth, 0)) intersectiontimes ss4); 1712 | if (x > 0): 1713 | ss6 := subpath (0, x) of ss4; 1714 | else: 1715 | ss6 := point 0 of ss4; 1716 | fi; 1717 | x := ypart((subpath (0, 3) of ss2 shifted (-springstep + 3minStrokeWidth, 0)) intersectiontimes ss4); 1718 | if (x > 0): 1719 | ss7 := subpath (x, length(ss4)) of ss4; 1720 | else: 1721 | ss7 := point length(ss4) of ss4; 1722 | fi; 1723 | fi; 1724 | springsegment := image( 1725 | draw brush (ss2)(minStrokeWidth + sin(offsetPathLength*pi)*minStrokeWidth); 1726 | if (unknown(ss6)): 1727 | if (arclength(ss4) > minStrokeWidth): draw ss4 withpen thinpen; fi; 1728 | else: 1729 | if (arclength(ss6) > minStrokeWidth): draw ss6 withpen thinpen; fi 1730 | if (arclength(ss7) > minStrokeWidth): draw ss7 withpen thinpen; fi 1731 | fi; 1732 | if (arclength(ss5) > minStrokeWidth): draw ss5 withpen thinpen; fi; 1733 | ); 1734 | ss8 := (ss2 shifted (-2minStrokeWidth, 0)) rotated angle(q-p) shifted ((springwidth + 1/2springstep)/arclength(p--q))[p, q]; 1735 | for i := springwidth + 1/2springstep step springstep until arclength(p--q) - springwidth - 1/2springstep + 1: 1736 | t := identity rotated angle(q-p) shifted (i/arclength(p--q))[p, q]; 1737 | draw springsegment transformed t; 1738 | if (i <= springwidth + 1/2springstep + 2/3springwidth): 1739 | ss9 := ss3 transformed t; 1740 | ss10 := subpath ( 1741 | xpart(ss9 intersectiontimes (subpath (0, 3) of ss8)), 1742 | xpart(ss9 intersectiontimes (subpath (3, 6) of ss8)) 1743 | ) of ss9; 1744 | if (arclength(ss10) > minStrokeWidth): draw ss10 withpen thinpen; fi; 1745 | fi; 1746 | endfor; 1747 | draw brush (((springwidth)/arclength(p--q))[p, q] shifted (dir(angle(p-q) + 90)*springwidth * springcoef){(p-q)} .. {(p-q)}p)(minStrokeWidth); 1748 | draw brush (((springwidth)/arclength(p--q))[q, p] shifted (dir(angle(p-q) + 90)*springwidth * springcoef){(q-p)} .. {(q-p)}q)(minStrokeWidth); 1749 | ) 1750 | enddef; 1751 | 1752 | % 1753 | % This macro draws some kind of weight. Not very nice one at the moment 1754 | % 1755 | 1756 | vardef weight.h (expr h) = 1757 | save auricle, q, r; 1758 | path q[]; 1759 | auricle.d := 2mm; 1760 | auricle.t := 2shadingDensity; 1761 | r := 2/5(h-auricle.d); 1762 | image( 1763 | q0 := offsetPathSubdivide((0, -h) -- (0, -auricle.d - 1/6h)); 1764 | q1 := offsetPathTemplate(q0, 0)(r-(offsetPathLength*(1/8r))); 1765 | q2 := offsetPathGenerate (q0, q1, 0); 1766 | q3 := offsetPathGenerate (q0, q1 yscaled -1, 0); 1767 | tubeGenerate (q2, q3, q1, 0); 1768 | draw reverse(q2) -- q3 withpen thinpen; 1769 | q0 := offsetPathSubdivide((0, -auricle.d - 1/6h) -- (0, -auricle.d)); 1770 | q1 := offsetPathTemplate(q0, 0)(2/8r + 5/8r*(sqrt(1-offsetPathLength**2))); 1771 | q2 := offsetPathGenerate (q0, q1, 0); 1772 | q3 := offsetPathGenerate (q0, q1 yscaled -1, 0); 1773 | tubeGenerateAlt (q2, q3, q1); 1774 | draw q3 -- reverse(q2) withpen thinpen; 1775 | q5 := offsetPathSubdivide(point 0 of q3 -- point 0 of q2); 1776 | q6 := tube.e((0,0) -- (0, -3/2auricle.t))(1/2auricle.t); 1777 | draw image( 1778 | q4 := (((0, -1/2) {dir(90)} .. (1/2, 1/2) .. (0, 1) .. {dir(-90)}(-1/2, 1/4)) shifted (0, -1)) scaled 2/3auricle.d; 1779 | draw shadedEdge(tube.e(q4) (1/4auricle.t)) shifted (0, -1/2auricle.t); 1780 | ) maskedWith (q3 -- reverse(q2) -- (q2 yscaled 0 shifted (0, -h)) -- (reverse(q3) yscaled 0 shifted (0, -h)) -- cycle) 1781 | maskedWith q6; 1782 | draw shadedEdge(q6); 1783 | ) 1784 | enddef; 1785 | 1786 | vardef weight.s (expr h) = 1787 | save q,r; 1788 | path q[]; 1789 | r := 2/5h; 1790 | image( 1791 | q0 := offsetPathSubdivide((0, 0) -- (0, h-2/3r)); 1792 | q1 := offsetPathTemplate(q0, 0)(r); 1793 | q2 := offsetPathGenerate (q0, q1, 0); 1794 | q3 := offsetPathGenerate (q0, q1 yscaled -1, 0); 1795 | tubeGenerate (q2, q3, q1, 0); 1796 | draw reverse(q2)--q3 withpen thinpen; 1797 | q0 := offsetPathSubdivide((0, h-2/3r) -- (0, h - 1/8r)); 1798 | q1 := offsetPathTemplate(q0, 0)(r-sqrt(1- (1- offsetPathLength*2)**2)*1/3r - 1/6r*offsetPathLength); 1799 | q2 := offsetPathGenerate (q0, q1, 0); 1800 | q3 := offsetPathGenerate (q0, q1 yscaled -1, 0); 1801 | tubeGenerateAlt (q2, q3, q1); 1802 | draw q2 withpen thinpen; 1803 | draw q3 withpen thinpen; 1804 | q0 := offsetPathSubdivide((0, h-1/8r) -- (0, h)); 1805 | q1 := offsetPathTemplate(q0, 0)((r-1/6r)+sqrt(1- (1- offsetPathLength*2)**2)*1/16r); 1806 | q2 := offsetPathGenerate (q0, q1, 0); 1807 | q3 := offsetPathGenerate (q0, q1 yscaled -1, 0); 1808 | tubeGenerateAlt (q2, q3, q1); 1809 | draw q2 --reverse(q3) withpen thinpen; 1810 | ) 1811 | enddef; 1812 | 1813 | % 1814 | % This macro makes a lens-shaped clockwise path with radii 1815 | % r = (left radius, right radius), thickness t and diameter d 1816 | % 1817 | 1818 | vardef lens (expr r, t, d, s) = 1819 | save p, q, m, c; 1820 | pair c[]; 1821 | path p[], q[]; 1822 | if (xpart(r) = infinity): 1823 | p1 := (0, d) -- (0, -d); 1824 | else: 1825 | p1 := subpath (2, 6) of fullcircle scaled 2xpart(r); 1826 | fi; 1827 | if (ypart(r) = infinity): 1828 | p2 := (0, d) -- (0, -d); 1829 | else: 1830 | p2 := subpath (-2, 2) of fullcircle scaled 2ypart(r); 1831 | fi; 1832 | q1 := (min(xpart(ulcorner(p1)), xpart(ulcorner(p2))) - 1, -1/2d)--(max(xpart(urcorner(p1)), xpart(urcorner(p2))) + 1,-1/2d); 1833 | q2 := q1 shifted (0, d); 1834 | q3 := q1 shifted (0, 1/2d); 1835 | c1 := p1 intersectiontimes q1; 1836 | c2 := p1 intersectiontimes q2; 1837 | c3 := p2 intersectiontimes q2; 1838 | c4 := p2 intersectiontimes q1; 1839 | if (xpart(c1) > 0): 1840 | p1 := subpath (xpart(c1), xpart(c2)) of p1; 1841 | fi; 1842 | if (xpart(c3) > 0): 1843 | p2 := subpath (xpart(c3), xpart(c4)) of p2; 1844 | fi; 1845 | p1 := p1 shifted (-xpart(point xpart(p1 intersectiontimes q3) of p1), 0); 1846 | p2 := p2 shifted (-xpart(point xpart(p2 intersectiontimes q3) of p2) + t, 0); 1847 | reverse(p1--p2--cycle) scaled s 1848 | enddef; 1849 | 1850 | % 1851 | % This one returns a picture of a pulley with diameter d and it's support rotated 1852 | % at angle a. pulleyOutline path changes every time 1853 | % 1854 | 1855 | path pulleyOutline; 1856 | numeric pulleySupportSize; 1857 | pulleySupportSize := 2/3; 1858 | 1859 | vardef pulley (expr d, a) = 1860 | save pw, p, r; 1861 | picture pw; 1862 | path p[]; 1863 | r1 := 3/5d; 1864 | r2 := 1/6d; 1865 | image( 1866 | p0 := fullcircle scaled d; 1867 | p1 := (subpath (3, 9) of fullcircle) scaled r1; 1868 | p0 := subpath ( 1869 | xpart(p0 intersectiontimes ((point 0 of p1) -- (point 0 of p1 shifted (0, d)))), 1870 | 8 + xpart(p0 intersectiontimes ((point 0 of reverse(p1)) -- (point 0 of reverse(p1) shifted (0, d))))) 1871 | of p0; 1872 | p0 := ((xpart(point 0 of reverse(p0)), pulleySupportSize*d) -- (xpart(point 0 of p0), pulleySupportSize*d) -- p0 -- cycle) rotated a; 1873 | pulleyOutline := p0; 1874 | p1 := (p1 -- (xpart(point 0 of reverse(p1)), pulleySupportSize*d) -- (xpart(point 0 of p1), pulleySupportSize*d) -- cycle) rotated a; 1875 | pw := pulleyWheel(d) maskedWith p1; 1876 | draw pw; 1877 | draw p1 withpen thinpen; 1878 | draw shadedEdge(reverse(fullcircle) scaled r2); 1879 | ) 1880 | enddef; 1881 | 1882 | vardef pulleyWheel (expr d) = 1883 | save pw, r, i; 1884 | picture pw; 1885 | r1 := 7/9d; 1886 | r2 := 8/9d; 1887 | r3 := 3/5d; 1888 | r4 := 1/8d; 1889 | if (r2-r1) > shadingDensity: 1890 | pw := image( 1891 | for i := r3 step 2shadingDensity until r2: 1892 | if (i <= r1) or (i >= r2): 1893 | thinBrushGenerate (fullcircle scaled i, 1894 | offsetPathTemplate (fullcircle scaled i, 0) ( 1895 | 2/3minStrokeWidth + minStrokeWidth 1896 | * normalVectorToLightness( 1897 | sphereAnglesToNormalVector( 1898 | (angleRad(point offsetPathTime of fullcircle), arcsin(i/4d)) 1899 | ), 0, point offsetPathTime of fullcircle scaled i 1900 | ) 1901 | ), 0); 1902 | else: 1903 | thinBrushGenerate (fullcircle scaled i, 1904 | offsetPathTemplate (fullcircle scaled i, 0) ( 1905 | 1/4minStrokeWidth + minStrokeWidth 1906 | * normalVectorToLightness( 1907 | sphereAnglesToNormalVector( 1908 | (angleRad(point offsetPathTime of fullcircle) + pi, arcsin(1/2)) 1909 | ), 0, point offsetPathTime of fullcircle scaled i 1910 | ) 1911 | ), 0); 1912 | fi; 1913 | endfor; 1914 | draw brush (fullcircle scaled r1)(minStrokeWidth); 1915 | draw brush (fullcircle scaled r2)(minStrokeWidth); 1916 | draw fullcircle scaled d withpen thinpen; 1917 | draw fullcircle scaled r3 withpen thinpen; 1918 | draw shadedEdge(reverse(fullcircle) scaled r4); 1919 | ); 1920 | else: 1921 | pw := image( 1922 | draw shadedEdge (reverse(fullcircle) scaled r1); 1923 | draw fullcircle scaled d withpen thinpen; 1924 | draw fullcircle scaled r4 withpen thickpen; 1925 | ) 1926 | fi; 1927 | pw 1928 | enddef; 1929 | 1930 | % 1931 | % This macro draws a wheel 1932 | % 1933 | 1934 | vardef wheel (expr d, a) = 1935 | save pc, p, r, i; 1936 | picture pc[]; 1937 | path p[]; 1938 | r1 := 2/8d; 1939 | r2 := d-6minStrokeWidth; 1940 | r3 := 7/8d-2shadingDensity; 1941 | if r1 > 3shadingDensity: 1942 | pc1 := image( 1943 | for i := r1 step 2shadingDensity until r3: 1944 | thinBrushGenerate (fullcircle scaled i, 1945 | offsetPathTemplate (fullcircle scaled i, 0) ( 1946 | 2/3minStrokeWidth + minStrokeWidth 1947 | * normalVectorToLightness( 1948 | sphereAnglesToNormalVector( 1949 | (angleRad(point offsetPathTime of fullcircle) + pi, arcsin(i/4d)) 1950 | ), 0, point offsetPathTime of fullcircle scaled i 1951 | ) 1952 | ), 0); 1953 | endfor; 1954 | draw sphere.c(r1); 1955 | draw shadedEdge (reverse(fullcircle) scaled r3); 1956 | ); 1957 | else: 1958 | pc1 := image( 1959 | draw shadedEdge (fullcircle scaled d); 1960 | draw shadedEdge (fullcircle scaled r1); 1961 | draw shadedEdge (reverse(fullcircle) scaled r2); 1962 | ); 1963 | fi; 1964 | pc2 := image(fill fullcircle scaled d;) maskedWith (fullcircle scaled r2); 1965 | pc3 := image( 1966 | p1 := reverse((1/3d, 1/4d) -- (-1/3d, 1/4d) -- (-1/2d, 1/2d) -- (1/2d, 1/2d) -- cycle) rotated a; 1967 | draw p1 withpen thinpen; 1968 | draw gradientShade(p1, 180); 1969 | ); 1970 | pc3 := pc3 maskedWith (fullcircle scaled d); 1971 | image( 1972 | draw pc1; 1973 | draw pc2; 1974 | draw pc3; 1975 | ) 1976 | enddef; 1977 | 1978 | 1979 | % 1980 | % This one roughly finds the center of mass for a closed shape 1981 | % 1982 | 1983 | vardef shapeCenterOfMass (expr p) = 1984 | save i, a, aTotal, q; 1985 | numeric i, a, aTotal; 1986 | pair rv, q[]; 1987 | q0 := point 0 of p; 1988 | aTotal := 0; 1989 | rv := (0, 0); 1990 | for i := 1 step 1 until (length(p)-2): 1991 | q1 := point i of p; 1992 | q2 := point (i+1) of p; 1993 | if (xpart(q1-q0) = 0): 1994 | a := (abs(ypart(q1-q0)/cm)*abs(xpart(q2-q0)/cm))/2; 1995 | elseif (ypart(q1-q0) = 0): 1996 | a := (abs(xpart(q1-q0)/cm)*abs(ypart(q2-q0)/cm))/2; 1997 | elseif (abs(xpart(q1-q0)) > abs(ypart(q1-q0))): 1998 | begingroup 1999 | save qA; 2000 | pair qA; 2001 | qA = whatever[q0, q0 + (0,1)]; 2002 | qA = whatever[q2, q2 + (q1-q0)]; 2003 | a := (abs(ypart(qA-q0)/cm)*abs(xpart(q1-q0)/cm))/2; 2004 | endgroup 2005 | else: 2006 | begingroup 2007 | save qA; 2008 | pair qA; 2009 | qA = whatever[q0, q0 + (1,0)]; 2010 | qA = whatever[q2, q2 + (q1-q0)]; 2011 | a := (abs(xpart(qA-q0)/cm)*abs(ypart(q1-q0)/cm))/2; 2012 | endgroup 2013 | fi; 2014 | %a := 2; 2015 | aTotal := aTotal + a; 2016 | rv := rv + ((q0 + q1 + q2) scaled (a/3)); 2017 | endfor; 2018 | if (aTotal > 0): 2019 | rv := rv scaled (1/aTotal); 2020 | else: 2021 | rv := (0, 0); 2022 | fi; 2023 | rv 2024 | enddef; 2025 | 2026 | % 2027 | % This macro is for drawing shaded flat surfaces 2028 | % 2029 | 2030 | vardef flatSurface@#(expr surfPath, normalVector, hatchAngle) = 2031 | save p, aHatch, hatchImage, surfLight, totalHeight, totalWidth, lineDensity, distFromEdge, hatchLength; 2032 | path p, aHatch; 2033 | picture hatchImage; 2034 | numeric distFromEdge, hatchLength; 2035 | surfLight := normalVectorToLightness(normalVector, 0, (0, 0)); 2036 | p := surfPath rotated -hatchAngle; 2037 | if (str @# = "") or (str @# = "hatches"): 2038 | lineDensity := shadingDensity; 2039 | elseif (str @# = "stipples"): 2040 | lineDensity := stippleShadingDensity; 2041 | fi; 2042 | hatchImage := image( 2043 | totalHeight := abs(ypart(llcorner(p)) - ypart(urcorner(p))); 2044 | totalWidth := abs(xpart(llcorner(p)) - xpart(urcorner(p))); 2045 | %fill surfPath withcolor (surfLight, surfLight, surfLight); 2046 | for i := ypart(llcorner(p)) step (totalHeight/round(totalHeight/lineDensity)) until ypart(urcorner(p)): 2047 | distFromEdge := abs((i - ypart(llcorner(p)))/(ypart(urcorner(p))-ypart(llcorner(p)))); 2048 | aHatch := (xpart(llcorner(p)),i) -- (xpart(lrcorner(p)), i); 2049 | aHatch := (point xpart(aHatch firstIntersectionTimes p) of aHatch) -- 2050 | (point xpart(reverse(aHatch) firstIntersectionTimes p) of reverse(aHatch)); 2051 | hatchLength := arclength(aHatch); 2052 | if arclength(aHatch) > 0: 2053 | aHatch := aHatch rotated hatchAngle; 2054 | aHatch := pathSubdivide(aHatch,3+round(uniformdeviate(2))); 2055 | if (str @# = "") or (str @# = "hatches"): 2056 | draw brush(aHatch)( 2057 | (2minStrokeWidth*(1/15+surfLight))* 2058 | (1-6/7sqrt( 2059 | sin(offsetPathLength*pi)*(hatchLength/totalWidth)* 2060 | sin(distFromEdge*pi) 2061 | )) 2062 | ); 2063 | elseif (str @# = "stipples"): 2064 | draw thinBrush.stipples(aHatch)( 2065 | (stippleSize*(1/15+surfLight))* 2066 | (1-5/6sqrt( 2067 | sin(offsetPathLength*pi)*(hatchLength/totalWidth)* 2068 | sin(distFromEdge*pi) 2069 | )) 2070 | ); 2071 | fi; 2072 | fi; 2073 | endfor; 2074 | ); 2075 | clip hatchImage to surfPath; 2076 | image( 2077 | draw hatchImage; 2078 | ) 2079 | enddef; 2080 | 2081 | % 2082 | % These macros are for drawing wood texture. A bunch of wood-related global 2083 | % variables are also here. 2084 | % 2085 | 2086 | woodBlockRes := 1/3mm; 2087 | woodBlockDetail := 1/5; 2088 | woodBlockYRdensity := 1/24; 2089 | woodKnotAngle := 1/3pi; 2090 | woodKnotRadius := 1/8cm; 2091 | woodKnotDensity := 2cm; 2092 | 2093 | % wField returns a value on a scalar field, that is surface of year ring 2094 | 2095 | vardef wField (suffix wk)(expr i, j, cs, nwk)= 2096 | save x, y, csx, csy, ba, a, r, outputValue, k, bd; 2097 | csx := xpart(cs); 2098 | csy := ypart(cs); 2099 | x := i*woodBlockDetail; 2100 | y := j*woodBlockDetail; 2101 | bd := 1/2(woodKnotRadius/woodBlockRes)*woodBlockDetail; 2102 | outputValue := 0; 2103 | for k := 0 upto nwk: 2104 | r := (abs(((x, y) shifted -wk[k]) yscaled (sin(woodKnotAngle)))); 2105 | a := angleRad((x, y) shifted -wk[k]); 2106 | if (r >= 2bd) and (1/2r-bd < 8): 2107 | outputValue := outputValue + ((sqrt(1/2r-bd)/(3**(1/2r-bd)))*(sin(woodKnotAngle)*(1/2sin(-a)) + 1)*(1/3 + 2/3abs(cos(a))))**2; 2108 | elseif (r < 2bd): 2109 | outputValue := outputValue - 10sqrt(1-(r/2bd)**4); 2110 | fi; 2111 | outputValue := outputValue + 1/64cos(2pi*1/30r); 2112 | endfor; 2113 | outputValue := outputValue - (i*woodBlockYRdensity)/5 + 1/32sin(pi*i/xpart(cs) + 4pi*j/ypart(cs)); 2114 | outputValue 2115 | enddef; 2116 | 2117 | % woodBlock generates coordinates of knots, calls wField to 2118 | % generate matrix of heights (one for all years, that's simplification, of course) 2119 | % and then calls isoLines for each year ring (shifting values in matrix by woodBlockYRdensity) 2120 | 2121 | vardef woodBlock (expr w, l) = 2122 | save wood, isoLinesMask, maskCoordinates, minWithinMask, maxWithinMask, isNotMasked, wKnot, nwKnot, p, q, i, j, k, cl, tr, wS, lS; 2123 | numeric wood[][]; 2124 | boolean isNotMasked, isoLinesMask[][]; 2125 | isNotMasked := true; 2126 | pair wKnot[], maskCoordinates; 2127 | path q; 2128 | picture p; 2129 | if (l > w): 2130 | wS := round(w/woodBlockRes); 2131 | lS := round(l/woodBlockRes); 2132 | else: 2133 | wS := round(l/woodBlockRes); 2134 | lS := round(w/woodBlockRes); 2135 | fi; 2136 | for i := -1 step 1 until wS + 1: 2137 | for j := -1 step 1 until lS + 1: 2138 | isoLinesMask[i][j] := true; 2139 | if (path woodBlockMaskPath): 2140 | if (l > w): 2141 | maskCoordinates := (i, j); 2142 | else: 2143 | maskCoordinates := (j, i); 2144 | fi; 2145 | if not (maskCoordinates*woodBlockRes isInside woodBlockMaskPath): 2146 | isoLinesMask[i][j] := false; 2147 | fi; 2148 | fi; 2149 | endfor; 2150 | endfor; 2151 | image( 2152 | p := image( 2153 | i := -1; 2154 | j := 0; 2155 | forever: 2156 | wKnot[-1] := (uniformdeviate(wS*woodBlockDetail + woodKnotRadius*woodBlockDetail/woodBlockRes), uniformdeviate(lS*woodBlockDetail + woodKnotRadius*woodBlockDetail/woodBlockRes)) shifted (-1/2woodKnotRadius*woodBlockDetail/woodBlockRes, -1/2woodKnotRadius*woodBlockDetail/woodBlockRes); 2157 | cl := 0; 2158 | if (i > -1): 2159 | for k := 0 step 1 until i: 2160 | if (woodBlockRes*abs(wKnot[k]-wKnot[-1])/woodBlockDetail) < woodKnotDensity: 2161 | cl := 1; 2162 | fi; 2163 | endfor; 2164 | fi; 2165 | if cl > 0: 2166 | j := j + 1; 2167 | else: 2168 | i := i + 1; 2169 | wKnot[i] := wKnot[-1]; 2170 | for tr := 2woodKnotRadius step -8minStrokeWidth until 2minStrokeWidth: 2171 | draw brush( 2172 | ((fullcircle scaled tr yscaled (1/sin(woodKnotAngle))) shifted (woodBlockRes*wKnot[i]/woodBlockDetail)) 2173 | )( 2174 | minStrokeWidth*(1/2+abs(sin(woodKnotAngle))*abs(sin(angleRad(point offsetPathTime of fullcircle)))) 2175 | ); 2176 | endfor; 2177 | fi; 2178 | exitif (j >= 10) or (i >= 1/2((w/cm)*(l*cm))/(woodKnotDensity/cm)); 2179 | endfor; 2180 | nwKnot := i; 2181 | minWithinMask := infinity; 2182 | maxWithinMask := -infinity; 2183 | for i := 0 step 1 until wS: 2184 | k := uniformdeviate(1/8woodBlockYRdensity); 2185 | for j := 0 step 1 until lS: 2186 | if (boolean isoLinesMask[i][j]): 2187 | isNotMasked := isoLinesMask[i][j]; 2188 | fi; 2189 | wood[i][j] := wField (wKnot)(i, j, (wS, lS), nwKnot) + k; 2190 | if isNotMasked: 2191 | if wood[i][j] > maxWithinMask: 2192 | maxWithinMask := wood[i][j]; 2193 | fi; 2194 | if wood[i][j] < minWithinMask: 2195 | minWithinMask := wood[i][j]; 2196 | fi; 2197 | fi; 2198 | endfor; 2199 | endfor; 2200 | for i := -maxWithinMask/woodBlockYRdensity - 1 upto -minWithinMask/woodBlockYRdensity + 1: 2201 | if (((minWithinMask + woodBlockYRdensity*i) < 0) and ((maxWithinMask + woodBlockYRdensity*i) > 0)): 2202 | draw isoLines(wood)((wS, lS), woodBlockYRdensity*i + uniformdeviate(1/8woodBlockYRdensity), woodBlockRes); 2203 | fi; 2204 | endfor; 2205 | ); 2206 | q := (0, 0) -- (w, 0) -- (w, l) -- (0, l) -- cycle; 2207 | if (w > l): q := q xscaled -1 rotated -90; fi; 2208 | clip p to q; 2209 | draw p; 2210 | draw q withpen thinpen; 2211 | ) if (l < w): xscaled -1 rotated -90 fi 2212 | enddef; 2213 | 2214 | % woodenThing fits a woodBlock into thingOutline at a given woodAngle 2215 | 2216 | vardef woodenThing (expr thingOutline, woodAngle) = 2217 | save shiftedThing, woodBlockMaskPath, thingOrigin, thingWoodBlock; 2218 | path shiftedThing, woodBlockMaskPath; 2219 | pair thingOrigin; 2220 | picture thingWoodBlock; 2221 | shiftedThing := thingOutline rotated -woodAngle; 2222 | thingOrigin := llcorner(shiftedThing); 2223 | shiftedThing := shiftedThing shifted -thingOrigin; 2224 | if turningnumber(shiftedThing) > 0: 2225 | woodBlockMaskPath := offsetPath(shiftedThing, -woodBlockRes); 2226 | else: 2227 | woodBlockMaskPath := offsetPath(shiftedThing, woodBlockRes); 2228 | fi; 2229 | thingWoodBlock := woodBlock(xpart(urcorner(shiftedThing)), ypart(urcorner(shiftedThing))); 2230 | clip thingWoodBlock to shiftedThing; 2231 | thingWoodBlock := (thingWoodBlock shifted thingOrigin) rotated woodAngle; 2232 | image( 2233 | draw thingOutline withpen thinpen; 2234 | draw thingWoodBlock; 2235 | ) 2236 | enddef; 2237 | 2238 | % similar to solidSurfece, but with wood texture 2239 | 2240 | vardef woodenSurface (expr p) = 2241 | save surfaceOutline, surfaceAngle; 2242 | numeric surfaceAngle; 2243 | path surfaceOutline; 2244 | surfaceOutline := p -- reverse(offsetPath(p) (-solidSurfaceThickness)) -- cycle; 2245 | surfaceAngle := findNarrowest(surfaceOutline); 2246 | woodenThing (surfaceOutline,-surfaceAngle) 2247 | enddef; 2248 | 2249 | % finds the orientation for path p in which it is the narrowest 2250 | 2251 | vardef findNarrowest (expr p) = 2252 | save minWidth, currentWidth, minWidthAngle, rotatedPath, i; 2253 | numeric minWidth, currentWidth, minWidthAngle, i; 2254 | path rotatedPath; 2255 | minWidth := infinity; 2256 | for i := 0 step 10 until 170: 2257 | rotatedPath := p rotated i; 2258 | currentWidth := ypart(urcorner(rotatedPath)-llcorner(rotatedPath)); 2259 | if currentWidth < minWidth: 2260 | minWidth := currentWidth; 2261 | minWidthAngle := i; 2262 | fi; 2263 | endfor; 2264 | for i := minWidthAngle -9 step 1 until minWidthAngle + 9: 2265 | rotatedPath := p rotated i; 2266 | currentWidth := ypart(urcorner(rotatedPath)-llcorner(rotatedPath)); 2267 | if currentWidth < minWidth: 2268 | minWidth := currentWidth; 2269 | minWidthAngle := i; 2270 | fi; 2271 | endfor; 2272 | minWidthAngle 2273 | enddef; 2274 | 2275 | % 2276 | % This part is related to knots 2277 | % 2278 | 2279 | % lists are only used in knots so far. 2280 | % The following two macros are taken from byrne.mp 2281 | 2282 | vardef appendList@#(suffix listName)(expr valueToAdd, whereToAdd, omitDuplicates) = 2283 | save v, valueExists; 2284 | string v; 2285 | boolean valueExists; 2286 | if str @# = "": 2287 | if not string listName: 2288 | string listName; 2289 | fi; 2290 | else: 2291 | if not string listName0: 2292 | string listName[]; 2293 | fi; 2294 | fi; 2295 | if unknown listName@#: 2296 | listName@# := ""; 2297 | fi; 2298 | valueExists := false; 2299 | if omitDuplicates: 2300 | valueExists := isInList@#(valueToAdd, listName) 2301 | fi; 2302 | if not valueExists: 2303 | if string valueToAdd: 2304 | v := valueToAdd; 2305 | else: 2306 | v := decimal(valueToAdd); 2307 | fi; 2308 | if length(listName@#) = 0: 2309 | listName@# := v; 2310 | else: 2311 | if (whereToAdd = 1): 2312 | listName@# := listName@# & ", " & v; 2313 | else: 2314 | listName@# := v & ", " & listName@#; 2315 | fi; 2316 | fi; 2317 | fi; 2318 | enddef; 2319 | 2320 | vardef isInList@#(expr valueToLookFor)(suffix listName) = 2321 | save rv, i; 2322 | boolean rv; 2323 | rv := false; 2324 | if str @# = "": 2325 | if not string listName: 2326 | string listName; 2327 | fi; 2328 | else: 2329 | if not string listName0: 2330 | string listName[]; 2331 | fi; 2332 | fi; 2333 | if unknown listName@#: 2334 | listName@# := ""; 2335 | fi; 2336 | if string valueToLookFor: 2337 | forsuffixes i=scantokens(listName@#): 2338 | if (str i = valueToLookFor): 2339 | rv := true; 2340 | fi; 2341 | endfor; 2342 | else: 2343 | for i=scantokens(listName@#): 2344 | if (i = valueToLookFor): 2345 | rv := true; 2346 | fi; 2347 | endfor; 2348 | fi; 2349 | rv 2350 | enddef; 2351 | 2352 | vardef sortList (expr listToSort, ascending) = 2353 | save nPre, nPost, pivot, isSorted, lastValue, preList, postList, rv; 2354 | numeric nPre, nPost, pivot; 2355 | boolean isSorted; 2356 | string preList, postList, rv; 2357 | nPre := 0; 2358 | nPost := 0; 2359 | isSorted := true; 2360 | if ascending: 2361 | lastValue := -infinity; 2362 | else: 2363 | lastValue := infinity; 2364 | fi; 2365 | for i=scantokens(listToSort): 2366 | if (unknown pivot): 2367 | pivot := i; 2368 | fi; 2369 | if ((i < pivot) and ascending) or ((i > pivot) and not ascending): 2370 | appendList (preList, i, -1, false); 2371 | nPre := nPre + 1; 2372 | else: 2373 | appendList (postList, i, -1, false); 2374 | nPost := nPost + 1; 2375 | fi; 2376 | if ((lastValue > i) and ascending) or ((lastValue < i) and not ascending): 2377 | isSorted := false; 2378 | fi; 2379 | lastValue := i; 2380 | endfor; 2381 | if isSorted: 2382 | rv := listToSort; 2383 | else: 2384 | if nPre > 1: 2385 | preList := sortList(preList, ascending); 2386 | fi; 2387 | if nPre > 0: 2388 | preList := preList & ", "; 2389 | else: 2390 | preList := ""; 2391 | fi; 2392 | if nPost > 1: 2393 | postList := sortList(postList, ascending); 2394 | fi; 2395 | rv := preList & postList; 2396 | fi; 2397 | rv 2398 | enddef; 2399 | 2400 | 2401 | % When looking for intersections, knot is browsed with knotStepSize step. 2402 | % Affects nothing interesting. 2403 | numeric knotStepSize; 2404 | knotStepSize := 1/8; 2405 | 2406 | vardef knotFromStrands (suffix knotName) = 2407 | save slidingSegment, timeToAdd, pathSegments, intTimes, tSegWidth, tSegStyle, numberOfSegments, segmentWidth, totalNumberOfSegments, intersections, intersectionsList, layerContents, layersList, b, e, n, layerContents, segmentPicture; 2408 | save shadowsEnabled, allShadowPaths, totalNumberOfShadows, numberOfShadows, shadowPath, tmpShadows; 2409 | boolean shadowsEnabled; 2410 | path shadowPath[], allShadowPaths[]; 2411 | numeric timeToAdd, numberOfShadows, totalNumberOfShadows; 2412 | totalNumberOfShadows := -1; 2413 | tmpShadows := -1; 2414 | path inspectedPath, slidingSegment, pathSegments[]; 2415 | pair intTimes[]; 2416 | numeric intersections[], numberOfSegments[], segmentWidth[], totalNumberOfSegments, tSegWidth, b, e, n; 2417 | picture layerPicture[]; 2418 | string layerContents[], segmentStyle[], tSegStyle; 2419 | totalNumberOfSegments := 0; 2420 | for sNa := 1 step 1 until knotName.nStrands: 2421 | inspectedPath := knotName.strandPath[sNa]; 2422 | tSegWidth := knotName.strandWidth[sNa]; 2423 | tSegStyle := knotName.strandStyle[sNa]; 2424 | for sNb := 1 step 1 until knotName.nStrands: 2425 | for i := -knotStepSize step knotStepSize until length(knotName.strandPath[sNb]): 2426 | slidingSegment := subpath (i, i + 2knotStepSize) of knotName.strandPath[sNb]; 2427 | intTimes0 := (inspectedPath firstIntersectionTimes slidingSegment); 2428 | intTimes1 := (reverse(inspectedPath) firstIntersectionTimes slidingSegment); 2429 | if (sNb = sNa): 2430 | if (xpart(intTimes0) >= i) 2431 | and (xpart(intTimes0) <= i + 2knotStepSize): 2432 | intTimes0 := (-1, -1); 2433 | fi; 2434 | if ((length(inspectedPath) - xpart(intTimes1)) >= i) 2435 | and ((length(inspectedPath) - xpart(intTimes1)) <= i + 2knotStepSize): 2436 | intTimes1 := (-1, -1); 2437 | fi; 2438 | if (i+knotStepSize >= length(inspectedPath)): 2439 | if (xpart(intTimes0) <= knotStepSize) 2440 | or (xpart(intTimes0) = length(inspectedPath)): 2441 | intTimes0 := (-1, -1); 2442 | fi; 2443 | if ((length(inspectedPath) - xpart(intTimes1)) <= knotStepSize) 2444 | or (xpart(intTimes1) = 0): 2445 | intTimes1 := (-1, -1); 2446 | fi; 2447 | fi; 2448 | if (i-knotStepSize <= length(inspectedPath)): 2449 | if (xpart(intTimes0) >= (length(inspectedPath) - knotStepSize)) 2450 | or (xpart(intTimes0) = 0): 2451 | intTimes0 := (-1, -1); 2452 | fi; 2453 | if ((length(inspectedPath) - xpart(intTimes1)) >= (length(inspectedPath) - knotStepSize)) 2454 | or (xpart(intTimes1) = length(inspectedPath)): 2455 | intTimes1 := (-1, -1); 2456 | fi; 2457 | fi; 2458 | fi; 2459 | timeToAdd := -1; 2460 | if ((ypart(intTimes0) > 0) and (ypart(intTimes0) < length(slidingSegment))) 2461 | and ((xpart(intTimes0) >= 0) and (xpart(intTimes0) <= length(inspectedPath))) 2462 | and ((sNb <> sNa) or ((xpart(intTimes0) < i) or (xpart(intTimes0) > i + 1))): 2463 | timeToAdd := xpart(intTimes0); 2464 | elseif (sNb = sNa): 2465 | if ((ypart(intTimes1) > 0) and (ypart(intTimes1) < length(slidingSegment))) 2466 | and ((xpart(intTimes1) >= 0) and (xpart(intTimes1) <= length(inspectedPath))) 2467 | and ((length(inspectedPath) - xpart(intTimes1) < i) or (length(inspectedPath) - xpart(intTimes1) > i + 1)): 2468 | timeToAdd := length(inspectedPath) - xpart(intTimes1); 2469 | fi; 2470 | fi; 2471 | if (timeToAdd >= 0): 2472 | if (timeToAdd = length(inspectedPath)): 2473 | timeToAdd := 0; 2474 | fi; 2475 | appendList[sNa](intersectionsList, round(timeToAdd*10)/10, 1, true); 2476 | fi; 2477 | endfor; 2478 | endfor; 2479 | if known intersectionsList[sNa]: 2480 | numberOfSegments[sNa] := 0; 2481 | for i := scantokens(sortList(intersectionsList[sNa], true)): 2482 | numberOfSegments[sNa] := numberOfSegments[sNa] + 1; 2483 | intersections[numberOfSegments[sNa]] := i; 2484 | endfor; 2485 | intersections[0] := 0; 2486 | if (not cycle knotName.strandPath[sNa]): 2487 | intersections[numberOfSegments[sNa] + 1] := length(knotName.strandPath[sNa]); 2488 | fi; 2489 | for i := 1 step 1 until numberOfSegments[sNa]: 2490 | totalNumberOfSegments := totalNumberOfSegments + 1; 2491 | if (i > 1): 2492 | b := 1/2[intersections[i-1], intersections[i]]; 2493 | else: 2494 | if (not cycle knotName.strandPath[sNa]): 2495 | b := 0; 2496 | else: 2497 | b := 1/2[intersections[numberOfSegments[sNa]] - length(knotName.strandPath[sNa]), intersections[i]]; 2498 | fi; 2499 | fi; 2500 | if (i < numberOfSegments[sNa]): 2501 | e := 1/2[intersections[i], intersections[i+1]]; 2502 | else: 2503 | if (not cycle knotName.strandPath[sNa]): 2504 | e := length(inspectedPath); 2505 | else: 2506 | e := 1/2[intersections[i], intersections[1] + length(knotName.strandPath[sNa])]; 2507 | fi; 2508 | fi; 2509 | pathSegments[totalNumberOfSegments] := subpath (b, e) of inspectedPath; 2510 | if (length(pathSegments[totalNumberOfSegments])<=2): 2511 | pathSegments[totalNumberOfSegments] := pathSubdivide(pathSegments[totalNumberOfSegments], 2); 2512 | fi; 2513 | segmentWidth[totalNumberOfSegments] := tSegWidth; 2514 | segmentStyle[totalNumberOfSegments] := tSegStyle; 2515 | endfor; 2516 | else: 2517 | totalNumberOfSegments := totalNumberOfSegments + 1; 2518 | numberOfSegments[sNa] := 1; 2519 | pathSegments[totalNumberOfSegments] := inspectedPath; 2520 | segmentWidth[totalNumberOfSegments] := tSegWidth; 2521 | segmentStyle[totalNumberOfSegments] := tSegStyle; 2522 | fi; 2523 | n := 0; 2524 | for i := scantokens(knotName.intLayers[sNa]): 2525 | n := n + 1; 2526 | if (n <= numberOfSegments[sNa]): 2527 | appendList[i](layerContents, totalNumberOfSegments - numberOfSegments[sNa] + n, 1, true); 2528 | appendList(layersList, i, 1, true); 2529 | fi; 2530 | endfor; 2531 | if n > 0: 2532 | if n < numberOfSegments[sNa]: 2533 | for i := n + 1 step 1 until numberOfSegments[sNa]: 2534 | appendList0(layerContents, totalNumberOfSegments - numberOfSegments[sNa] + i, 1, true); 2535 | endfor; 2536 | appendList(layersList, 0, 1, true); 2537 | fi; 2538 | else: 2539 | for i := 1 step 1 until numberOfSegments[sNa]: 2540 | appendList0(layerContents, totalNumberOfSegments - numberOfSegments[sNa] + i, 1, true); 2541 | endfor; 2542 | appendList(layersList, 0, 1, true); 2543 | fi; 2544 | endfor; 2545 | image( 2546 | for i := scantokens(sortList(layersList, false)): 2547 | layerPicture[i] := image( 2548 | for j := scantokens(layerContents[i]): 2549 | numberOfShadows := -1; 2550 | shadowsEnabled := false; 2551 | for k := 0 step 1 until totalNumberOfShadows: 2552 | if xpart((subpath (1/10, length(pathSegments[j]) - 1/10) of pathSegments[j]) 2553 | intersectiontimes allShadowPaths[k]) > 0: 2554 | shadowsEnabled := true; 2555 | numberOfShadows := numberOfShadows + 1; 2556 | shadowPath[numberOfShadows] := allShadowPaths[k]; 2557 | shadowDepth[numberOfShadows] := 3/2segmentWidth[j]; 2558 | fi; 2559 | endfor; 2560 | save drawTubeEnds; 2561 | boolean drawTubeEnds; 2562 | drawTubeEnds := false; 2563 | draw tube.scantokens(segmentStyle[j])(pathSegments[j])(segmentWidth[j]) if segmentStyle[j] = "e": withpen thickpen fi; 2564 | tmpShadows := tmpShadows + 1; 2565 | allShadowPaths[tmpShadows] := tubeOutline; 2566 | endfor; 2567 | ); 2568 | for j := 0 step 1 until totalNumberOfShadows: 2569 | layerPicture[i] := layerPicture[i] maskedWith allShadowPaths[j]; 2570 | endfor; 2571 | totalNumberOfShadows := tmpShadows; 2572 | endfor; 2573 | for i := scantokens(sortList(layersList, true)): 2574 | draw layerPicture[i]; 2575 | endfor; 2576 | ) 2577 | enddef; 2578 | 2579 | vardef initKnot (suffix knotName) = 2580 | numeric knotName.nStrands; 2581 | knotName.nStrands := 0; 2582 | path knotName.strandPath[]; 2583 | numeric knotName.strandWidth[]; 2584 | string knotName.strandStyle[]; 2585 | string knotName.intLayers[]; 2586 | enddef; 2587 | 2588 | vardef addStrandToKnot (suffix knotName) (expr p, w, s, intersectionLayers) = 2589 | save n; 2590 | if not known knotName.nStrands: 2591 | numeric knotName.nStrands; 2592 | knotName.nStrands := 0; 2593 | fi; 2594 | if not path knotName.strandPath0: 2595 | path knotName.strandPath[]; 2596 | fi; 2597 | if not numeric knotName.strandWidth0: 2598 | numeric knotName.strandWidth[]; 2599 | fi; 2600 | if not string knotName.strandStyle0: 2601 | string knotName.strandStyle[]; 2602 | fi; 2603 | if not string knotName.intLayers0: 2604 | string knotName.intLayers[]; 2605 | fi; 2606 | knotName.nStrands := knotName.nStrands + 1; 2607 | n := knotName.nStrands; 2608 | knotName.strandPath[n] := p; 2609 | knotName.strandWidth[n] := w; 2610 | knotName.strandStyle[n] := s; 2611 | knotName.intLayers[n] := intersectionLayers; 2612 | enddef; 2613 | --------------------------------------------------------------------------------