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
14 * ./output-64 <dense-64.cfm 0.1 50 >t.stl
19 * http://www.ennex.com/~fabbers/StL.asp
20 * http://en.wikipedia.org/wiki/STL_%28file_format%29
21 * saved here as stl-format-wikipedia.txt
25 * We add thickness by adding vertices as follows:
33 * *E *G | :*E *G *E *G *E *G *E
35 * *D ____________|*D ____________ *D ____________ *D ____________ *D __
37 * / \ / :\ / \ / \ / \
38 * \ *A 4/ \: \5 *B / \ *B / \ *B / \
41 * *B \ / *B2| \2 1/ 0*A \ / *A \ / *A
42 * \ / : | \ / . ' \ / \ /
43 * _______ *C _____ :_|___ *C' __________ *C ___________ *C _________
44 * /\ : | 3 /\. 0 /\ /\
45 * / \ :3| / \ ` . / \ / \
46 * *A / \ *A | /4 5\ 5*B / \ *B / \ *B
47 * / \ 1: / / \ / \ / \
48 * / \ :/ / 4 \ / \ / \
49 * / *B2 2\ / /1 *A \ / *A \ / *A \ /
50 * \ / \/:/ 0 \ / \ / \ /
51 * *C ____________|*C ____________ *C ___________ *C ___________ *C __
53 * / \ / :\ / \ / \ / \
54 * \ *A3 4/ \: \5 5*B / \ *B / \ *B / \
57 * *B \ / *B | \ / *A \ / *A \ / *A
58 * \ / : | \ / . ' \ / \ /
59 * _______ *C _____ :_|___ *C' __________ *C ___________ *C _________
67 * _______ *C _____ :_|___ *C ___________ *C ___________ *C _________
70 * *A / \ *A | /4 5\ *B / \ *B / \ *B
71 * / \ 1: / / \ / \ / \
73 * / *B2 2\ / /1 0*A \ / *A \ / *A \ /
74 * \ / \/:/ \ / \ / \ /
75 * *D ____________|*D ____________ *D ___________ *D ___________ *D __
77 * *E *G | :*E *G *E *G *E *G *E
82 * Each A,B,C,D represents two vertices - one on each side of the
83 * surface. Each E,F,G represents a several vertices in an arc around
84 * the rim. Digits are `e' values for edges or relative AB
87 * The constructions we use are:
89 * A, B: Extend the normal vector of the containing intriangle
90 * from its centroid for thickness.
92 * C: Take mean position (centroid) of all surrounding
93 * computed A and B, and extend from base point in
94 * direction of that centroid for thickness.
97 * Compute notional rim vector R as mean of the two
98 * adjoining rim edges, and consider plane P as
99 * that passing through the base point normal to R.
100 * Project the centroid of the two adjoining non-rim
101 * vertices onto P. Now D(EF)+ED is the semicircle
102 * in P centred on the base point with radius thickness
103 * and which is opposite that centroid.
105 * G: Each F is the mean of those two adjacent Es with the
106 * same angle in their respective Ps.
110 * For each input vertex on each side, the six (or perhaps only three)
111 * triangles formed by its C or D and the surrounding Cs and/or Ds.
113 * For each G, the six triangles formed by that G and the adjacent
114 * four Fs (or two Fs and two Ds) and two Es.
120 /*---------- declarations and useful subroutines ----------*/
122 #define FOR_SIDE for (side=0; side<2; side++)
129 #define NDEF (NG*2+1)
131 #define OUTPUT_ARRAY_LIST(DO_OUTPUT_ARRAY) \
132 DO_OUTPUT_ARRAY(ovAB) \
133 DO_OUTPUT_ARRAY(ovC) \
134 DO_OUTPUT_ARRAY(ovDEF) \
137 static OutVertex ovAB[N][2][2]; /* indices: vertex to W, A=0 B=1, side */
138 static OutVertex ovC[N][2];
139 static OutVertex ovDEF[X][2][NDEF]; /* x, !!y, angle */
140 static OutVertex ovG[X][2][NG]; /* x, !!y, angle; for G to the East of x */
144 static double thick; /* in input units */
147 static void outfacet(int rev, const OutVertex *a,
148 const OutVertex *b, const OutVertex *c);
150 typedef int int_map(int);
151 static int defs_aroundmap_swap(int around) { return NDEF-1-around; }
152 static int int_identity_function(int i) { return i; }
154 static void normalise_thick(double a[D3]) {
155 /* multiplies a by a scalar so that its magnitude is thick */
157 double multby= thick / magnD(a);
161 static void triangle_normal(double normal[D3], const double a[D3],
162 const double b[D3], const double c[D3]) {
163 double ab[D3], ac[D3];
166 K ab[k]= b[k] - a[k];
167 K ac[k]= c[k] - a[k];
171 static OutVertex *invertex2outvertexab(int v0, int e, int side) {
174 case 0: vref=v0; vchk=EDGE_END2(v0,1); ab=0; break;
175 case 1: vref= vchk=EDGE_END2(v0,2); ab=1; break;
176 case 2: vref=EDGE_END2(v0,3); vchk=EDGE_END2(v0,2); ab=0; break;
177 case 3: vref=EDGE_END2(v0,3); vchk=EDGE_END2(v0,4); ab=1; break;
178 case 4: vref= vchk=EDGE_END2(v0,4); ab=0; break;
179 case 5: vref=v0; vchk=EDGE_END2(v0,5); ab=1; break;
182 if (vchk<0) return 0;
183 int sw= vertices_span_join_p(v0,vref);
184 return &ovAB[vref][ab^sw][side^sw];
187 /*---------- output vertices ----------*/
189 #define Ok(ov, value) ((ov).p[k]= outvertex_coord_check(value))
191 static double outvertex_coord_check(double value) {
192 assert(-10 < value && value < 10);
196 static void compute_outvertices(void) {
197 int v0,k,side,ab,x,y;
200 for (ab=0; ab<2; ab++) {
201 int v1= EDGE_END2(v0, ab?5:0);
202 int v2= EDGE_END2(v0, ab?0:1);
205 double normal[D3], centroid[D3];
206 triangle_normal(normal, in[v0],in[v1],in[v2]);
207 normalise_thick(normal);
208 K centroid[k]= (in[v0][k] + in[v1][k] + in[v2][k]) / 3.0;
209 K Ok(ovAB[v0][ab][0], centroid[k] + normal[k]);
210 K Ok(ovAB[v0][ab][1], centroid[k] - normal[k]);
214 int vw= EDGE_END2(v0,3);
215 int vnw= EDGE_END2(v0,2);
216 int vsw= EDGE_END2(v0,4);
217 if (vnw<0 || vsw<0 || vw<0)
224 OutVertex *ovab= invertex2outvertexab(v0,e,side);
226 assert(!isnan(ovab->p[k]));
227 adjust[k] += ovab->p[k];
231 K adjust[k] -= in[v0][k];
232 normalise_thick(adjust);
233 K Ok(ovC[v0][side], in[v0][k] + adjust[k]);
236 FOR_RIM_VERTEX(y,x,v0) {
237 double rim[D3], inner[D3], radius_cos[D3], radius_sin[D3];
238 int vback, vfwd, around;
240 /* compute mean rim vector, which is just the vector between
241 * the two adjacent rim vertex (ignoring the base vertex) */
242 vback= EDGE_END2(v0,3);
243 vfwd= EDGE_END2(v0,0);
244 assert(vback>=0 && vfwd>=0);
245 K rim[k]= in[vfwd][k] - in[vback][k];
247 /* compute the inner centroid */
248 vback= EDGE_END2(v0,4);
249 if (vback>=0) { /* North rim */
250 vfwd= EDGE_END2(v0,5);
251 } else { /* South rim */
252 vback= EDGE_END2(v0,2);
253 vfwd= EDGE_END2(v0,1);
255 assert(vback>=0 && vfwd>=0);
256 K inner[k]= (in[vback][k] + in[vfwd][k]) / 2;
257 K inner[k] -= in[v0][k];
259 /* we compute the radius cos and sin vectors by cross producting
260 * the vector to the inner with the rim, and then again, and
262 xprod(radius_cos,rim,inner);
263 xprod(radius_sin,rim,radius_cos);
264 normalise_thick(radius_cos);
265 normalise_thick(radius_sin);
267 int_map *around_map= y ? int_identity_function : defs_aroundmap_swap;
269 for (around=0; around<NDEF; around++) {
270 double angle= around_map(around) * M_PI / (NDEF-1);
271 K Ok(ovDEF[x][!!y][around],
273 cos(angle) * radius_cos[k] +
274 sin(angle) * radius_sin[k]);
277 FOR_RIM_VERTEX(y,x,v0) {
278 int vfwd= EDGE_END2(v0,0);
281 int_map *around_map= vertices_span_join_p(v0,vfwd)
282 ? defs_aroundmap_swap : int_identity_function;
283 for (aroung=0; aroung<NG; aroung++) {
284 K Ok(ovG[x][!!y][aroung],
285 0.5 * (ovDEF[ x ][!! y ][aroung*2+1].p[k] +
286 ovDEF[vfwd & XMASK][!!(vfwd & ~XMASK)][around_map(aroung*2+1)].p[k]));
291 /*---------- output facets ----------*/
293 static void outfacets_around(int reverse, OutVertex *middle,
294 int nsurr, OutVertex *surround[nsurr]) {
295 /* Some entries in surround may be 0, in which case all affected
296 * facets will be skipped */
298 for (i=0; i<nsurr; i++) {
299 OutVertex *s0= surround[i];
300 OutVertex *s1= surround[(i+1) % nsurr];
301 if (!s0 || !s1) continue;
302 outfacet(reverse, middle,s0,s1);
306 static OutVertex *invertex2outvertexcd(v0,side) {
307 if (!RIM_VERTEX_P(v0)) return &ovC[v0][side];
309 int around= side ? NDEF-1 : 0;
310 int rimy= !!(v0 & ~XMASK);
311 return &ovDEF[v0 & XMASK][rimy][around];
314 static void outfacets(void) {
315 int v0,e,side,aroung;
318 OutVertex *defs=0, *defs1=0;
320 int_map *defs1aroundmap= 0;
321 if (RIM_VERTEX_P(v0)) {
323 rimy= !!(v0 & ~XMASK);
324 int v1= EDGE_END2(v0,0); assert(v1>=0);
325 gs= ovG [v0 & XMASK][rimy];
326 defs= ovDEF[v0 & XMASK][rimy];
327 defs1= ovDEF[v1 & XMASK][!!(v1 & ~XMASK)];
328 defs1aroundmap= vertices_span_join_p(v0,v1)
329 ? defs_aroundmap_swap : int_identity_function;
331 for (aroung=0; aroung<NG; aroung++) {
332 int around= aroung*2;
333 OutVertex *surround[6];
334 for (e=0; e<3; e++) {
335 surround[e ]= &defs1[defs1aroundmap(around +e)];
336 surround[e+3]= &defs [ around+2-e ];
338 outfacets_around(rimy, &gs[aroung], 6,surround);
344 for (ab=0; ab<2; ab++) {
345 int v1= EDGE_END2(v0, ab ? 5 : 0);
346 int v2= EDGE_END2(v0, ab ? 0 : 1);
347 if (v1<0 || v2<0) continue;
349 invertex2outvertexcd(v0,side),
350 invertex2outvertexcd(v1,side^vertices_span_join_p(v0,v1)),
351 invertex2outvertexcd(v2,side^vertices_span_join_p(v0,v2)));
357 /*---------- operations on very output vertex ----------*/
359 #define DO_OUTPUT_ARRAY_OUTVERTEX_ARRAY(fn,ovX) \
360 ((fn)(sizeof((ovX))/sizeof(OutVertex), (OutVertex*)(ovX)))
362 static void blank_outvertex_array(int n, OutVertex ovX[n]) {
368 static void blank_outvertices(void) {
369 #define BLANK_OUTPUT_ARRAY(ovX) \
370 DO_OUTPUT_ARRAY_OUTVERTEX_ARRAY(blank_outvertex_array, ovX);
371 OUTPUT_ARRAY_LIST(BLANK_OUTPUT_ARRAY)
374 static void transform_outvertex_array(int n, OutVertex ovX[n]) {
377 K ovX[i].p[k] *= scale;
379 * double min[D3]= thick;
380 * if (ovX[i].p[k] < min)
382 * for (i=0; i<n; i++) {
383 * K ovX[k].p[k] -= min;
387 static void transform_outvertices(void) {
388 #define TRANSFORM_OUTPUT_ARRAY(ovX) \
389 DO_OUTPUT_ARRAY_OUTVERTEX_ARRAY(transform_outvertex_array, ovX);
390 OUTPUT_ARRAY_LIST(TRANSFORM_OUTPUT_ARRAY)
393 /*---------- output file ----------*/
395 static void wr(const void *p, size_t sz) {
396 if (fwrite(p,sz,1,stdout) != 1)
400 #define WR(x) wr((const void*)&(x), sizeof((x)))
402 static void wf(double d) {
403 typedef float ieee754single;
405 assert(sizeof(ieee754single)==4);
408 assert(d >= -1e3 && d <= 1e3);
410 #if BYTE_ORDER==BIG_ENDIAN
411 union { uint8_t b[4]; ieee754single f; } value; value.f= d;
412 int i; for (i=3; i>=0; i--) WR(value.b[i]);
413 #elif BYTE_ORDER==LITTLE_ENDIAN
417 # error not little or big endian!
421 static uint32_t noutfacets;
422 static uint32_t noutfacets_counted;
423 static long badfacets;
425 static void outfacet(int rev, const OutVertex *a,
426 const OutVertex *b, const OutVertex *c) {
427 if (rev) { outfacet(0, c,b,a); return; }
433 assert(!isnan(a->p[k]));
434 assert(!isnan(b->p[k]));
435 assert(!isnan(c->p[k]));
438 triangle_normal(normal, a->p, b->p, c->p);
439 double multby= 1/magnD(normal);
447 if (!~noutfacets_counted) return;
449 K normal[k] *= multby;
459 static void write_file(void) {
460 static const char header[80]= "#!/usr/bin/meshlab\n" "binary STL file\n";
462 if (isatty(1)) fail("will not write binary stl to tty!\n");
466 noutfacets_counted=~(uint32_t)0;
471 noutfacets_counted= noutfacets;
474 assert(noutfacets == noutfacets_counted);
476 if (fflush(stdout)) diee("fflush stdout");
479 fprintf(stderr,"%ld degenerate facets!\n",badfacets);
485 /*---------- main program etc. ----------*/
487 int main(int argc, const char *const *argv) {
490 if (argc!=3 || argv[1][0]=='-') { fputs("bad usage\n",stderr); exit(8); }
491 thick= atof(argv[1]);
492 scale= atof(argv[2]) * 0.5; /* circle is unit radius but arg is diameter */
494 errno= 0; r= fread(&in,sizeof(in),1,stdin);
495 if (r!=1) diee("fread");
498 compute_outvertices();
499 transform_outvertices();
501 if (fclose(stdout)) diee("fclose stdout");