Voro++
cell.cc
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1 // Voro++, a 3D cell-based Voronoi library
2 //
3 // Author : Chris H. Rycroft (LBL / UC Berkeley)
4 // Email : chr@alum.mit.edu
5 // Date : August 30th 2011
6 
7 /** \file cell.cc
8  * \brief Function implementations for the voronoicell and related classes. */
9 
10 #include <cmath>
11 #include <cstring>
12 
13 #include "config.hh"
14 #include "common.hh"
15 #include "cell.hh"
16 
17 namespace voro {
18 
19 /** Constructs a Voronoi cell and sets up the initial memory. */
21  current_vertices(init_vertices), current_vertex_order(init_vertex_order),
22  current_delete_size(init_delete_size), current_delete2_size(init_delete2_size),
23  ed(new int*[current_vertices]), nu(new int[current_vertices]),
24  pts(new double[3*current_vertices]), mem(new int[current_vertex_order]),
25  mec(new int[current_vertex_order]), mep(new int*[current_vertex_order]),
26  ds(new int[current_delete_size]), stacke(ds+current_delete_size),
27  ds2(new int[current_delete2_size]), stacke2(ds2+current_delete_size),
28  current_marginal(init_marginal), marg(new int[current_marginal]) {
29  int i;
30  for(i=0;i<3;i++) {
31  mem[i]=init_n_vertices;mec[i]=0;
32  mep[i]=new int[init_n_vertices*((i<<1)+1)];
33  }
34  mem[3]=init_3_vertices;mec[3]=0;
35  mep[3]=new int[init_3_vertices*7];
36  for(i=4;i<current_vertex_order;i++) {
37  mem[i]=init_n_vertices;mec[i]=0;
38  mep[i]=new int[init_n_vertices*((i<<1)+1)];
39  }
40 }
41 
42 /** The voronoicell destructor deallocates all the dynamic memory. */
44  for(int i=current_vertex_order-1;i>=0;i--) if(mem[i]>0) delete [] mep[i];
45  delete [] marg;
46  delete [] ds2;delete [] ds;
47  delete [] mep;delete [] mec;
48  delete [] mem;delete [] pts;
49  delete [] nu;delete [] ed;
50 }
51 
52 /** Ensures that enough memory is allocated prior to carrying out a copy.
53  * \param[in] vc a reference to the specialized version of the calling class.
54  * \param[in] vb a pointered to the class to be copied. */
55 template<class vc_class>
57  while(current_vertex_order<vb->current_vertex_order) add_memory_vorder(vc);
58  for(int i=0;i<current_vertex_order;i++) while(mem[i]<vb->mec[i]) add_memory(vc,i,ds2);
59  while(current_vertices<vb->p) add_memory_vertices(vc);
60 }
61 
62 /** Copies the vertex and edge information from another class. The routine
63  * assumes that enough memory is available for the copy.
64  * \param[in] vb a pointer to the class to copy. */
66  int i,j;
67  p=vb->p;up=0;
68  for(i=0;i<current_vertex_order;i++) {
69  mec[i]=vb->mec[i];
70  for(j=0;j<mec[i]*(2*i+1);j++) mep[i][j]=vb->mep[i][j];
71  for(j=0;j<mec[i]*(2*i+1);j+=2*i+1) ed[mep[i][j+2*i]]=mep[i]+j;
72  }
73  for(i=0;i<p;i++) nu[i]=vb->nu[i];
74  for(i=0;i<3*p;i++) pts[i]=vb->pts[i];
75 }
76 
77 /** Copies the information from another voronoicell class into this
78  * class, extending memory allocation if necessary.
79  * \param[in] c the class to copy. */
82  check_memory_for_copy(*this,vb);copy(vb);
83  int i,j;
84  for(i=0;i<c.current_vertex_order;i++) {
85  for(j=0;j<c.mec[i]*i;j++) mne[i][j]=0;
86  for(j=0;j<c.mec[i];j++) ne[c.mep[i][(2*i+1)*j+2*i]]=mne[i]+(j*i);
87  }
88 }
89 
90 /** Copies the information from another voronoicell_neighbor class into this
91  * class, extending memory allocation if necessary.
92  * \param[in] c the class to copy. */
95  check_memory_for_copy(*this,vb);copy(vb);
96  int i,j;
97  for(i=0;i<c.current_vertex_order;i++) {
98  for(j=0;j<c.mec[i]*i;j++) mne[i][j]=c.mne[i][j];
99  for(j=0;j<c.mec[i];j++) ne[c.mep[i][(2*i+1)*j+2*i]]=mne[i]+(j*i);
100  }
101 }
102 
103 /** Translates the vertices of the Voronoi cell by a given vector.
104  * \param[in] (x,y,z) the coordinates of the vector. */
105 void voronoicell_base::translate(double x,double y,double z) {
106  x*=2;y*=2;z*=2;
107  double *ptsp=pts;
108  while(ptsp<pts+3*p) {
109  *(ptsp++)=x;*(ptsp++)=y;*(ptsp++)=z;
110  }
111 }
112 
113 /** Increases the memory storage for a particular vertex order, by increasing
114  * the size of the of the corresponding mep array. If the arrays already exist,
115  * their size is doubled; if they don't exist, then new ones of size
116  * init_n_vertices are allocated. The routine also ensures that the pointers in
117  * the ed array are updated, by making use of the back pointers. For the cases
118  * where the back pointer has been temporarily overwritten in the marginal
119  * vertex code, the auxiliary delete stack is scanned to find out how to update
120  * the ed value. If the template has been instantiated with the neighbor
121  * tracking turned on, then the routine also reallocates the corresponding mne
122  * array.
123  * \param[in] i the order of the vertex memory to be increased. */
124 template<class vc_class>
125 void voronoicell_base::add_memory(vc_class &vc,int i,int *stackp2) {
126  int s=(i<<1)+1;
127  if(mem[i]==0) {
128  vc.n_allocate(i,init_n_vertices);
129  mep[i]=new int[init_n_vertices*s];
130  mem[i]=init_n_vertices;
131 #if VOROPP_VERBOSE >=2
132  fprintf(stderr,"Order %d vertex memory created\n",i);
133 #endif
134  } else {
135  int j=0,k,*l;
136  mem[i]<<=1;
137  if(mem[i]>max_n_vertices) voro_fatal_error("Point memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
138 #if VOROPP_VERBOSE >=2
139  fprintf(stderr,"Order %d vertex memory scaled up to %d\n",i,mem[i]);
140 #endif
141  l=new int[s*mem[i]];
142  int m=0;
143  vc.n_allocate_aux1(i);
144  while(j<s*mec[i]) {
145  k=mep[i][j+(i<<1)];
146  if(k>=0) {
147  ed[k]=l+j;
148  vc.n_set_to_aux1_offset(k,m);
149  } else {
150  int *dsp;
151  for(dsp=ds2;dsp<stackp2;dsp++) {
152  if(ed[*dsp]==mep[i]+j) {
153  ed[*dsp]=l+j;
154  vc.n_set_to_aux1_offset(*dsp,m);
155  break;
156  }
157  }
158  if(dsp==stackp2) voro_fatal_error("Couldn't relocate dangling pointer",VOROPP_INTERNAL_ERROR);
159 #if VOROPP_VERBOSE >=3
160  fputs("Relocated dangling pointer",stderr);
161 #endif
162  }
163  for(k=0;k<s;k++,j++) l[j]=mep[i][j];
164  for(k=0;k<i;k++,m++) vc.n_copy_to_aux1(i,m);
165  }
166  delete [] mep[i];
167  mep[i]=l;
168  vc.n_switch_to_aux1(i);
169  }
170 }
171 
172 /** Doubles the maximum number of vertices allowed, by reallocating the ed, nu,
173  * and pts arrays. If the allocation exceeds the absolute maximum set in
174  * max_vertices, then the routine exits with a fatal error. If the template has
175  * been instantiated with the neighbor tracking turned on, then the routine
176  * also reallocates the ne array. */
177 template<class vc_class>
178 void voronoicell_base::add_memory_vertices(vc_class &vc) {
179  int i=(current_vertices<<1),j,**pp,*pnu;
180  if(i>max_vertices) voro_fatal_error("Vertex memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
181 #if VOROPP_VERBOSE >=2
182  fprintf(stderr,"Vertex memory scaled up to %d\n",i);
183 #endif
184  double *ppts;
185  pp=new int*[i];
186  for(j=0;j<current_vertices;j++) pp[j]=ed[j];
187  delete [] ed;ed=pp;
188  vc.n_add_memory_vertices(i);
189  pnu=new int[i];
190  for(j=0;j<current_vertices;j++) pnu[j]=nu[j];
191  delete [] nu;nu=pnu;
192  ppts=new double[3*i];
193  for(j=0;j<3*current_vertices;j++) ppts[j]=pts[j];
194  delete [] pts;pts=ppts;
195  current_vertices=i;
196 }
197 
198 /** Doubles the maximum allowed vertex order, by reallocating mem, mep, and mec
199  * arrays. If the allocation exceeds the absolute maximum set in
200  * max_vertex_order, then the routine causes a fatal error. If the template has
201  * been instantiated with the neighbor tracking turned on, then the routine
202  * also reallocates the mne array. */
203 template<class vc_class>
204 void voronoicell_base::add_memory_vorder(vc_class &vc) {
205  int i=(current_vertex_order<<1),j,*p1,**p2;
206  if(i>max_vertex_order) voro_fatal_error("Vertex order memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
207 #if VOROPP_VERBOSE >=2
208  fprintf(stderr,"Vertex order memory scaled up to %d\n",i);
209 #endif
210  p1=new int[i];
211  for(j=0;j<current_vertex_order;j++) p1[j]=mem[j];while(j<i) p1[j++]=0;
212  delete [] mem;mem=p1;
213  p2=new int*[i];
214  for(j=0;j<current_vertex_order;j++) p2[j]=mep[j];
215  delete [] mep;mep=p2;
216  p1=new int[i];
217  for(j=0;j<current_vertex_order;j++) p1[j]=mec[j];while(j<i) p1[j++]=0;
218  delete [] mec;mec=p1;
219  vc.n_add_memory_vorder(i);
220  current_vertex_order=i;
221 }
222 
223 /** Doubles the size allocation of the main delete stack. If the allocation
224  * exceeds the absolute maximum set in max_delete_size, then routine causes a
225  * fatal error. */
226 void voronoicell_base::add_memory_ds(int *&stackp) {
228  if(current_delete_size>max_delete_size) voro_fatal_error("Delete stack 1 memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
229 #if VOROPP_VERBOSE >=2
230  fprintf(stderr,"Delete stack 1 memory scaled up to %d\n",current_delete_size);
231 #endif
232  int *dsn=new int[current_delete_size],*dsnp=dsn,*dsp=ds;
233  while(dsp<stackp) *(dsnp++)=*(dsp++);
234  delete [] ds;ds=dsn;stackp=dsnp;
235  stacke=ds+current_delete_size;
236 }
237 
238 /** Doubles the size allocation of the auxiliary delete stack. If the
239  * allocation exceeds the absolute maximum set in max_delete2_size, then the
240  * routine causes a fatal error. */
241 void voronoicell_base::add_memory_ds2(int *&stackp2) {
243  if(current_delete2_size>max_delete2_size) voro_fatal_error("Delete stack 2 memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
244 #if VOROPP_VERBOSE >=2
245  fprintf(stderr,"Delete stack 2 memory scaled up to %d\n",current_delete2_size);
246 #endif
247  int *dsn=new int[current_delete2_size],*dsnp=dsn,*dsp=ds2;
248  while(dsp<stackp2) *(dsnp++)=*(dsp++);
249  delete [] ds2;ds2=dsn;stackp2=dsnp;
250  stacke2=ds2+current_delete2_size;
251 }
252 
253 /** Initializes a Voronoi cell as a rectangular box with the given dimensions.
254  * \param[in] (xmin,xmax) the minimum and maximum x coordinates.
255  * \param[in] (ymin,ymax) the minimum and maximum y coordinates.
256  * \param[in] (zmin,zmax) the minimum and maximum z coordinates. */
257 void voronoicell_base::init_base(double xmin,double xmax,double ymin,double ymax,double zmin,double zmax) {
258  for(int i=0;i<current_vertex_order;i++) mec[i]=0;up=0;
259  mec[3]=p=8;xmin*=2;xmax*=2;ymin*=2;ymax*=2;zmin*=2;zmax*=2;
260  *pts=xmin;pts[1]=ymin;pts[2]=zmin;
261  pts[3]=xmax;pts[4]=ymin;pts[5]=zmin;
262  pts[6]=xmin;pts[7]=ymax;pts[8]=zmin;
263  pts[9]=xmax;pts[10]=ymax;pts[11]=zmin;
264  pts[12]=xmin;pts[13]=ymin;pts[14]=zmax;
265  pts[15]=xmax;pts[16]=ymin;pts[17]=zmax;
266  pts[18]=xmin;pts[19]=ymax;pts[20]=zmax;
267  pts[21]=xmax;pts[22]=ymax;pts[23]=zmax;
268  int *q=mep[3];
269  *q=1;q[1]=4;q[2]=2;q[3]=2;q[4]=1;q[5]=0;q[6]=0;
270  q[7]=3;q[8]=5;q[9]=0;q[10]=2;q[11]=1;q[12]=0;q[13]=1;
271  q[14]=0;q[15]=6;q[16]=3;q[17]=2;q[18]=1;q[19]=0;q[20]=2;
272  q[21]=2;q[22]=7;q[23]=1;q[24]=2;q[25]=1;q[26]=0;q[27]=3;
273  q[28]=6;q[29]=0;q[30]=5;q[31]=2;q[32]=1;q[33]=0;q[34]=4;
274  q[35]=4;q[36]=1;q[37]=7;q[38]=2;q[39]=1;q[40]=0;q[41]=5;
275  q[42]=7;q[43]=2;q[44]=4;q[45]=2;q[46]=1;q[47]=0;q[48]=6;
276  q[49]=5;q[50]=3;q[51]=6;q[52]=2;q[53]=1;q[54]=0;q[55]=7;
277  *ed=q;ed[1]=q+7;ed[2]=q+14;ed[3]=q+21;
278  ed[4]=q+28;ed[5]=q+35;ed[6]=q+42;ed[7]=q+49;
279  *nu=nu[1]=nu[2]=nu[3]=nu[4]=nu[5]=nu[6]=nu[7]=3;
280 }
281 
282 /** Initializes a Voronoi cell as a regular octahedron.
283  * \param[in] l The distance from the octahedron center to a vertex. Six
284  * vertices are initialized at (-l,0,0), (l,0,0), (0,-l,0),
285  * (0,l,0), (0,0,-l), and (0,0,l). */
287  for(int i=0;i<current_vertex_order;i++) mec[i]=0;up=0;
288  mec[4]=p=6;l*=2;
289  *pts=-l;pts[1]=0;pts[2]=0;
290  pts[3]=l;pts[4]=0;pts[5]=0;
291  pts[6]=0;pts[7]=-l;pts[8]=0;
292  pts[9]=0;pts[10]=l;pts[11]=0;
293  pts[12]=0;pts[13]=0;pts[14]=-l;
294  pts[15]=0;pts[16]=0;pts[17]=l;
295  int *q=mep[4];
296  *q=2;q[1]=5;q[2]=3;q[3]=4;q[4]=0;q[5]=0;q[6]=0;q[7]=0;q[8]=0;
297  q[9]=2;q[10]=4;q[11]=3;q[12]=5;q[13]=2;q[14]=2;q[15]=2;q[16]=2;q[17]=1;
298  q[18]=0;q[19]=4;q[20]=1;q[21]=5;q[22]=0;q[23]=3;q[24]=0;q[25]=1;q[26]=2;
299  q[27]=0;q[28]=5;q[29]=1;q[30]=4;q[31]=2;q[32]=3;q[33]=2;q[34]=1;q[35]=3;
300  q[36]=0;q[37]=3;q[38]=1;q[39]=2;q[40]=3;q[41]=3;q[42]=1;q[43]=1;q[44]=4;
301  q[45]=0;q[46]=2;q[47]=1;q[48]=3;q[49]=1;q[50]=3;q[51]=3;q[52]=1;q[53]=5;
302  *ed=q;ed[1]=q+9;ed[2]=q+18;ed[3]=q+27;ed[4]=q+36;ed[5]=q+45;
303  *nu=nu[1]=nu[2]=nu[3]=nu[4]=nu[5]=4;
304 }
305 
306 /** Initializes a Voronoi cell as a tetrahedron. It assumes that the normal to
307  * the face for the first three vertices points inside.
308  * \param (x0,y0,z0) a position vector for the first vertex.
309  * \param (x1,y1,z1) a position vector for the second vertex.
310  * \param (x2,y2,z2) a position vector for the third vertex.
311  * \param (x3,y3,z3) a position vector for the fourth vertex. */
312 void voronoicell_base::init_tetrahedron_base(double x0,double y0,double z0,double x1,double y1,double z1,double x2,double y2,double z2,double x3,double y3,double z3) {
313  for(int i=0;i<current_vertex_order;i++) mec[i]=0;up=0;
314  mec[3]=p=4;
315  *pts=x0*2;pts[1]=y0*2;pts[2]=z0*2;
316  pts[3]=x1*2;pts[4]=y1*2;pts[5]=z1*2;
317  pts[6]=x2*2;pts[7]=y2*2;pts[8]=z2*2;
318  pts[9]=x3*2;pts[10]=y3*2;pts[11]=z3*2;
319  int *q=mep[3];
320  *q=1;q[1]=3;q[2]=2;q[3]=0;q[4]=0;q[5]=0;q[6]=0;
321  q[7]=0;q[8]=2;q[9]=3;q[10]=0;q[11]=2;q[12]=1;q[13]=1;
322  q[14]=0;q[15]=3;q[16]=1;q[17]=2;q[18]=2;q[19]=1;q[20]=2;
323  q[21]=0;q[22]=1;q[23]=2;q[24]=1;q[25]=2;q[26]=1;q[27]=3;
324  *ed=q;ed[1]=q+7;ed[2]=q+14;ed[3]=q+21;
325  *nu=nu[1]=nu[2]=nu[3]=3;
326 }
327 
328 /** Checks that the relational table of the Voronoi cell is accurate, and
329  * prints out any errors. This algorithm is O(p), so running it every time the
330  * plane routine is called will result in a significant slowdown. */
332  int i,j;
333  for(i=0;i<p;i++) for(j=0;j<nu[i];j++) if(ed[ed[i][j]][ed[i][nu[i]+j]]!=i)
334  printf("Relational error at point %d, edge %d.\n",i,j);
335 }
336 
337 /** This routine checks for any two vertices that are connected by more than
338  * one edge. The plane algorithm is designed so that this should not happen, so
339  * any occurrences are most likely errors. Note that the routine is O(p), so
340  * running it every time the plane routine is called will result in a
341  * significant slowdown. */
343  int i,j,k;
344  for(i=0;i<p;i++) for(j=1;j<nu[i];j++) for(k=0;k<j;k++) if(ed[i][j]==ed[i][k])
345  printf("Duplicate edges: (%d,%d) and (%d,%d) [%d]\n",i,j,i,k,ed[i][j]);
346 }
347 
348 /** Constructs the relational table if the edges have been specified. */
350  int i,j,k,l;
351  for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
352  k=ed[i][j];
353  l=0;
354  while(ed[k][l]!=i) {
355  l++;
356  if(l==nu[k]) voro_fatal_error("Relation table construction failed",VOROPP_INTERNAL_ERROR);
357  }
358  ed[i][nu[i]+j]=l;
359  }
360 }
361 
362 /** Starting from a point within the current cutting plane, this routine attempts
363  * to find an edge to a point outside the cutting plane. This prevents the plane
364  * routine from .
365  * \param[in] vc a reference to the specialized version of the calling class.
366  * \param[in,out] up */
367 template<class vc_class>
368 inline bool voronoicell_base::search_for_outside_edge(vc_class &vc,int &up) {
369  int i,lp,lw,*j(ds2),*stackp2(ds2);
370  double l;
371  *(stackp2++)=up;
372  while(j<stackp2) {
373  up=*(j++);
374  for(i=0;i<nu[up];i++) {
375  lp=ed[up][i];
376  lw=m_test(lp,l);
377  if(lw==-1) return true;
378  else if(lw==0) add_to_stack(vc,lp,stackp2);
379  }
380  }
381  return false;
382 }
383 
384 /** Adds a point to the auxiliary delete stack if it is not already there.
385  * \param[in] vc a reference to the specialized version of the calling class.
386  * \param[in] lp the index of the point to add.
387  * \param[in,out] stackp2 a pointer to the end of the stack entries. */
388 template<class vc_class>
389 inline void voronoicell_base::add_to_stack(vc_class &vc,int lp,int *&stackp2) {
390  for(int *k(ds2);k<stackp2;k++) if(*k==lp) return;
391  if(stackp2==stacke2) add_memory_ds2(stackp2);
392  *(stackp2++)=lp;
393 }
394 
395 /** Cuts the Voronoi cell by a particle whose center is at a separation of
396  * (x,y,z) from the cell center. The value of rsq should be initially set to
397  * \f$x^2+y^2+z^2\f$.
398  * \param[in] vc a reference to the specialized version of the calling class.
399  * \param[in] (x,y,z) the normal vector to the plane.
400  * \param[in] rsq the distance along this vector of the plane.
401  * \param[in] p_id the plane ID (for neighbor tracking only).
402  * \return False if the plane cut deleted the cell entirely, true otherwise. */
403 template<class vc_class>
404 bool voronoicell_base::nplane(vc_class &vc,double x,double y,double z,double rsq,int p_id) {
405  int count=0,i,j,k,lp=up,cp,qp,rp,*stackp(ds),*stackp2(ds2),*dsp;
406  int us=0,ls=0,qs,iqs,cs,uw,qw,lw;
407  int *edp,*edd;
408  double u,l,r,q;bool complicated_setup=false,new_double_edge=false,double_edge=false;
409 
410  // Initialize the safe testing routine
411  n_marg=0;px=x;py=y;pz=z;prsq=rsq;
412 
413  // Test approximately sqrt(n)/4 points for their proximity to the plane
414  // and keep the one which is closest
415  uw=m_test(up,u);
416 
417  // Starting from an initial guess, we now move from vertex to vertex,
418  // to try and find an edge which intersects the cutting plane,
419  // or a vertex which is on the plane
420  try {
421  if(uw==1) {
422 
423  // The test point is inside the cutting plane.
424  us=0;
425  do {
426  lp=ed[up][us];
427  lw=m_test(lp,l);
428  if(l<u) break;
429  us++;
430  } while (us<nu[up]);
431 
432  if(us==nu[up]) {
433  return false;
434  }
435 
436  ls=ed[up][nu[up]+us];
437  while(lw==1) {
438  if(++count>=p) throw true;
439  u=l;up=lp;
440  for(us=0;us<ls;us++) {
441  lp=ed[up][us];
442  lw=m_test(lp,l);
443  if(l<u) break;
444  }
445  if(us==ls) {
446  us++;
447  while(us<nu[up]) {
448  lp=ed[up][us];
449  lw=m_test(lp,l);
450  if(l<u) break;
451  us++;
452  }
453  if(us==nu[up]) {
454  return false;
455  }
456  }
457  ls=ed[up][nu[up]+us];
458  }
459 
460  // If the last point in the iteration is within the
461  // plane, we need to do the complicated setup
462  // routine. Otherwise, we use the regular iteration.
463  if(lw==0) {
464  up=lp;
465  complicated_setup=true;
466  } else complicated_setup=false;
467  } else if(uw==-1) {
468  us=0;
469  do {
470  qp=ed[up][us];
471  qw=m_test(qp,q);
472  if(u<q) break;
473  us++;
474  } while (us<nu[up]);
475  if(us==nu[up]) return true;
476 
477  while(qw==-1) {
478  qs=ed[up][nu[up]+us];
479  if(++count>=p) throw true;
480  u=q;up=qp;
481  for(us=0;us<qs;us++) {
482  qp=ed[up][us];
483  qw=m_test(qp,q);
484  if(u<q) break;
485  }
486  if(us==qs) {
487  us++;
488  while(us<nu[up]) {
489  qp=ed[up][us];
490  qw=m_test(qp,q);
491  if(u<q) break;
492  us++;
493  }
494  if(us==nu[up]) return true;
495  }
496  }
497  if(qw==1) {
498  lp=up;ls=us;l=u;
499  up=qp;us=ed[lp][nu[lp]+ls];u=q;
500  complicated_setup=false;
501  } else {
502  up=qp;
503  complicated_setup=true;
504  }
505  } else {
506 
507  // Our original test point was on the plane, so we
508  // automatically head for the complicated setup
509  // routine
510  complicated_setup=true;
511  }
512  }
513  catch(bool except) {
514  // This routine is a fall-back, in case floating point errors
515  // cause the usual search routine to fail. In the fall-back
516  // routine, we just test every edge to find one straddling
517  // the plane.
518 #if VOROPP_VERBOSE >=1
519  fputs("Bailed out of convex calculation\n",stderr);
520 #endif
521  qw=1;lw=0;
522  for(qp=0;qp<p;qp++) {
523  qw=m_test(qp,q);
524  if(qw==1) {
525 
526  // The point is inside the cutting space. Now
527  // see if we can find a neighbor which isn't.
528  for(us=0;us<nu[qp];us++) {
529  lp=ed[qp][us];
530  if(lp<qp) {
531  lw=m_test(lp,l);
532  if(lw!=1) break;
533  }
534  }
535  if(us<nu[qp]) {
536  up=qp;
537  if(lw==0) {
538  complicated_setup=true;
539  } else {
540  complicated_setup=false;
541  u=q;
542  ls=ed[up][nu[up]+us];
543  }
544  break;
545  }
546  } else if(qw==-1) {
547 
548  // The point is outside the cutting space. See
549  // if we can find a neighbor which isn't.
550  for(ls=0;ls<nu[qp];ls++) {
551  up=ed[qp][ls];
552  if(up<qp) {
553  uw=m_test(up,u);
554  if(uw!=-1) break;
555  }
556  }
557  if(ls<nu[qp]) {
558  if(uw==0) {
559  up=qp;
560  complicated_setup=true;
561  } else {
562  complicated_setup=false;
563  lp=qp;l=q;
564  us=ed[lp][nu[lp]+ls];
565  }
566  break;
567  }
568  } else {
569 
570  // The point is in the plane, so we just
571  // proceed with the complicated setup routine
572  up=qp;
573  complicated_setup=true;
574  break;
575  }
576  }
577  if(qp==p) return qw==-1?true:false;
578  }
579 
580  // We're about to add the first point of the new facet. In either
581  // routine, we have to add a point, so first check there's space for
582  // it.
583  if(p==current_vertices) add_memory_vertices(vc);
584 
585  if(complicated_setup) {
586 
587  // We want to be strict about reaching the conclusion that the
588  // cell is entirely within the cutting plane. It's not enough
589  // to find a vertex that has edges which are all inside or on
590  // the plane. If the vertex has neighbors that are also on the
591  // plane, we should check those too.
592  if(!search_for_outside_edge(vc,up)) return false;
593 
594  // The search algorithm found a point which is on the cutting
595  // plane. We leave that point in place, and create a new one at
596  // the same location.
597  pts[3*p]=pts[3*up];
598  pts[3*p+1]=pts[3*up+1];
599  pts[3*p+2]=pts[3*up+2];
600 
601  // Search for a collection of edges of the test vertex which
602  // are outside of the cutting space. Begin by testing the
603  // zeroth edge.
604  i=0;
605  lp=*ed[up];
606  lw=m_test(lp,l);
607  if(lw!=-1) {
608 
609  // The first edge is either inside the cutting space,
610  // or lies within the cutting plane. Test the edges
611  // sequentially until we find one that is outside.
612  rp=lw;
613  do {
614  i++;
615 
616  // If we reached the last edge with no luck
617  // then all of the vertices are inside
618  // or on the plane, so the cell is completely
619  // deleted
620  if(i==nu[up]) return false;
621  lp=ed[up][i];
622  lw=m_test(lp,l);
623  } while (lw!=-1);
624  j=i+1;
625 
626  // We found an edge outside the cutting space. Keep
627  // moving through these edges until we find one that's
628  // inside or on the plane.
629  while(j<nu[up]) {
630  lp=ed[up][j];
631  lw=m_test(lp,l);
632  if(lw!=-1) break;
633  j++;
634  }
635 
636  // Compute the number of edges for the new vertex. In
637  // general it will be the number of outside edges
638  // found, plus two. But we need to recognize the
639  // special case when all but one edge is outside, and
640  // the remaining one is on the plane. For that case we
641  // have to reduce the edge count by one to prevent
642  // doubling up.
643  if(j==nu[up]&&i==1&&rp==0) {
644  nu[p]=nu[up];
645  double_edge=true;
646  } else nu[p]=j-i+2;
647  k=1;
648 
649  // Add memory for the new vertex if needed, and
650  // initialize
651  while (nu[p]>=current_vertex_order) add_memory_vorder(vc);
652  if(mec[nu[p]]==mem[nu[p]]) add_memory(vc,nu[p],stackp2);
653  vc.n_set_pointer(p,nu[p]);
654  ed[p]=mep[nu[p]]+((nu[p]<<1)+1)*mec[nu[p]]++;
655  ed[p][nu[p]<<1]=p;
656 
657  // Copy the edges of the original vertex into the new
658  // one. Delete the edges of the original vertex, and
659  // update the relational table.
660  us=cycle_down(i,up);
661  while(i<j) {
662  qp=ed[up][i];
663  qs=ed[up][nu[up]+i];
664  vc.n_copy(p,k,up,i);
665  ed[p][k]=qp;
666  ed[p][nu[p]+k]=qs;
667  ed[qp][qs]=p;
668  ed[qp][nu[qp]+qs]=k;
669  ed[up][i]=-1;
670  i++;k++;
671  }
672  qs=i==nu[up]?0:i;
673  } else {
674 
675  // In this case, the zeroth edge is outside the cutting
676  // plane. Begin by searching backwards from the last
677  // edge until we find an edge which isn't outside.
678  i=nu[up]-1;
679  lp=ed[up][i];
680  lw=m_test(lp,l);
681  while(lw==-1) {
682  i--;
683 
684  // If i reaches zero, then we have a point in
685  // the plane all of whose edges are outside
686  // the cutting space, so we just exit
687  if(i==0) return true;
688  lp=ed[up][i];
689  lw=m_test(lp,l);
690  }
691 
692  // Now search forwards from zero
693  j=1;
694  qp=ed[up][j];
695  qw=m_test(qp,q);
696  while(qw==-1) {
697  j++;
698  qp=ed[up][j];
699  qw=m_test(qp,l);
700  }
701 
702  // Compute the number of edges for the new vertex. In
703  // general it will be the number of outside edges
704  // found, plus two. But we need to recognize the
705  // special case when all but one edge is outside, and
706  // the remaining one is on the plane. For that case we
707  // have to reduce the edge count by one to prevent
708  // doubling up.
709  if(i==j&&qw==0) {
710  double_edge=true;
711  nu[p]=nu[up];
712  } else {
713  nu[p]=nu[up]-i+j+1;
714  }
715 
716  // Add memory to store the vertex if it doesn't exist
717  // already
718  k=1;
719  while(nu[p]>=current_vertex_order) add_memory_vorder(vc);
720  if(mec[nu[p]]==mem[nu[p]]) add_memory(vc,nu[p],stackp2);
721 
722  // Copy the edges of the original vertex into the new
723  // one. Delete the edges of the original vertex, and
724  // update the relational table.
725  vc.n_set_pointer(p,nu[p]);
726  ed[p]=mep[nu[p]]+((nu[p]<<1)+1)*mec[nu[p]]++;
727  ed[p][nu[p]<<1]=p;
728  us=i++;
729  while(i<nu[up]) {
730  qp=ed[up][i];
731  qs=ed[up][nu[up]+i];
732  vc.n_copy(p,k,up,i);
733  ed[p][k]=qp;
734  ed[p][nu[p]+k]=qs;
735  ed[qp][qs]=p;
736  ed[qp][nu[qp]+qs]=k;
737  ed[up][i]=-1;
738  i++;k++;
739  }
740  i=0;
741  while(i<j) {
742  qp=ed[up][i];
743  qs=ed[up][nu[up]+i];
744  vc.n_copy(p,k,up,i);
745  ed[p][k]=qp;
746  ed[p][nu[p]+k]=qs;
747  ed[qp][qs]=p;
748  ed[qp][nu[qp]+qs]=k;
749  ed[up][i]=-1;
750  i++;k++;
751  }
752  qs=j;
753  }
754  if(!double_edge) {
755  vc.n_copy(p,k,up,qs);
756  vc.n_set(p,0,p_id);
757  } else vc.n_copy(p,0,up,qs);
758 
759  // Add this point to the auxiliary delete stack
760  if(stackp2==stacke2) add_memory_ds2(stackp2);
761  *(stackp2++)=up;
762 
763  // Look at the edges on either side of the group that was
764  // detected. We're going to commence facet computation by
765  // moving along one of them. We are going to end up coming back
766  // along the other one.
767  cs=k;
768  qp=up;q=u;
769  i=ed[up][us];
770  us=ed[up][nu[up]+us];
771  up=i;
772  ed[qp][nu[qp]<<1]=-p;
773 
774  } else {
775 
776  // The search algorithm found an intersected edge between the
777  // points lp and up. Create a new vertex between them which
778  // lies on the cutting plane. Since u and l differ by at least
779  // the tolerance, this division should never screw up.
780  if(stackp==stacke) add_memory_ds(stackp);
781  *(stackp++)=up;
782  r=u/(u-l);l=1-r;
783  pts[3*p]=pts[3*lp]*r+pts[3*up]*l;
784  pts[3*p+1]=pts[3*lp+1]*r+pts[3*up+1]*l;
785  pts[3*p+2]=pts[3*lp+2]*r+pts[3*up+2]*l;
786 
787  // This point will always have three edges. Connect one of them
788  // to lp.
789  nu[p]=3;
790  if(mec[3]==mem[3]) add_memory(vc,3,stackp2);
791  vc.n_set_pointer(p,3);
792  vc.n_set(p,0,p_id);
793  vc.n_copy(p,1,up,us);
794  vc.n_copy(p,2,lp,ls);
795  ed[p]=mep[3]+7*mec[3]++;
796  ed[p][6]=p;
797  ed[up][us]=-1;
798  ed[lp][ls]=p;
799  ed[lp][nu[lp]+ls]=1;
800  ed[p][1]=lp;
801  ed[p][nu[p]+1]=ls;
802  cs=2;
803 
804  // Set the direction to move in
805  qs=cycle_up(us,up);
806  qp=up;q=u;
807  }
808 
809  // When the code reaches here, we have initialized the first point, and
810  // we have a direction for moving it to construct the rest of the facet
811  cp=p;rp=p;p++;
812  while(qp!=up||qs!=us) {
813 
814  // We're currently tracing round an intersected facet. Keep
815  // moving around it until we find a point or edge which
816  // intersects the plane.
817  lp=ed[qp][qs];
818  lw=m_test(lp,l);
819 
820  if(lw==1) {
821 
822  // The point is still in the cutting space. Just add it
823  // to the delete stack and keep moving.
824  qs=cycle_up(ed[qp][nu[qp]+qs],lp);
825  qp=lp;
826  q=l;
827  if(stackp==stacke) add_memory_ds(stackp);
828  *(stackp++)=qp;
829 
830  } else if(lw==-1) {
831 
832  // The point is outside of the cutting space, so we've
833  // found an intersected edge. Introduce a regular point
834  // at the point of intersection. Connect it to the
835  // point we just tested. Also connect it to the previous
836  // new point in the facet we're constructing.
837  if(p==current_vertices) add_memory_vertices(vc);
838  r=q/(q-l);l=1-r;
839  pts[3*p]=pts[3*lp]*r+pts[3*qp]*l;
840  pts[3*p+1]=pts[3*lp+1]*r+pts[3*qp+1]*l;
841  pts[3*p+2]=pts[3*lp+2]*r+pts[3*qp+2]*l;
842  nu[p]=3;
843  if(mec[3]==mem[3]) add_memory(vc,3,stackp2);
844  ls=ed[qp][qs+nu[qp]];
845  vc.n_set_pointer(p,3);
846  vc.n_set(p,0,p_id);
847  vc.n_copy(p,1,qp,qs);
848  vc.n_copy(p,2,lp,ls);
849  ed[p]=mep[3]+7*mec[3]++;
850  *ed[p]=cp;
851  ed[p][1]=lp;
852  ed[p][3]=cs;
853  ed[p][4]=ls;
854  ed[p][6]=p;
855  ed[lp][ls]=p;
856  ed[lp][nu[lp]+ls]=1;
857  ed[cp][cs]=p;
858  ed[cp][nu[cp]+cs]=0;
859  ed[qp][qs]=-1;
860  qs=cycle_up(qs,qp);
861  cp=p++;
862  cs=2;
863  } else {
864 
865  // We've found a point which is on the cutting plane.
866  // We're going to introduce a new point right here, but
867  // first we need to figure out the number of edges it
868  // has.
869  if(p==current_vertices) add_memory_vertices(vc);
870 
871  // If the previous vertex detected a double edge, our
872  // new vertex will have one less edge.
873  k=double_edge?0:1;
874  qs=ed[qp][nu[qp]+qs];
875  qp=lp;
876  iqs=qs;
877 
878  // Start testing the edges of the current point until
879  // we find one which isn't outside the cutting space
880  do {
881  k++;
882  qs=cycle_up(qs,qp);
883  lp=ed[qp][qs];
884  lw=m_test(lp,l);
885  } while (lw==-1);
886 
887  // Now we need to find out whether this marginal vertex
888  // we are on has been visited before, because if that's
889  // the case, we need to add vertices to the existing
890  // new vertex, rather than creating a fresh one. We also
891  // need to figure out whether we're in a case where we
892  // might be creating a duplicate edge.
893  j=-ed[qp][nu[qp]<<1];
894  if(qp==up&&qs==us) {
895 
896  // If we're heading into the final part of the
897  // new facet, then we never worry about the
898  // duplicate edge calculation.
899  new_double_edge=false;
900  if(j>0) k+=nu[j];
901  } else {
902  if(j>0) {
903 
904  // This vertex was visited before, so
905  // count those vertices to the ones we
906  // already have.
907  k+=nu[j];
908 
909  // The only time when we might make a
910  // duplicate edge is if the point we're
911  // going to move to next is also a
912  // marginal point, so test for that
913  // first.
914  if(lw==0) {
915 
916  // Now see whether this marginal point
917  // has been visited before.
918  i=-ed[lp][nu[lp]<<1];
919  if(i>0) {
920 
921  // Now see if the last edge of that other
922  // marginal point actually ends up here.
923  if(ed[i][nu[i]-1]==j) {
924  new_double_edge=true;
925  k-=1;
926  } else new_double_edge=false;
927  } else {
928 
929  // That marginal point hasn't been visited
930  // before, so we probably don't have to worry
931  // about duplicate edges, except in the
932  // case when that's the way into the end
933  // of the facet, because that way always creates
934  // an edge.
935  if(j==rp&&lp==up&&ed[qp][nu[qp]+qs]==us) {
936  new_double_edge=true;
937  k-=1;
938  } else new_double_edge=false;
939  }
940  } else new_double_edge=false;
941  } else {
942 
943  // The vertex hasn't been visited
944  // before, but let's see if it's
945  // marginal
946  if(lw==0) {
947 
948  // If it is, we need to check
949  // for the case that it's a
950  // small branch, and that we're
951  // heading right back to where
952  // we came from
953  i=-ed[lp][nu[lp]<<1];
954  if(i==cp) {
955  new_double_edge=true;
956  k-=1;
957  } else new_double_edge=false;
958  } else new_double_edge=false;
959  }
960  }
961 
962  // k now holds the number of edges of the new vertex
963  // we are forming. Add memory for it if it doesn't exist
964  // already.
965  while(k>=current_vertex_order) add_memory_vorder(vc);
966  if(mec[k]==mem[k]) add_memory(vc,k,stackp2);
967 
968  // Now create a new vertex with order k, or augment
969  // the existing one
970  if(j>0) {
971 
972  // If we're augmenting a vertex but we don't
973  // actually need any more edges, just skip this
974  // routine to avoid memory confusion
975  if(nu[j]!=k) {
976  // Allocate memory and copy the edges
977  // of the previous instance into it
978  vc.n_set_aux1(k);
979  edp=mep[k]+((k<<1)+1)*mec[k]++;
980  i=0;
981  while(i<nu[j]) {
982  vc.n_copy_aux1(j,i);
983  edp[i]=ed[j][i];
984  edp[k+i]=ed[j][nu[j]+i];
985  i++;
986  }
987  edp[k<<1]=j;
988 
989  // Remove the previous instance with
990  // fewer vertices from the memory
991  // structure
992  edd=mep[nu[j]]+((nu[j]<<1)+1)*--mec[nu[j]];
993  if(edd!=ed[j]) {
994  for(lw=0;lw<=(nu[j]<<1);lw++) ed[j][lw]=edd[lw];
995  vc.n_set_aux2_copy(j,nu[j]);
996  vc.n_copy_pointer(edd[nu[j]<<1],j);
997  ed[edd[nu[j]<<1]]=ed[j];
998  }
999  vc.n_set_to_aux1(j);
1000  ed[j]=edp;
1001  } else i=nu[j];
1002  } else {
1003 
1004  // Allocate a new vertex of order k
1005  vc.n_set_pointer(p,k);
1006  ed[p]=mep[k]+((k<<1)+1)*mec[k]++;
1007  ed[p][k<<1]=p;
1008  if(stackp2==stacke2) add_memory_ds2(stackp2);
1009  *(stackp2++)=qp;
1010  pts[3*p]=pts[3*qp];
1011  pts[3*p+1]=pts[3*qp+1];
1012  pts[3*p+2]=pts[3*qp+2];
1013  ed[qp][nu[qp]<<1]=-p;
1014  j=p++;
1015  i=0;
1016  }
1017  nu[j]=k;
1018 
1019  // Unless the previous case was a double edge, connect
1020  // the first available edge of the new vertex to the
1021  // last one in the facet
1022  if(!double_edge) {
1023  ed[j][i]=cp;
1024  ed[j][nu[j]+i]=cs;
1025  vc.n_set(j,i,p_id);
1026  ed[cp][cs]=j;
1027  ed[cp][nu[cp]+cs]=i;
1028  i++;
1029  }
1030 
1031  // Copy in the edges of the underlying vertex,
1032  // and do one less if this was a double edge
1033  qs=iqs;
1034  while(i<(new_double_edge?k:k-1)) {
1035  qs=cycle_up(qs,qp);
1036  lp=ed[qp][qs];ls=ed[qp][nu[qp]+qs];
1037  vc.n_copy(j,i,qp,qs);
1038  ed[j][i]=lp;
1039  ed[j][nu[j]+i]=ls;
1040  ed[lp][ls]=j;
1041  ed[lp][nu[lp]+ls]=i;
1042  ed[qp][qs]=-1;
1043  i++;
1044  }
1045  qs=cycle_up(qs,qp);
1046  cs=i;
1047  cp=j;
1048  vc.n_copy(j,new_double_edge?0:cs,qp,qs);
1049 
1050  // Update the double_edge flag, to pass it
1051  // to the next instance of this routine
1052  double_edge=new_double_edge;
1053  }
1054  }
1055 
1056  // Connect the final created vertex to the initial one
1057  ed[cp][cs]=rp;
1058  *ed[rp]=cp;
1059  ed[cp][nu[cp]+cs]=0;
1060  ed[rp][nu[rp]]=cs;
1061 
1062  // Delete points: first, remove any duplicates
1063  dsp=ds;
1064  while(dsp<stackp) {
1065  j=*dsp;
1066  if(ed[j][nu[j]]!=-1) {
1067  ed[j][nu[j]]=-1;
1068  dsp++;
1069  } else *dsp=*(--stackp);
1070  }
1071 
1072  // Add the points in the auxiliary delete stack,
1073  // and reset their back pointers
1074  for(dsp=ds2;dsp<stackp2;dsp++) {
1075  j=*dsp;
1076  ed[j][nu[j]<<1]=j;
1077  if(ed[j][nu[j]]!=-1) {
1078  ed[j][nu[j]]=-1;
1079  if(stackp==stacke) add_memory_ds(stackp);
1080  *(stackp++)=j;
1081  }
1082  }
1083 
1084  // Scan connections and add in extras
1085  for(dsp=ds;dsp<stackp;dsp++) {
1086  cp=*dsp;
1087  for(edp=ed[cp];edp<ed[cp]+nu[cp];edp++) {
1088  qp=*edp;
1089  if(qp!=-1&&ed[qp][nu[qp]]!=-1) {
1090  if(stackp==stacke) {
1091  int dis=stackp-dsp;
1092  add_memory_ds(stackp);
1093  dsp=ds+dis;
1094  }
1095  *(stackp++)=qp;
1096  ed[qp][nu[qp]]=-1;
1097  }
1098  }
1099  }
1100  up=0;
1101 
1102  // Delete them from the array structure
1103  while(stackp>ds) {
1104  --p;
1105  while(ed[p][nu[p]]==-1) {
1106  j=nu[p];
1107  edp=ed[p];edd=(mep[j]+((j<<1)+1)*--mec[j]);
1108  while(edp<ed[p]+(j<<1)+1) *(edp++)=*(edd++);
1109  vc.n_set_aux2_copy(p,j);
1110  vc.n_copy_pointer(ed[p][(j<<1)],p);
1111  ed[ed[p][(j<<1)]]=ed[p];
1112  --p;
1113  }
1114  up=*(--stackp);
1115  if(up<p) {
1116 
1117  // Vertex management
1118  pts[3*up]=pts[3*p];
1119  pts[3*up+1]=pts[3*p+1];
1120  pts[3*up+2]=pts[3*p+2];
1121 
1122  // Memory management
1123  j=nu[up];
1124  edp=ed[up];edd=(mep[j]+((j<<1)+1)*--mec[j]);
1125  while(edp<ed[up]+(j<<1)+1) *(edp++)=*(edd++);
1126  vc.n_set_aux2_copy(up,j);
1127  vc.n_copy_pointer(ed[up][j<<1],up);
1128  vc.n_copy_pointer(up,p);
1129  ed[ed[up][j<<1]]=ed[up];
1130 
1131  // Edge management
1132  ed[up]=ed[p];
1133  nu[up]=nu[p];
1134  for(i=0;i<nu[up];i++) ed[ed[up][i]][ed[up][nu[up]+i]]=up;
1135  ed[up][nu[up]<<1]=up;
1136  } else up=p++;
1137  }
1138 
1139  // Check for any vertices of zero order
1140  if(*mec>0) voro_fatal_error("Zero order vertex formed",VOROPP_INTERNAL_ERROR);
1141 
1142  // Collapse any order 2 vertices and exit
1143  return collapse_order2(vc);
1144 }
1145 
1146 /** During the creation of a new facet in the plane routine, it is possible
1147  * that some order two vertices may arise. This routine removes them.
1148  * Suppose an order two vertex joins c and d. If there's a edge between
1149  * c and d already, then the order two vertex is just removed; otherwise,
1150  * the order two vertex is removed and c and d are joined together directly.
1151  * It is possible this process will create order two or order one vertices,
1152  * and the routine is continually run until all of them are removed.
1153  * \return False if the vertex removal was unsuccessful, indicative of the cell
1154  * reducing to zero volume and disappearing; true if the vertex removal
1155  * was successful. */
1156 template<class vc_class>
1157 inline bool voronoicell_base::collapse_order2(vc_class &vc) {
1158  if(!collapse_order1(vc)) return false;
1159  int a,b,i,j,k,l;
1160  while(mec[2]>0) {
1161 
1162  // Pick a order 2 vertex and read in its edges
1163  i=--mec[2];
1164  j=mep[2][5*i];k=mep[2][5*i+1];
1165  if(j==k) {
1166 #if VOROPP_VERBOSE >=1
1167  fputs("Order two vertex joins itself",stderr);
1168 #endif
1169  return false;
1170  }
1171 
1172  // Scan the edges of j to see if joins k
1173  for(l=0;l<nu[j];l++) {
1174  if(ed[j][l]==k) break;
1175  }
1176 
1177  // If j doesn't already join k, join them together.
1178  // Otherwise delete the connection to the current
1179  // vertex from j and k.
1180  a=mep[2][5*i+2];b=mep[2][5*i+3];i=mep[2][5*i+4];
1181  if(l==nu[j]) {
1182  ed[j][a]=k;
1183  ed[k][b]=j;
1184  ed[j][nu[j]+a]=b;
1185  ed[k][nu[k]+b]=a;
1186  } else {
1187  if(!delete_connection(vc,j,a,false)) return false;
1188  if(!delete_connection(vc,k,b,true)) return false;
1189  }
1190 
1191  // Compact the memory
1192  --p;
1193  if(up==i) up=0;
1194  if(p!=i) {
1195  if(up==p) up=i;
1196  pts[3*i]=pts[3*p];
1197  pts[3*i+1]=pts[3*p+1];
1198  pts[3*i+2]=pts[3*p+2];
1199  for(k=0;k<nu[p];k++) ed[ed[p][k]][ed[p][nu[p]+k]]=i;
1200  vc.n_copy_pointer(i,p);
1201  ed[i]=ed[p];
1202  nu[i]=nu[p];
1203  ed[i][nu[i]<<1]=i;
1204  }
1205 
1206  // Collapse any order 1 vertices if they were created
1207  if(!collapse_order1(vc)) return false;
1208  }
1209  return true;
1210 }
1211 
1212 /** Order one vertices can potentially be created during the order two collapse
1213  * routine. This routine keeps removing them until there are none left.
1214  * \return False if the vertex removal was unsuccessful, indicative of the cell
1215  * having zero volume and disappearing; true if the vertex removal was
1216  * successful. */
1217 template<class vc_class>
1218 inline bool voronoicell_base::collapse_order1(vc_class &vc) {
1219  int i,j,k;
1220  while(mec[1]>0) {
1221  up=0;
1222 #if VOROPP_VERBOSE >=1
1223  fputs("Order one collapse\n",stderr);
1224 #endif
1225  i=--mec[1];
1226  j=mep[1][3*i];k=mep[1][3*i+1];
1227  i=mep[1][3*i+2];
1228  if(!delete_connection(vc,j,k,false)) return false;
1229  --p;
1230  if(up==i) up=0;
1231  if(p!=i) {
1232  if(up==p) up=i;
1233  pts[3*i]=pts[3*p];
1234  pts[3*i+1]=pts[3*p+1];
1235  pts[3*i+2]=pts[3*p+2];
1236  for(k=0;k<nu[p];k++) ed[ed[p][k]][ed[p][nu[p]+k]]=i;
1237  vc.n_copy_pointer(i,p);
1238  ed[i]=ed[p];
1239  nu[i]=nu[p];
1240  ed[i][nu[i]<<1]=i;
1241  }
1242  }
1243  return true;
1244 }
1245 
1246 /** This routine deletes the kth edge of vertex j and reorganizes the memory.
1247  * If the neighbor computation is enabled, we also have to supply an handedness
1248  * flag to decide whether to preserve the plane on the left or right of the
1249  * connection.
1250  * \return False if a zero order vertex was formed, indicative of the cell
1251  * disappearing; true if the vertex removal was successful. */
1252 template<class vc_class>
1253 inline bool voronoicell_base::delete_connection(vc_class &vc,int j,int k,bool hand) {
1254  int q=hand?k:cycle_up(k,j);
1255  int i=nu[j]-1,l,*edp,*edd,m;
1256 #if VOROPP_VERBOSE >=1
1257  if(i<1) {
1258  fputs("Zero order vertex formed\n",stderr);
1259  return false;
1260  }
1261 #endif
1262  if(mec[i]==mem[i]) add_memory(vc,i,ds2);
1263  vc.n_set_aux1(i);
1264  for(l=0;l<q;l++) vc.n_copy_aux1(j,l);
1265  while(l<i) {
1266  vc.n_copy_aux1_shift(j,l);
1267  l++;
1268  }
1269  edp=mep[i]+((i<<1)+1)*mec[i]++;
1270  edp[i<<1]=j;
1271  for(l=0;l<k;l++) {
1272  edp[l]=ed[j][l];
1273  edp[l+i]=ed[j][l+nu[j]];
1274  }
1275  while(l<i) {
1276  m=ed[j][l+1];
1277  edp[l]=m;
1278  k=ed[j][l+nu[j]+1];
1279  edp[l+i]=k;
1280  ed[m][nu[m]+k]--;
1281  l++;
1282  }
1283 
1284  edd=mep[nu[j]]+((nu[j]<<1)+1)*--mec[nu[j]];
1285  for(l=0;l<=(nu[j]<<1);l++) ed[j][l]=edd[l];
1286  vc.n_set_aux2_copy(j,nu[j]);
1287  vc.n_set_to_aux2(edd[nu[j]<<1]);
1288  vc.n_set_to_aux1(j);
1289  ed[edd[nu[j]<<1]]=edd;
1290  ed[j]=edp;
1291  nu[j]=i;
1292  return true;
1293 }
1294 
1295 /** Calculates the volume of the Voronoi cell, by decomposing the cell into
1296  * tetrahedra extending outward from the zeroth vertex, whose volumes are
1297  * evaluated using a scalar triple product.
1298  * \return A floating point number holding the calculated volume. */
1300  const double fe=1/48.0;
1301  double vol=0;
1302  int i,j,k,l,m,n;
1303  double ux,uy,uz,vx,vy,vz,wx,wy,wz;
1304  for(i=1;i<p;i++) {
1305  ux=*pts-pts[3*i];
1306  uy=pts[1]-pts[3*i+1];
1307  uz=pts[2]-pts[3*i+2];
1308  for(j=0;j<nu[i];j++) {
1309  k=ed[i][j];
1310  if(k>=0) {
1311  ed[i][j]=-1-k;
1312  l=cycle_up(ed[i][nu[i]+j],k);
1313  vx=pts[3*k]-*pts;
1314  vy=pts[3*k+1]-pts[1];
1315  vz=pts[3*k+2]-pts[2];
1316  m=ed[k][l];ed[k][l]=-1-m;
1317  while(m!=i) {
1318  n=cycle_up(ed[k][nu[k]+l],m);
1319  wx=pts[3*m]-*pts;
1320  wy=pts[3*m+1]-pts[1];
1321  wz=pts[3*m+2]-pts[2];
1322  vol+=ux*vy*wz+uy*vz*wx+uz*vx*wy-uz*vy*wx-uy*vx*wz-ux*vz*wy;
1323  k=m;l=n;vx=wx;vy=wy;vz=wz;
1324  m=ed[k][l];ed[k][l]=-1-m;
1325  }
1326  }
1327  }
1328  }
1329  reset_edges();
1330  return vol*fe;
1331 }
1332 
1333 /** Calculates the areas of each face of the Voronoi cell and prints the
1334  * results to an output stream.
1335  * \param[out] v the vector to store the results in. */
1336 void voronoicell_base::face_areas(std::vector<double> &v) {
1337  double area;
1338  v.clear();
1339  int i,j,k,l,m,n;
1340  double ux,uy,uz,vx,vy,vz,wx,wy,wz;
1341  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
1342  k=ed[i][j];
1343  if(k>=0) {
1344  area=0;
1345  ed[i][j]=-1-k;
1346  l=cycle_up(ed[i][nu[i]+j],k);
1347  m=ed[k][l];ed[k][l]=-1-m;
1348  while(m!=i) {
1349  n=cycle_up(ed[k][nu[k]+l],m);
1350  ux=pts[3*k]-pts[3*i];
1351  uy=pts[3*k+1]-pts[3*i+1];
1352  uz=pts[3*k+2]-pts[3*i+2];
1353  vx=pts[3*m]-pts[3*i];
1354  vy=pts[3*m+1]-pts[3*i+1];
1355  vz=pts[3*m+2]-pts[3*i+2];
1356  wx=uy*vz-uz*vy;
1357  wy=uz*vx-ux*vz;
1358  wz=ux*vy-uy*vx;
1359  area+=sqrt(wx*wx+wy*wy+wz*wz);
1360  k=m;l=n;
1361  m=ed[k][l];ed[k][l]=-1-m;
1362  }
1363  v.push_back(0.125*area);
1364  }
1365  }
1366  reset_edges();
1367 }
1368 
1369 
1370 /** Calculates the total surface area of the Voronoi cell.
1371  * \return The computed area. */
1373  double area=0;
1374  int i,j,k,l,m,n;
1375  double ux,uy,uz,vx,vy,vz,wx,wy,wz;
1376  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
1377  k=ed[i][j];
1378  if(k>=0) {
1379  ed[i][j]=-1-k;
1380  l=cycle_up(ed[i][nu[i]+j],k);
1381  m=ed[k][l];ed[k][l]=-1-m;
1382  while(m!=i) {
1383  n=cycle_up(ed[k][nu[k]+l],m);
1384  ux=pts[3*k]-pts[3*i];
1385  uy=pts[3*k+1]-pts[3*i+1];
1386  uz=pts[3*k+2]-pts[3*i+2];
1387  vx=pts[3*m]-pts[3*i];
1388  vy=pts[3*m+1]-pts[3*i+1];
1389  vz=pts[3*m+2]-pts[3*i+2];
1390  wx=uy*vz-uz*vy;
1391  wy=uz*vx-ux*vz;
1392  wz=ux*vy-uy*vx;
1393  area+=sqrt(wx*wx+wy*wy+wz*wz);
1394  k=m;l=n;
1395  m=ed[k][l];ed[k][l]=-1-m;
1396  }
1397  }
1398  }
1399  reset_edges();
1400  return 0.125*area;
1401 }
1402 
1403 
1404 /** Calculates the centroid of the Voronoi cell, by decomposing the cell into
1405  * tetrahedra extending outward from the zeroth vertex.
1406  * \param[out] (cx,cy,cz) references to floating point numbers in which to
1407  * pass back the centroid vector. */
1408 void voronoicell_base::centroid(double &cx,double &cy,double &cz) {
1409  double tvol,vol=0;cx=cy=cz=0;
1410  int i,j,k,l,m,n;
1411  double ux,uy,uz,vx,vy,vz,wx,wy,wz;
1412  for(i=1;i<p;i++) {
1413  ux=*pts-pts[3*i];
1414  uy=pts[1]-pts[3*i+1];
1415  uz=pts[2]-pts[3*i+2];
1416  for(j=0;j<nu[i];j++) {
1417  k=ed[i][j];
1418  if(k>=0) {
1419  ed[i][j]=-1-k;
1420  l=cycle_up(ed[i][nu[i]+j],k);
1421  vx=pts[3*k]-*pts;
1422  vy=pts[3*k+1]-pts[1];
1423  vz=pts[3*k+2]-pts[2];
1424  m=ed[k][l];ed[k][l]=-1-m;
1425  while(m!=i) {
1426  n=cycle_up(ed[k][nu[k]+l],m);
1427  wx=pts[3*m]-*pts;
1428  wy=pts[3*m+1]-pts[1];
1429  wz=pts[3*m+2]-pts[2];
1430  tvol=ux*vy*wz+uy*vz*wx+uz*vx*wy-uz*vy*wx-uy*vx*wz-ux*vz*wy;
1431  vol+=tvol;
1432  cx+=(wx+vx-ux)*tvol;
1433  cy+=(wy+vy-uy)*tvol;
1434  cz+=(wz+vz-uz)*tvol;
1435  k=m;l=n;vx=wx;vy=wy;vz=wz;
1436  m=ed[k][l];ed[k][l]=-1-m;
1437  }
1438  }
1439  }
1440  }
1441  reset_edges();
1442  if(vol>tolerance_sq) {
1443  vol=0.125/vol;
1444  cx=cx*vol+0.5*(*pts);
1445  cy=cy*vol+0.5*pts[1];
1446  cz=cz*vol+0.5*pts[2];
1447  } else cx=cy=cz=0;
1448 }
1449 
1450 /** Computes the maximum radius squared of a vertex from the center of the
1451  * cell. It can be used to determine when enough particles have been testing an
1452  * all planes that could cut the cell have been considered.
1453  * \return The maximum radius squared of a vertex.*/
1455  double r,s,*ptsp=pts+3,*ptse=pts+3*p;
1456  r=*pts*(*pts)+pts[1]*pts[1]+pts[2]*pts[2];
1457  while(ptsp<ptse) {
1458  s=*ptsp*(*ptsp);ptsp++;
1459  s+=*ptsp*(*ptsp);ptsp++;
1460  s+=*ptsp*(*ptsp);ptsp++;
1461  if(s>r) r=s;
1462  }
1463  return r;
1464 }
1465 
1466 /** Calculates the total edge distance of the Voronoi cell.
1467  * \return A floating point number holding the calculated distance. */
1469  int i,j,k;
1470  double dis=0,dx,dy,dz;
1471  for(i=0;i<p-1;i++) for(j=0;j<nu[i];j++) {
1472  k=ed[i][j];
1473  if(k>i) {
1474  dx=pts[3*k]-pts[3*i];
1475  dy=pts[3*k+1]-pts[3*i+1];
1476  dz=pts[3*k+2]-pts[3*i+2];
1477  dis+=sqrt(dx*dx+dy*dy+dz*dz);
1478  }
1479  }
1480  return 0.5*dis;
1481 }
1482 
1483 /** Outputs the edges of the Voronoi cell in POV-Ray format to an open file
1484  * stream, displacing the cell by given vector.
1485  * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
1486  * \param[in] fp a file handle to write to. */
1487 void voronoicell_base::draw_pov(double x,double y,double z,FILE* fp) {
1488  int i,j,k;double *ptsp=pts,*pt2;
1489  char posbuf1[128],posbuf2[128];
1490  for(i=0;i<p;i++,ptsp+=3) {
1491  sprintf(posbuf1,"%g,%g,%g",x+*ptsp*0.5,y+ptsp[1]*0.5,z+ptsp[2]*0.5);
1492  fprintf(fp,"sphere{<%s>,r}\n",posbuf1);
1493  for(j=0;j<nu[i];j++) {
1494  k=ed[i][j];
1495  if(k<i) {
1496  pt2=pts+3*k;
1497  sprintf(posbuf2,"%g,%g,%g",x+*pt2*0.5,y+0.5*pt2[1],z+0.5*pt2[2]);
1498  if(strcmp(posbuf1,posbuf2)!=0) fprintf(fp,"cylinder{<%s>,<%s>,r}\n",posbuf1,posbuf2);
1499  }
1500  }
1501  }
1502 }
1503 
1504 /** Outputs the edges of the Voronoi cell in gnuplot format to an output stream.
1505  * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
1506  * \param[in] fp a file handle to write to. */
1507 void voronoicell_base::draw_gnuplot(double x,double y,double z,FILE *fp) {
1508  int i,j,k,l,m;
1509  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
1510  k=ed[i][j];
1511  if(k>=0) {
1512  fprintf(fp,"%g %g %g\n",x+0.5*pts[3*i],y+0.5*pts[3*i+1],z+0.5*pts[3*i+2]);
1513  l=i;m=j;
1514  do {
1515  ed[k][ed[l][nu[l]+m]]=-1-l;
1516  ed[l][m]=-1-k;
1517  l=k;
1518  fprintf(fp,"%g %g %g\n",x+0.5*pts[3*k],y+0.5*pts[3*k+1],z+0.5*pts[3*k+2]);
1519  } while (search_edge(l,m,k));
1520  fputs("\n\n",fp);
1521  }
1522  }
1523  reset_edges();
1524 }
1525 
1526 inline bool voronoicell_base::search_edge(int l,int &m,int &k) {
1527  for(m=0;m<nu[l];m++) {
1528  k=ed[l][m];
1529  if(k>=0) return true;
1530  }
1531  return false;
1532 }
1533 
1534 /** Outputs the Voronoi cell in the POV mesh2 format, described in section
1535  * 1.3.2.2 of the POV-Ray documentation. The mesh2 output consists of a list of
1536  * vertex vectors, followed by a list of triangular faces. The routine also
1537  * makes use of the optional inside_vector specification, which makes the mesh
1538  * object solid, so the the POV-Ray Constructive Solid Geometry (CSG) can be
1539  * applied.
1540  * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
1541  * \param[in] fp a file handle to write to. */
1542 void voronoicell_base::draw_pov_mesh(double x,double y,double z,FILE *fp) {
1543  int i,j,k,l,m,n;
1544  double *ptsp=pts;
1545  fprintf(fp,"mesh2 {\nvertex_vectors {\n%d\n",p);
1546  for(i=0;i<p;i++,ptsp+=3) fprintf(fp,",<%g,%g,%g>\n",x+*ptsp*0.5,y+ptsp[1]*0.5,z+ptsp[2]*0.5);
1547  fprintf(fp,"}\nface_indices {\n%d\n",(p-2)<<1);
1548  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
1549  k=ed[i][j];
1550  if(k>=0) {
1551  ed[i][j]=-1-k;
1552  l=cycle_up(ed[i][nu[i]+j],k);
1553  m=ed[k][l];ed[k][l]=-1-m;
1554  while(m!=i) {
1555  n=cycle_up(ed[k][nu[k]+l],m);
1556  fprintf(fp,",<%d,%d,%d>\n",i,k,m);
1557  k=m;l=n;
1558  m=ed[k][l];ed[k][l]=-1-m;
1559  }
1560  }
1561  }
1562  fputs("}\ninside_vector <0,0,1>\n}\n",fp);
1563  reset_edges();
1564 }
1565 
1566 /** Several routines in the class that gather cell-based statistics internally
1567  * track their progress by flipping edges to negative so that they know what
1568  * parts of the cell have already been tested. This function resets them back
1569  * to positive. When it is called, it assumes that every edge in the routine
1570  * should have already been flipped to negative, and it bails out with an
1571  * internal error if it encounters a positive edge. */
1573  int i,j;
1574  for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
1575  if(ed[i][j]>=0) voro_fatal_error("Edge reset routine found a previously untested edge",VOROPP_INTERNAL_ERROR);
1576  ed[i][j]=-1-ed[i][j];
1577  }
1578 }
1579 
1580 /** Checks to see if a given vertex is inside, outside or within the test
1581  * plane. If the point is far away from the test plane, the routine immediately
1582  * returns whether it is inside or outside. If the routine is close the the
1583  * plane and within the specified tolerance, then the special check_marginal()
1584  * routine is called.
1585  * \param[in] n the vertex to test.
1586  * \param[out] ans the result of the scalar product used in evaluating the
1587  * location of the point.
1588  * \return -1 if the point is inside the plane, 1 if the point is outside the
1589  * plane, or 0 if the point is within the plane. */
1590 inline int voronoicell_base::m_test(int n,double &ans) {
1591  double *pp=pts+n+(n<<1);
1592  ans=*(pp++)*px;
1593  ans+=*(pp++)*py;
1594  ans+=*pp*pz-prsq;
1595  if(ans<-tolerance2) {
1596  return -1;
1597  } else if(ans>tolerance2) {
1598  return 1;
1599  }
1600  return check_marginal(n,ans);
1601 }
1602 
1603 /** Checks to see if a given vertex is inside, outside or within the test
1604  * plane, for the case when the point has been detected to be very close to the
1605  * plane. The routine ensures that the returned results are always consistent
1606  * with previous tests, by keeping a table of any marginal results. The routine
1607  * first sees if the vertex is in the table, and if it finds a previously
1608  * computed result it uses that. Otherwise, it computes a result for this
1609  * vertex and adds it the table.
1610  * \param[in] n the vertex to test.
1611  * \param[in] ans the result of the scalar product used in evaluating
1612  * the location of the point.
1613  * \return -1 if the point is inside the plane, 1 if the point is outside the
1614  * plane, or 0 if the point is within the plane. */
1615 int voronoicell_base::check_marginal(int n,double &ans) {
1616  int i;
1617  for(i=0;i<n_marg;i+=2) if(marg[i]==n) return marg[i+1];
1618  if(n_marg==current_marginal) {
1619  current_marginal<<=1;
1620  if(current_marginal>max_marginal)
1621  voro_fatal_error("Marginal case buffer allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
1622 #if VOROPP_VERBOSE >=2
1623  fprintf(stderr,"Marginal cases buffer scaled up to %d\n",i);
1624 #endif
1625  int *pmarg=new int[current_marginal];
1626  for(int j=0;j<n_marg;j++) pmarg[j]=marg[j];
1627  delete [] marg;
1628  marg=pmarg;
1629  }
1630  marg[n_marg++]=n;
1631  marg[n_marg++]=ans>tolerance?1:(ans<-tolerance?-1:0);
1632  return marg[n_marg-1];
1633 }
1634 
1635 /** For each face of the Voronoi cell, this routine prints the out the normal
1636  * vector of the face, and scales it to the distance from the cell center to
1637  * that plane.
1638  * \param[out] v the vector to store the results in. */
1639 void voronoicell_base::normals(std::vector<double> &v) {
1640  int i,j,k;
1641  v.clear();
1642  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
1643  k=ed[i][j];
1644  if(k>=0) normals_search(v,i,j,k);
1645  }
1646  reset_edges();
1647 }
1648 
1649 /** This inline routine is called by normals(). It attempts to construct a
1650  * single normal vector that is associated with a particular face. It first
1651  * traces around the face, trying to find two vectors along the face edges
1652  * whose vector product is above the numerical tolerance. It then constructs
1653  * the normal vector using this product. If the face is too small, and none of
1654  * the vector products are large enough, the routine may return (0,0,0) as the
1655  * normal vector.
1656  * \param[in] v the vector to store the results in.
1657  * \param[in] i the initial vertex of the face to test.
1658  * \param[in] j the index of an edge of the vertex.
1659  * \param[in] k the neighboring vertex of i, set to ed[i][j]. */
1660 inline void voronoicell_base::normals_search(std::vector<double> &v,int i,int j,int k) {
1661  ed[i][j]=-1-k;
1662  int l=cycle_up(ed[i][nu[i]+j],k),m;
1663  double ux,uy,uz,vx,vy,vz,wx,wy,wz,wmag;
1664  do {
1665  m=ed[k][l];ed[k][l]=-1-m;
1666  ux=pts[3*m]-pts[3*k];
1667  uy=pts[3*m+1]-pts[3*k+1];
1668  uz=pts[3*m+2]-pts[3*k+2];
1669 
1670  // Test to see if the length of this edge is above the tolerance
1671  if(ux*ux+uy*uy+uz*uz>tolerance_sq) {
1672  while(m!=i) {
1673  l=cycle_up(ed[k][nu[k]+l],m);
1674  k=m;m=ed[k][l];ed[k][l]=-1-m;
1675  vx=pts[3*m]-pts[3*k];
1676  vy=pts[3*m+1]-pts[3*k+1];
1677  vz=pts[3*m+2]-pts[3*k+2];
1678 
1679  // Construct the vector product of this edge with
1680  // the previous one
1681  wx=uz*vy-uy*vz;
1682  wy=ux*vz-uz*vx;
1683  wz=uy*vx-ux*vy;
1684  wmag=wx*wx+wy*wy+wz*wz;
1685 
1686  // Test to see if this vector product of the
1687  // two edges is above the tolerance
1688  if(wmag>tolerance_sq) {
1689 
1690  // Construct the normal vector and print it
1691  wmag=1/sqrt(wmag);
1692  v.push_back(wx*wmag);
1693  v.push_back(wy*wmag);
1694  v.push_back(wz*wmag);
1695 
1696  // Mark all of the remaining edges of this
1697  // face and exit
1698  while(m!=i) {
1699  l=cycle_up(ed[k][nu[k]+l],m);
1700  k=m;m=ed[k][l];ed[k][l]=-1-m;
1701  }
1702  return;
1703  }
1704  }
1705  v.push_back(0);
1706  v.push_back(0);
1707  v.push_back(0);
1708  return;
1709  }
1710  l=cycle_up(ed[k][nu[k]+l],m);
1711  k=m;
1712  } while (k!=i);
1713  v.push_back(0);
1714  v.push_back(0);
1715  v.push_back(0);
1716 }
1717 
1718 
1719 /** Returns the number of faces of a computed Voronoi cell.
1720  * \return The number of faces. */
1722  int i,j,k,l,m,s=0;
1723  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
1724  k=ed[i][j];
1725  if(k>=0) {
1726  s++;
1727  ed[i][j]=-1-k;
1728  l=cycle_up(ed[i][nu[i]+j],k);
1729  do {
1730  m=ed[k][l];
1731  ed[k][l]=-1-m;
1732  l=cycle_up(ed[k][nu[k]+l],m);
1733  k=m;
1734  } while (k!=i);
1735 
1736  }
1737  }
1738  reset_edges();
1739  return s;
1740 }
1741 
1742 /** Returns a vector of the vertex orders.
1743  * \param[out] v the vector to store the results in. */
1744 void voronoicell_base::vertex_orders(std::vector<int> &v) {
1745  v.resize(p);
1746  for(int i=0;i<p;i++) v[i]=nu[i];
1747 }
1748 
1749 /** Outputs the vertex orders.
1750  * \param[out] fp the file handle to write to. */
1752  if(p>0) {
1753  fprintf(fp,"%d",*nu);
1754  for(int *nup=nu+1;nup<nu+p;nup++) fprintf(fp," %d",*nup);
1755  }
1756 }
1757 
1758 /** Returns a vector of the vertex vectors using the local coordinate system.
1759  * \param[out] v the vector to store the results in. */
1760 void voronoicell_base::vertices(std::vector<double> &v) {
1761  v.resize(3*p);
1762  double *ptsp=pts;
1763  for(int i=0;i<3*p;i+=3) {
1764  v[i]=*(ptsp++)*0.5;
1765  v[i+1]=*(ptsp++)*0.5;
1766  v[i+2]=*(ptsp++)*0.5;
1767  }
1768 }
1769 
1770 /** Outputs the vertex vectors using the local coordinate system.
1771  * \param[out] fp the file handle to write to. */
1773  if(p>0) {
1774  fprintf(fp,"(%g,%g,%g)",*pts*0.5,pts[1]*0.5,pts[2]*0.5);
1775  for(double *ptsp=pts+3;ptsp<pts+3*p;ptsp+=3) fprintf(fp," (%g,%g,%g)",*ptsp*0.5,ptsp[1]*0.5,ptsp[2]*0.5);
1776  }
1777 }
1778 
1779 
1780 /** Returns a vector of the vertex vectors in the global coordinate system.
1781  * \param[out] v the vector to store the results in.
1782  * \param[in] (x,y,z) the position vector of the particle in the global
1783  * coordinate system. */
1784 void voronoicell_base::vertices(double x,double y,double z,std::vector<double> &v) {
1785  v.resize(3*p);
1786  double *ptsp=pts;
1787  for(int i=0;i<3*p;i+=3) {
1788  v[i]=x+*(ptsp++)*0.5;
1789  v[i+1]=y+*(ptsp++)*0.5;
1790  v[i+2]=z+*(ptsp++)*0.5;
1791  }
1792 }
1793 
1794 /** Outputs the vertex vectors using the global coordinate system.
1795  * \param[out] fp the file handle to write to.
1796  * \param[in] (x,y,z) the position vector of the particle in the global
1797  * coordinate system. */
1798 void voronoicell_base::output_vertices(double x,double y,double z,FILE *fp) {
1799  if(p>0) {
1800  fprintf(fp,"(%g,%g,%g)",x+*pts*0.5,y+pts[1]*0.5,z+pts[2]*0.5);
1801  for(double *ptsp=pts+3;ptsp<pts+3*p;ptsp+=3) fprintf(fp," (%g,%g,%g)",x+*ptsp*0.5,y+ptsp[1]*0.5,z+ptsp[2]*0.5);
1802  }
1803 }
1804 
1805 /** This routine returns the perimeters of each face.
1806  * \param[out] v the vector to store the results in. */
1807 void voronoicell_base::face_perimeters(std::vector<double> &v) {
1808  v.clear();
1809  int i,j,k,l,m;
1810  double dx,dy,dz,perim;
1811  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
1812  k=ed[i][j];
1813  if(k>=0) {
1814  dx=pts[3*k]-pts[3*i];
1815  dy=pts[3*k+1]-pts[3*i+1];
1816  dz=pts[3*k+2]-pts[3*i+2];
1817  perim=sqrt(dx*dx+dy*dy+dz*dz);
1818  ed[i][j]=-1-k;
1819  l=cycle_up(ed[i][nu[i]+j],k);
1820  do {
1821  m=ed[k][l];
1822  dx=pts[3*m]-pts[3*k];
1823  dy=pts[3*m+1]-pts[3*k+1];
1824  dz=pts[3*m+2]-pts[3*k+2];
1825  perim+=sqrt(dx*dx+dy*dy+dz*dz);
1826  ed[k][l]=-1-m;
1827  l=cycle_up(ed[k][nu[k]+l],m);
1828  k=m;
1829  } while (k!=i);
1830  v.push_back(0.5*perim);
1831  }
1832  }
1833  reset_edges();
1834 }
1835 
1836 /** For each face, this routine outputs a bracketed sequence of numbers
1837  * containing a list of all the vertices that make up that face.
1838  * \param[out] v the vector to store the results in. */
1839 void voronoicell_base::face_vertices(std::vector<int> &v) {
1840  int i,j,k,l,m,vp(0),vn;
1841  v.clear();
1842  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
1843  k=ed[i][j];
1844  if(k>=0) {
1845  v.push_back(0);
1846  v.push_back(i);
1847  ed[i][j]=-1-k;
1848  l=cycle_up(ed[i][nu[i]+j],k);
1849  do {
1850  v.push_back(k);
1851  m=ed[k][l];
1852  ed[k][l]=-1-m;
1853  l=cycle_up(ed[k][nu[k]+l],m);
1854  k=m;
1855  } while (k!=i);
1856  vn=v.size();
1857  v[vp]=vn-vp-1;
1858  vp=vn;
1859  }
1860  }
1861  reset_edges();
1862 }
1863 
1864 /** Outputs a list of the number of edges in each face.
1865  * \param[out] v the vector to store the results in. */
1866 void voronoicell_base::face_orders(std::vector<int> &v) {
1867  int i,j,k,l,m,q;
1868  v.clear();
1869  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
1870  k=ed[i][j];
1871  if(k>=0) {
1872  q=1;
1873  ed[i][j]=-1-k;
1874  l=cycle_up(ed[i][nu[i]+j],k);
1875  do {
1876  q++;
1877  m=ed[k][l];
1878  ed[k][l]=-1-m;
1879  l=cycle_up(ed[k][nu[k]+l],m);
1880  k=m;
1881  } while (k!=i);
1882  v.push_back(q);;
1883  }
1884  }
1885  reset_edges();
1886 }
1887 
1888 /** Computes the number of edges that each face has and outputs a frequency
1889  * table of the results.
1890  * \param[out] v the vector to store the results in. */
1891 void voronoicell_base::face_freq_table(std::vector<int> &v) {
1892  int i,j,k,l,m,q;
1893  v.clear();
1894  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
1895  k=ed[i][j];
1896  if(k>=0) {
1897  q=1;
1898  ed[i][j]=-1-k;
1899  l=cycle_up(ed[i][nu[i]+j],k);
1900  do {
1901  q++;
1902  m=ed[k][l];
1903  ed[k][l]=-1-m;
1904  l=cycle_up(ed[k][nu[k]+l],m);
1905  k=m;
1906  } while (k!=i);
1907  if((unsigned int) q>=v.size()) v.resize(q+1,0);
1908  v[q]++;
1909  }
1910  }
1911  reset_edges();
1912 }
1913 
1914 /** This routine tests to see whether the cell intersects a plane by starting
1915  * from the guess point up. If up intersects, then it immediately returns true.
1916  * Otherwise, it calls the plane_intersects_track() routine.
1917  * \param[in] (x,y,z) the normal vector to the plane.
1918  * \param[in] rsq the distance along this vector of the plane.
1919  * \return False if the plane does not intersect the plane, true if it does. */
1920 bool voronoicell_base::plane_intersects(double x,double y,double z,double rsq) {
1921  double g=x*pts[3*up]+y*pts[3*up+1]+z*pts[3*up+2];
1922  if(g<rsq) return plane_intersects_track(x,y,z,rsq,g);
1923  return true;
1924 }
1925 
1926 /** This routine tests to see if a cell intersects a plane. It first tests a
1927  * random sample of approximately sqrt(p)/4 points. If any of those are
1928  * intersect, then it immediately returns true. Otherwise, it takes the closest
1929  * point and passes that to plane_intersect_track() routine.
1930  * \param[in] (x,y,z) the normal vector to the plane.
1931  * \param[in] rsq the distance along this vector of the plane.
1932  * \return False if the plane does not intersect the plane, true if it does. */
1933 bool voronoicell_base::plane_intersects_guess(double x,double y,double z,double rsq) {
1934  up=0;
1935  double g=x*pts[3*up]+y*pts[3*up+1]+z*pts[3*up+2];
1936  if(g<rsq) {
1937  int ca=1,cc=p>>3,mp=1;
1938  double m;
1939  while(ca<cc) {
1940  m=x*pts[3*mp]+y*pts[3*mp+1]+z*pts[3*mp+2];
1941  if(m>g) {
1942  if(m>rsq) return true;
1943  g=m;up=mp;
1944  }
1945  ca+=mp++;
1946  }
1947  return plane_intersects_track(x,y,z,rsq,g);
1948  }
1949  return true;
1950 }
1951 
1952 /* This routine tests to see if a cell intersects a plane, by tracing over the cell from
1953  * vertex to vertex, starting at up. It is meant to be called either by plane_intersects()
1954  * or plane_intersects_track(), when those routines cannot immediately resolve the case.
1955  * \param[in] (x,y,z) the normal vector to the plane.
1956  * \param[in] rsq the distance along this vector of the plane.
1957  * \param[in] g the distance of up from the plane.
1958  * \return False if the plane does not intersect the plane, true if it does. */
1959 inline bool voronoicell_base::plane_intersects_track(double x,double y,double z,double rsq,double g) {
1960  int count=0,ls,us,tp;
1961  double t;
1962 
1963  // The test point is outside of the cutting space
1964  for(us=0;us<nu[up];us++) {
1965  tp=ed[up][us];
1966  t=x*pts[3*tp]+y*pts[3*tp+1]+z*pts[3*tp+2];
1967  if(t>g) {
1968  ls=ed[up][nu[up]+us];
1969  up=tp;
1970  while (t<rsq) {
1971  if(++count>=p) {
1972 #if VOROPP_VERBOSE >=1
1973  fputs("Bailed out of convex calculation",stderr);
1974 #endif
1975  for(tp=0;tp<p;tp++) if(x*pts[3*tp]+y*pts[3*tp+1]+z*pts[3*tp+2]>rsq) return true;
1976  return false;
1977  }
1978 
1979  // Test all the neighbors of the current point
1980  // and find the one which is closest to the
1981  // plane
1982  for(us=0;us<ls;us++) {
1983  tp=ed[up][us];
1984  g=x*pts[3*tp]+y*pts[3*tp+1]+z*pts[3*tp+2];
1985  if(g>t) break;
1986  }
1987  if(us==ls) {
1988  us++;
1989  while(us<nu[up]) {
1990  tp=ed[up][us];
1991  g=x*pts[3*tp]+y*pts[3*tp+1]+z*pts[3*tp+2];
1992  if(g>t) break;
1993  us++;
1994  }
1995  if(us==nu[up]) return false;
1996  }
1997  ls=ed[up][nu[up]+us];up=tp;t=g;
1998  }
1999  return true;
2000  }
2001  }
2002  return false;
2003 }
2004 
2005 /** Counts the number of edges of the Voronoi cell.
2006  * \return the number of edges. */
2008  int edges=0,*nup=nu;
2009  while(nup<nu+p) edges+=*(nup++);
2010  return edges>>1;
2011 }
2012 
2013 /** Outputs a custom string of information about the Voronoi cell. The string
2014  * of information follows a similar style as the C printf command, and detailed
2015  * information about its format is available at
2016  * http://math.lbl.gov/voro++/doc/custom.html.
2017  * \param[in] format the custom string to print.
2018  * \param[in] i the ID of the particle associated with this Voronoi cell.
2019  * \param[in] (x,y,z) the position of the particle associated with this Voronoi
2020  * cell.
2021  * \param[in] r a radius associated with the particle.
2022  * \param[in] fp the file handle to write to. */
2023 void voronoicell_base::output_custom(const char *format,int i,double x,double y,double z,double r,FILE *fp) {
2024  char *fmp=(const_cast<char*>(format));
2025  std::vector<int> vi;
2026  std::vector<double> vd;
2027  while(*fmp!=0) {
2028  if(*fmp=='%') {
2029  fmp++;
2030  switch(*fmp) {
2031 
2032  // Particle-related output
2033  case 'i': fprintf(fp,"%d",i);break;
2034  case 'x': fprintf(fp,"%g",x);break;
2035  case 'y': fprintf(fp,"%g",y);break;
2036  case 'z': fprintf(fp,"%g",z);break;
2037  case 'q': fprintf(fp,"%g %g %g",x,y,z);break;
2038  case 'r': fprintf(fp,"%g",r);break;
2039 
2040  // Vertex-related output
2041  case 'w': fprintf(fp,"%d",p);break;
2042  case 'p': output_vertices(fp);break;
2043  case 'P': output_vertices(x,y,z,fp);break;
2044  case 'o': output_vertex_orders(fp);break;
2045  case 'm': fprintf(fp,"%g",0.25*max_radius_squared());break;
2046 
2047  // Edge-related output
2048  case 'g': fprintf(fp,"%d",number_of_edges());break;
2049  case 'E': fprintf(fp,"%g",total_edge_distance());break;
2050  case 'e': face_perimeters(vd);voro_print_vector(vd,fp);break;
2051 
2052  // Face-related output
2053  case 's': fprintf(fp,"%d",number_of_faces());break;
2054  case 'F': fprintf(fp,"%g",surface_area());break;
2055  case 'A': {
2056  face_freq_table(vi);
2057  voro_print_vector(vi,fp);
2058  } break;
2059  case 'a': face_orders(vi);voro_print_vector(vi,fp);break;
2060  case 'f': face_areas(vd);voro_print_vector(vd,fp);break;
2061  case 't': {
2062  face_vertices(vi);
2063  voro_print_face_vertices(vi,fp);
2064  } break;
2065  case 'l': normals(vd);
2066  voro_print_positions(vd,fp);
2067  break;
2068  case 'n': neighbors(vi);
2069  voro_print_vector(vi,fp);
2070  break;
2071 
2072  // Volume-related output
2073  case 'v': fprintf(fp,"%g",volume());break;
2074  case 'c': {
2075  double cx,cy,cz;
2076  centroid(cx,cy,cz);
2077  fprintf(fp,"%g %g %g",cx,cy,cz);
2078  } break;
2079  case 'C': {
2080  double cx,cy,cz;
2081  centroid(cx,cy,cz);
2082  fprintf(fp,"%g %g %g",x+cx,y+cy,z+cz);
2083  } break;
2084 
2085  // End-of-string reached
2086  case 0: fmp--;break;
2087 
2088  // The percent sign is not part of a
2089  // control sequence
2090  default: putc('%',fp);putc(*fmp,fp);
2091  }
2092  } else putc(*fmp,fp);
2093  fmp++;
2094  }
2095  fputs("\n",fp);
2096 }
2097 
2098 /** This initializes the class to be a rectangular box. It calls the base class
2099  * initialization routine to set up the edge and vertex information, and then
2100  * sets up the neighbor information, with initial faces being assigned ID
2101  * numbers from -1 to -6.
2102  * \param[in] (xmin,xmax) the minimum and maximum x coordinates.
2103  * \param[in] (ymin,ymax) the minimum and maximum y coordinates.
2104  * \param[in] (zmin,zmax) the minimum and maximum z coordinates. */
2105 void voronoicell_neighbor::init(double xmin,double xmax,double ymin,double ymax,double zmin,double zmax) {
2106  init_base(xmin,xmax,ymin,ymax,zmin,zmax);
2107  int *q=mne[3];
2108  *q=-5;q[1]=-3;q[2]=-1;
2109  q[3]=-5;q[4]=-2;q[5]=-3;
2110  q[6]=-5;q[7]=-1;q[8]=-4;
2111  q[9]=-5;q[10]=-4;q[11]=-2;
2112  q[12]=-6;q[13]=-1;q[14]=-3;
2113  q[15]=-6;q[16]=-3;q[17]=-2;
2114  q[18]=-6;q[19]=-4;q[20]=-1;
2115  q[21]=-6;q[22]=-2;q[23]=-4;
2116  *ne=q;ne[1]=q+3;ne[2]=q+6;ne[3]=q+9;
2117  ne[4]=q+12;ne[5]=q+15;ne[6]=q+18;ne[7]=q+21;
2118 }
2119 
2120 /** This initializes the class to be an octahedron. It calls the base class
2121  * initialization routine to set up the edge and vertex information, and then
2122  * sets up the neighbor information, with the initial faces being assigned ID
2123  * numbers from -1 to -8.
2124  * \param[in] l The distance from the octahedron center to a vertex. Six
2125  * vertices are initialized at (-l,0,0), (l,0,0), (0,-l,0),
2126  * (0,l,0), (0,0,-l), and (0,0,l). */
2129  int *q=mne[4];
2130  *q=-5;q[1]=-6;q[2]=-7;q[3]=-8;
2131  q[4]=-1;q[5]=-2;q[6]=-3;q[7]=-4;
2132  q[8]=-6;q[9]=-5;q[10]=-2;q[11]=-1;
2133  q[12]=-8;q[13]=-7;q[14]=-4;q[15]=-3;
2134  q[16]=-5;q[17]=-8;q[18]=-3;q[19]=-2;
2135  q[20]=-7;q[21]=-6;q[22]=-1;q[23]=-4;
2136  *ne=q;ne[1]=q+4;ne[2]=q+8;ne[3]=q+12;ne[4]=q+16;ne[5]=q+20;
2137 }
2138 
2139 /** This initializes the class to be a tetrahedron. It calls the base class
2140  * initialization routine to set up the edge and vertex information, and then
2141  * sets up the neighbor information, with the initial faces being assigned ID
2142  * numbers from -1 to -4.
2143  * \param (x0,y0,z0) a position vector for the first vertex.
2144  * \param (x1,y1,z1) a position vector for the second vertex.
2145  * \param (x2,y2,z2) a position vector for the third vertex.
2146  * \param (x3,y3,z3) a position vector for the fourth vertex. */
2147 void voronoicell_neighbor::init_tetrahedron(double x0,double y0,double z0,double x1,double y1,double z1,double x2,double y2,double z2,double x3,double y3,double z3) {
2148  init_tetrahedron_base(x0,y0,z0,x1,y1,z1,x2,y2,z2,x3,y3,z3);
2149  int *q=mne[3];
2150  *q=-4;q[1]=-3;q[2]=-2;
2151  q[3]=-3;q[4]=-4;q[5]=-1;
2152  q[6]=-4;q[7]=-2;q[8]=-1;
2153  q[9]=-2;q[10]=-3;q[11]=-1;
2154  *ne=q;ne[1]=q+3;ne[2]=q+6;ne[3]=q+9;
2155 }
2156 
2157 /** This routine checks to make sure the neighbor information of each face is
2158  * consistent. */
2160  int i,j,k,l,m,q;
2161  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
2162  k=ed[i][j];
2163  if(k>=0) {
2164  ed[i][j]=-1-k;
2165  q=ne[i][j];
2166  l=cycle_up(ed[i][nu[i]+j],k);
2167  do {
2168  m=ed[k][l];
2169  ed[k][l]=-1-m;
2170  if(ne[k][l]!=q) fprintf(stderr,"Facet error at (%d,%d)=%d, started from (%d,%d)=%d\n",k,l,ne[k][l],i,j,q);
2171  l=cycle_up(ed[k][nu[k]+l],m);
2172  k=m;
2173  } while (k!=i);
2174  }
2175  }
2176  reset_edges();
2177 }
2178 
2179 /** The class constructor allocates memory for storing neighbor information. */
2181  int i;
2182  mne=new int*[current_vertex_order];
2183  ne=new int*[current_vertices];
2184  for(i=0;i<3;i++) mne[i]=new int[init_n_vertices*i];
2185  mne[3]=new int[init_3_vertices*3];
2186  for(i=4;i<current_vertex_order;i++) mne[i]=new int[init_n_vertices*i];
2187 }
2188 
2189 /** The class destructor frees the dynamically allocated memory for storing
2190  * neighbor information. */
2192  for(int i=current_vertex_order-1;i>=0;i--) if(mem[i]>0) delete [] mne[i];
2193  delete [] mne;
2194  delete [] ne;
2195 }
2196 
2197 /** Computes a vector list of neighbors. */
2198 void voronoicell_neighbor::neighbors(std::vector<int> &v) {
2199  v.clear();
2200  int i,j,k,l,m;
2201  for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
2202  k=ed[i][j];
2203  if(k>=0) {
2204  v.push_back(ne[i][j]);
2205  ed[i][j]=-1-k;
2206  l=cycle_up(ed[i][nu[i]+j],k);
2207  do {
2208  m=ed[k][l];
2209  ed[k][l]=-1-m;
2210  l=cycle_up(ed[k][nu[k]+l],m);
2211  k=m;
2212  } while (k!=i);
2213  }
2214  }
2215  reset_edges();
2216 }
2217 
2218 /** Prints the vertices, their edges, the relation table, and also notifies if
2219  * any memory errors are visible. */
2221  int j;
2222  double *ptsp=pts;
2223  for(int i=0;i<p;i++,ptsp+=3) {
2224  printf("%d %d ",i,nu[i]);
2225  for(j=0;j<nu[i];j++) printf(" %d",ed[i][j]);
2226  printf(" ");
2227  while(j<(nu[i]<<1)) printf(" %d",ed[i][j]);
2228  printf(" %d",ed[i][j]);
2230  printf(" %g %g %g %p",*ptsp,ptsp[1],ptsp[2],(void*) ed[i]);
2231  if(ed[i]>=mep[nu[i]]+mec[nu[i]]*((nu[i]<<1)+1)) puts(" Memory error");
2232  else puts("");
2233  }
2234 }
2235 
2236 /** This prints out the neighbor information for vertex i. */
2238  if(nu[i]>0) {
2239  int j=0;
2240  printf(" (");
2241  while(j<nu[i]-1) printf("%d,",ne[i][j++]);
2242  printf("%d)",ne[i][j]);
2243  } else printf(" ()");
2244 }
2245 
2246 // Explicit instantiation
2247 template bool voronoicell_base::nplane(voronoicell&,double,double,double,double,int);
2248 template bool voronoicell_base::nplane(voronoicell_neighbor&,double,double,double,double,int);
2251 
2252 }
void init_tetrahedron(double x0, double y0, double z0, double x1, double y1, double z1, double x2, double y2, double z2, double x3, double y3, double z3)
Definition: cell.cc:2147
void output_vertex_orders(FILE *fp=stdout)
Definition: cell.cc:1751
Extension of the voronoicell_base class to represent a Voronoi cell with neighbor information...
Definition: cell.hh:403
int cycle_down(int a, int p)
Definition: cell.hh:221
void centroid(double &cx, double &cy, double &cz)
Definition: cell.cc:1408
bool plane_intersects(double x, double y, double z, double rsq)
Definition: cell.cc:1920
void face_areas(std::vector< double > &v)
Definition: cell.cc:1336
#define VOROPP_MEMORY_ERROR
Definition: config.hh:113
void init_tetrahedron_base(double x0, double y0, double z0, double x1, double y1, double z1, double x2, double y2, double z2, double x3, double y3, double z3)
Definition: cell.cc:312
void draw_gnuplot(double x, double y, double z, FILE *fp=stdout)
Definition: cell.cc:1507
virtual void neighbors(std::vector< int > &v)
Definition: cell.hh:197
void check_duplicates()
Definition: cell.cc:342
void construct_relations()
Definition: cell.cc:349
void init(double xmin, double xmax, double ymin, double ymax, double zmin, double zmax)
Definition: cell.cc:2105
virtual void print_edges_neighbors(int i)
Definition: cell.cc:2237
Header file for the voronoicell and related classes.
int current_vertex_order
Definition: cell.hh:45
Master configuration file for setting various compile-time options.
bool nplane(vc_class &vc, double x, double y, double z, double rsq, int p_id)
Definition: cell.cc:404
double surface_area()
Definition: cell.cc:1372
void init_octahedron(double l)
Definition: cell.cc:2127
virtual void neighbors(std::vector< int > &v)
Definition: cell.cc:2198
void check_memory_for_copy(vc_class &vc, voronoicell_base *vb)
Definition: cell.cc:56
#define VOROPP_INTERNAL_ERROR
Definition: config.hh:119
void vertices(std::vector< double > &v)
Definition: cell.cc:1760
void face_perimeters(std::vector< double > &v)
Definition: cell.cc:1807
virtual void print_edges_neighbors(int i)
Definition: cell.hh:209
int current_delete2_size
Definition: cell.hh:49
void output_vertices(FILE *fp=stdout)
Definition: cell.cc:1772
void operator=(voronoicell &c)
Definition: cell.cc:80
void draw_pov(double x, double y, double z, FILE *fp=stdout)
Definition: cell.cc:1487
double max_radius_squared()
Definition: cell.cc:1454
void face_orders(std::vector< int > &v)
Definition: cell.cc:1866
int cycle_up(int a, int p)
Definition: cell.hh:215
void face_vertices(std::vector< int > &v)
Definition: cell.cc:1839
void init_octahedron_base(double l)
Definition: cell.cc:286
bool plane_intersects_guess(double x, double y, double z, double rsq)
Definition: cell.cc:1933
Header file for the small helper functions.
double total_edge_distance()
Definition: cell.cc:1468
void copy(voronoicell_base *vb)
Definition: cell.cc:65
void face_freq_table(std::vector< int > &v)
Definition: cell.cc:1891
void output_custom(const char *format, FILE *fp=stdout)
Definition: cell.hh:182
A class representing a single Voronoi cell.
Definition: cell.hh:33
Extension of the voronoicell_base class to represent a Voronoi cell without neighbor information...
Definition: cell.hh:300
void draw_pov_mesh(double x, double y, double z, FILE *fp=stdout)
Definition: cell.cc:1542
void init_base(double xmin, double xmax, double ymin, double ymax, double zmin, double zmax)
Definition: cell.cc:257
void vertex_orders(std::vector< int > &v)
Definition: cell.cc:1744
void translate(double x, double y, double z)
Definition: cell.cc:105
void normals(std::vector< double > &v)
Definition: cell.cc:1639
void check_relations()
Definition: cell.cc:331