2 * Generates an STL file
3 * usage: ./output+<size> <thickness> <unit-circle-diameter>
4 * thickness is in original moebius unit circle units
5 * unit circle diameter is in whatever dimensions the STL file uses
9 * - define a shape for the rim so that it is solid
10 * - scale the coordinates
11 * - translate the coordinates so they're all positive
15 * http://www.ennex.com/~fabbers/StL.asp
16 * http://en.wikipedia.org/wiki/STL_%28file_format%29
17 * saved here as stl-format-wikipedia.txt
21 * We add thickness by adding vertices as follows:
29 * *E *G | :*E *G *E *G *E *G *E
31 * *D ____________|*D ____________ *D ____________ *D ____________ *D __
33 * / \ / :\ / \ / \ / \
34 * \ *A 4/ \: \5 *B / \ *B / \ *B / \
37 * *B \ / *B2| \2 1/ 0*A \ / *A \ / *A
38 * \ / : | \ / . ' \ / \ /
39 * _______ *C _____ :_|___ *C' __________ *C ___________ *C _________
40 * /\ : | 3 /\. 0 /\ /\
41 * / \ :3| / \ ` . / \ / \
42 * *A / \ *A | /4 5\ 5*B / \ *B / \ *B
43 * / \ 1: / / \ / \ / \
44 * / \ :/ / 4 \ / \ / \
45 * / *B2 2\ / /1 *A \ / *A \ / *A \ /
46 * \ / \/:/ 0 \ / \ / \ /
47 * *C ____________|*C ____________ *C ___________ *C ___________ *C __
49 * / \ / :\ / \ / \ / \
50 * \ *A3 4/ \: \5 5*B / \ *B / \ *B / \
53 * *B \ / *B | \ / *A \ / *A \ / *A
54 * \ / : | \ / . ' \ / \ /
55 * _______ *C _____ :_|___ *C' __________ *C ___________ *C _________
63 * _______ *C _____ :_|___ *C ___________ *C ___________ *C _________
66 * *A / \ *A | /4 5\ *B / \ *B / \ *B
67 * / \ 1: / / \ / \ / \
69 * / *B2 2\ / /1 0*A \ / *A \ / *A \ /
70 * \ / \/:/ \ / \ / \ /
71 * *D ____________|*D ____________ *D ___________ *D ___________ *D __
73 * *E *G | :*E *G *E *G *E *G *E
78 * Each A,B,C,D represents two vertices - one on each side of the
79 * surface. Each E,F,G represents a several vertices in an arc around
80 * the rim. Digits are `e' values for edges or relative AB
83 * The constructions we use are:
85 * A, B: Extend the normal vector of the containing intriangle
86 * from its centroid for thickness.
88 * C: Take mean position (centroid) of all surrounding
89 * computed A and B, and extend from base point in
90 * direction of that centroid for thickness.
93 * Compute notional rim vector R as mean of the two
94 * adjoining rim edges, and consider plane P as
95 * that passing through the base point normal to R.
96 * Project the centroid of the two adjoining non-rim
97 * vertices onto P. Now D(EF)+ED is the semicircle
98 * in P centred on the base point with radius thickness
99 * and which is opposite that centroid.
101 * G: Each F is the mean of those two adjacent Es with the
102 * same angle in their respective Ps.
106 * For each non-rim vertex on each side, the six triangles formed by
107 * its C and the surrounding A's and B's.
109 * For each rim vertex on each side, the two triangles formed by its
110 * D and the nearest As and Bs (two As and one B or vice versa).
112 * For each rim edge on each side, the triangle formed by that edge's
113 * ends' Ds and the corresponding A or B.
115 * For each G, the six triangles formed by that G and the adjacent
116 * four Fs (or two Fs and two Ds) and two Es.
122 /*---------- declarations and useful subroutines ----------*/
124 #define FOR_SIDE for (side=0; side<2; side++)
131 #define NDEF (NG*2+1)
133 #define OUTPUT_ARRAY_LIST(DO_OUTPUT_ARRAY) \
134 DO_OUTPUT_ARRAY(ovAB) \
135 DO_OUTPUT_ARRAY(ovC) \
136 DO_OUTPUT_ARRAY(ovDEF) \
139 static OutVertex ovAB[N][2][2]; /* indices: vertex to W, A=0 B=1, side */
140 static OutVertex ovC[N][2];
141 static OutVertex ovDEF[X][2][NDEF]; /* x, !!y, angle */
142 static OutVertex ovG[X][2][NG]; /* x, !!y, angle; for G to the East of x */
146 static double thick; /* in input units */
149 static void outfacet(int rev, const OutVertex *a,
150 const OutVertex *b, const OutVertex *c);
152 static void normalise_thick(double a[D3]) {
153 /* multiplies a by a scalar so that its magnitude is thick */
155 double multby= thick / magnD(a);
159 static void triangle_normal(double normal[D3], const double a[D3],
160 const double b[D3], const double c[D3]) {
161 double ab[D3], ac[D3];
164 K ab[k]= b[k] - a[k];
165 K ac[k]= c[k] - a[k];
169 static OutVertex *invertex2outvertexab(int v0, int e, int side) {
172 case 0: vref=v0; vchk=EDGE_END2(v0,1); ab=0; break;
173 case 1: vref= vchk=EDGE_END2(v0,2); ab=1; break;
174 case 2: vref=EDGE_END2(v0,3); vchk=EDGE_END2(v0,2); ab=0; break;
175 case 3: vref=EDGE_END2(v0,3); vchk=EDGE_END2(v0,4); ab=1; break;
176 case 4: vref= vchk=EDGE_END2(v0,4); ab=0; break;
177 case 5: vref=v0; vchk=EDGE_END2(v0,5); ab=1; break;
180 if (vchk<0) return 0;
181 int sw= vertices_span_join_p(v0,vref);
182 return &ovAB[vref][ab^sw][side^sw];
185 /*---------- output vertices ----------*/
187 #define Ok(ov, value) ((ov).p[k]= outvertex_coord_check(value))
189 static double outvertex_coord_check(double value) {
190 assert(-10 < value && value < 10);
194 static void compute_outvertices(void) {
195 int v0,k,side,ab,x,y;
198 for (ab=0; ab<2; ab++) {
199 int v1= EDGE_END2(v0, ab?5:0);
200 int v2= EDGE_END2(v0, ab?0:1);
203 double normal[D3], centroid[D3];
204 triangle_normal(normal, in[v0],in[v1],in[v2]);
205 normalise_thick(normal);
206 K centroid[k]= (in[v0][k] + in[v1][k] + in[v2][k]) / 3.0;
207 K Ok(ovAB[v0][ab][0], centroid[k] + normal[k]);
208 K Ok(ovAB[v0][ab][1], centroid[k] - normal[k]);
212 int vw= EDGE_END2(v0,3);
213 int vnw= EDGE_END2(v0,2);
214 int vsw= EDGE_END2(v0,4);
215 if (vnw<0 || vsw<0 || vw<0)
222 OutVertex *ovab= invertex2outvertexab(v0,e,side);
224 assert(!isnan(ovab->p[k]));
225 adjust[k] += ovab->p[k];
229 K adjust[k] -= in[v0][k];
230 normalise_thick(adjust);
231 K Ok(ovC[v0][side], in[v0][k] + adjust[k]);
234 FOR_RIM_VERTEX(y,x,v0) {
235 double rim[D3], inner[D3], radius_cos[D3], radius_sin[D3];
236 int vback, vfwd, around;
238 /* compute mean rim vector, which is just the vector between
239 * the two adjacent rim vertex (ignoring the base vertex) */
240 vback= EDGE_END2(v0,3);
241 vfwd= EDGE_END2(v0,0);
242 assert(vback>=0 && vfwd>=0);
243 K rim[k]= in[vfwd][k] - in[vback][k];
245 /* compute the inner centroid */
246 vback= EDGE_END2(v0,4);
247 if (vback>=0) { /* North rim */
248 vfwd= EDGE_END2(v0,5);
249 } else { /* South rim */
250 vback= EDGE_END2(v0,2);
251 vfwd= EDGE_END2(v0,1);
253 assert(vback>=0 && vfwd>=0);
254 K inner[k]= (in[vback][k] + in[vfwd][k]) / 2;
255 K inner[k] -= in[v0][k];
257 /* we compute the radius cos and sin vectors by cross producting
258 * the vector to the inner with the rim, and then again, and
260 xprod(radius_cos,rim,inner);
261 xprod(radius_sin,rim,radius_cos);
262 normalise_thick(radius_cos);
263 normalise_thick(radius_sin);
265 for (around=0; around<NDEF; around++) {
266 double angle= around * M_PI / (NDEF-1);
267 K Ok(ovDEF[x][!!y][around],
269 cos(angle) * radius_cos[k] +
270 sin(angle) * radius_sin[k]);
273 FOR_RIM_VERTEX(y,x,v0) {
274 int vfwd= EDGE_END2(v0,0);
277 for (around=0; around<NG; around++) {
278 K Ok(ovG[x][!!y][around],
279 0.5 * (ovDEF[ x ][!!y][around*2].p[k] +
280 ovDEF[vfwd & XMASK][!!y][around*2].p[k]));
285 /*---------- output facets ----------*/
287 static void outfacets_around(int reverse, OutVertex *middle,
288 int nsurr, OutVertex *surround[nsurr]) {
289 /* Some entries in surround may be 0, in which case all affected
290 * facets will be skipped */
292 for (i=0; i<nsurr; i++) {
293 OutVertex *s0= surround[i];
294 OutVertex *s1= surround[(i+1) % nsurr];
295 if (!s0 || !s1) continue;
296 outfacet(reverse, middle,s0,s1);
300 static int defs_aroundmap_swap(int around) { return NDEF-around; }
301 static int int_identity_function(int i) { return i; }
303 static void outfacets(void) {
304 int v0,e,side,aroung, k;
307 OutVertex *defs=0, *defs1=0;
308 int (*defs1aroundmap)(int)=0, rimy=-1;
309 if (RIM_VERTEX_P(v0)) {
311 rimy= !!(v0 & ~XMASK);
312 int v1= EDGE_END2(v0,0); assert(v1>=0);
313 gs= ovG [v0 & XMASK][rimy];
314 defs= ovDEF[v0 & XMASK][rimy];
315 defs1= ovDEF[v1 & XMASK][rimy];
316 defs1aroundmap= vertices_span_join_p(v0,v1)
317 ? defs_aroundmap_swap : int_identity_function;
319 for (aroung=0; aroung<NG; aroung++) {
320 int around= aroung*2;
321 OutVertex *surround[6];
322 for (e=0; e<3; e++) {
323 surround[e ]= &defs1[defs1aroundmap(around +e)];
324 surround[e+3]= &defs [ around+2-e ];
326 outfacets_around(rimy, &gs[aroung], 6,surround);
333 int around= side ? NDEF-1 : 0;
335 OutVertex *ab= &ovAB[v0][!rimy][side];
336 OutVertex *cd1= &defs1[defs1aroundmap(around)];
337 outfacet(side^rimy,cd,ab,cd1);
343 ab[e]= invertex2outvertexab(v0,e,side);
345 K assert(!isnan(ab[e]->p[k]));
347 outfacets_around(side, cd, 6,ab);
352 /*---------- operations on very output vertex ----------*/
354 #define DO_OUTPUT_ARRAY_OUTVERTEX_ARRAY(fn,ovX) \
355 ((fn)(sizeof((ovX))/sizeof(OutVertex), (OutVertex*)(ovX)))
357 static void blank_outvertex_array(int n, OutVertex ovX[n]) {
363 static void blank_outvertices(void) {
364 #define BLANK_OUTPUT_ARRAY(ovX) \
365 DO_OUTPUT_ARRAY_OUTVERTEX_ARRAY(blank_outvertex_array, ovX);
366 OUTPUT_ARRAY_LIST(BLANK_OUTPUT_ARRAY)
369 static void transform_outvertex_array(int n, OutVertex ovX[n]) {
372 K ovX[i].p[k] *= scale;
374 * double min[D3]= thick;
375 * if (ovX[i].p[k] < min)
377 * for (i=0; i<n; i++) {
378 * K ovX[k].p[k] -= min;
382 static void transform_outvertices(void) {
383 #define TRANSFORM_OUTPUT_ARRAY(ovX) \
384 DO_OUTPUT_ARRAY_OUTVERTEX_ARRAY(transform_outvertex_array, ovX);
385 OUTPUT_ARRAY_LIST(TRANSFORM_OUTPUT_ARRAY)
388 /*---------- output file ----------*/
390 static void wr(const void *p, size_t sz) {
391 if (fwrite(p,sz,1,stdout) != 1)
395 #define WR(x) wr((const void*)&(x), sizeof((x)))
397 static void wf(double d) {
398 typedef float ieee754single;
400 assert(sizeof(ieee754single)==4);
403 assert(d >= -1e3 && d <= 1e3);
405 #if BYTE_ORDER==BIG_ENDIAN
406 union { uint8_t b[4]; ieee754single f; } value; value.f= d;
407 int i; for (i=3; i>=0; i--) WR(value.b[i]);
408 #elif BYTE_ORDER==LITTLE_ENDIAN
412 # error not little or big endian!
416 static uint32_t noutfacets;
417 static uint32_t noutfacets_counted;
419 static void outfacet(int rev, const OutVertex *a,
420 const OutVertex *b, const OutVertex *c) {
421 if (rev) { outfacet(0, c,b,a); return; }
427 assert(!isnan(a->p[k]));
428 assert(!isnan(b->p[k]));
429 assert(!isnan(c->p[k]));
432 triangle_normal(normal, a->p, b->p, c->p);
433 double multby= 1/magnD(normal);
439 if (!~noutfacets_counted) return;
441 K normal[k] *= multby;
451 static void write_file(void) {
452 static const char header[80]= "#!/usr/bin/meshlab\n" "binary STL file\n";
454 if (isatty(1)) fail("will not write binary stl to tty!\n");
458 noutfacets_counted=~(uint32_t)0;
463 noutfacets_counted= noutfacets;
466 assert(noutfacets == noutfacets_counted);
468 if (fflush(stdout)) diee("fflush stdout");
472 /*---------- main program etc. ----------*/
474 int main(int argc, const char *const *argv) {
477 if (argc!=3 || argv[1][0]=='-') { fputs("bad usage\n",stderr); exit(8); }
478 thick= atof(argv[1]);
479 scale= atof(argv[2]) * 0.5; /* circle is unit radius but arg is diameter */
481 errno= 0; r= fread(&in,sizeof(in),1,stdin);
482 if (r!=1) diee("fread");
485 compute_outvertices();
486 transform_outvertices();
488 if (fclose(stdout)) diee("fclose stdout");