branches/exact/src/cell.hh

   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.hh
   8  * \brief Header file for the voronoicell and related classes. */
   9
  10 #ifndef VOROPP_CELL_HH
  11 #define VOROPP_CELL_HH
  12
  13 #include <cstdio>
  14 #include <cstdlib>
  15 #include <cmath>
  16 #include <vector>
  17 #include <gmpxx.h>
  18 using namespace std;
  19
  20 #include "config.hh"
  21 #include "common.hh"
  22
  23 namespace voro {
  24
  25 /** \brief A class representing a single Voronoi cell.
  26  *
  27  * This class represents a single Voronoi cell, as a collection of vertices
  28  * that are connected by edges. The class contains routines for initializing
  29  * the Voronoi cell to be simple shapes such as a box, tetrahedron, or octahedron.
  30  * It the contains routines for recomputing the cell based on cutting it
  31  * by a plane, which forms the key routine for the Voronoi cell computation.
  32  * It contains numerous routine for computing statistics about the Voronoi cell,
  33  * and it can output the cell in several formats.
  34  *
  35  * This class is not intended for direct use, but forms the base of the
  36  * voronoicell and voronoicell_neighbor classes, which extend it based on
  37  * whether neighboring particle ID information needs to be tracked. */
  38 class voronoicell_base {
  39         public:
  40                 /** This holds the current size of the arrays ed and nu, which
  41                  * hold the vertex information. If more vertices are created
  42                  * than can fit in this array, then it is dynamically extended
  43                  * using the add_memory_vertices routine. */
  44                 int current_vertices;
  45                 /** This holds the current maximum allowed order of a vertex,
  46                  * which sets the size of the mem, mep, and mec arrays. If a
  47                  * vertex is created with more vertices than this, the arrays
  48                  * are dynamically extended using the add_memory_vorder routine.
  49                  */
  50                 int current_vertex_order;
  51                 /** This sets the size of the main delete stack. */
  52                 int current_delete_size;
  53                 /** This sets the size of the auxiliary delete stack. */
  54                 int current_delete2_size;
  55                 /** This sets the total number of vertices in the current cell.
  56                  */
  57                 int p;
  58                 /** This is the index of particular point in the cell, which is
  59                  * used to start the tracing routines for plane intersection
  60                  * and cutting. These routines will work starting from any
  61                  * point, but it's often most efficient to start from the last
  62                  * point considered, since in many cases, the cell construction
  63                  * algorithm may consider many planes with similar vectors
  64                  * concurrently. */
  65                 int up;
  66                 /** This is a two dimensional array that holds information
  67                  * about the edge connections of the vertices that make up the
  68                  * cell. The two dimensional array is not allocated in the
  69                  * usual method. To account for the fact the different vertices
  70                  * have different orders, and thus require different amounts of
  71                  * storage, the elements of ed[i] point to one-dimensional
  72                  * arrays in the mep[] array of different sizes.
  73                  *
  74                  * More specifically, if vertex i has order m, then ed[i]
  75                  * points to a one-dimensional array in mep[m] that has 2*m+1
  76                  * entries. The first m elements hold the neighboring edges, so
  77                  * that the jth edge of vertex i is held in ed[i][j]. The next
  78                  * m elements hold a table of relations which is redundant but
  79                  * helps speed up the computation. It satisfies the relation
  80                  * ed[ed[i][j]][ed[i][m+j]]=i. The final entry holds a back
  81                  * pointer, so that ed[i+2*m]=i. The back pointers are used
  82                  * when rearranging the memory. */
  83                 int **ed;
  84                 /** This array holds the order of the vertices in the Voronoi
  85                  * cell. This array is dynamically allocated, with its current
  86                  * size held by current_vertices. */
  87                 int *nu;
  88                 /** This in an array with size 3*current_vertices for holding
  89                  * the positions of the vertices. */
  90                 double *pts;
  91                 mpq_class *ptsq;
  92                 bool synced;
  93                 voronoicell_base();
  94                 ~voronoicell_base();
  95                 void init_base(double xmin,double xmax,double ymin,double ymax,double zmin,double zmax);
  96                 void init_octahedron_base(double l);
  97                 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);
  98                 void translate(double x,double y,double z);
  99                 void draw_pov(double x,double y,double z,FILE *fp=stdout);
 100                 /** Outputs the cell in POV-Ray format, using cylinders for edges
 101                  * and spheres for vertices, to a given file.
 102                  * \param[in] (x,y,z) a displacement to add to the cell's
 103                  *                    position.
 104                  * \param[in] filename the name of the file to write to. */
 105                 inline void draw_pov(double x,double y,double z,const char *filename) {
 106                         FILE *fp=safe_fopen(filename,"w");
 107                         draw_pov(x,y,z,fp);
 108                         fclose(fp);
 109                 };
 110                 void draw_pov_mesh(double x,double y,double z,FILE *fp=stdout);
 111                 /** Outputs the cell in POV-Ray format as a mesh2 object to a
 112                  * given file.
 113                  * \param[in] (x,y,z) a displacement to add to the cell's
 114                  *                    position.
 115                  * \param[in] filename the name of the file to write to. */
 116                 inline void draw_pov_mesh(double x,double y,double z,const char *filename) {
 117                         FILE *fp=safe_fopen(filename,"w");
 118                         draw_pov_mesh(x,y,z,fp);
 119                         fclose(fp);
 120                 }
 121                 void draw_gnuplot(double x,double y,double z,FILE *fp=stdout);
 122                 /** Outputs the cell in Gnuplot format a given file.
 123                  * \param[in] (x,y,z) a displacement to add to the cell's
 124                  *                    position.
 125                  * \param[in] filename the name of the file to write to. */
 126                 inline void draw_gnuplot(double x,double y,double z,const char *filename) {
 127                         FILE *fp=safe_fopen(filename,"w");
 128                         draw_gnuplot(x,y,z,fp);
 129                         fclose(fp);
 130                 }
 131                 void sync();
 132                 double volume();
 133                 double max_radius_squared();
 134                 double total_edge_distance();
 135                 double surface_area();
 136                 void centroid(double &cx,double &cy,double &cz);
 137                 int number_of_faces();
 138                 int number_of_edges();
 139                 void vertex_orders(vector<int> &v);
 140                 void output_vertex_orders(FILE *fp=stdout);
 141                 void vertices(vector<double> &v);
 142                 void output_vertices(FILE *fp=stdout);
 143                 void vertices(double x,double y,double z,vector<double> &v);
 144                 void output_vertices(double x,double y,double z,FILE *fp=stdout);
 145                 void face_areas(vector<double> &v);
 146                 /** Outputs the areas of the faces.
 147                  * \param[in] fp the file handle to write to. */
 148                 inline void output_face_areas(FILE *fp=stdout) {
 149                         vector<double> v;face_areas(v);
 150                         voro_print_vector(v,fp);
 151                 }
 152                 void face_orders(vector<int> &v);
 153                 /** Outputs a list of the number of sides of each face.
 154                  * \param[in] fp the file handle to write to. */
 155                 inline void output_face_orders(FILE *fp=stdout) {
 156                         vector<int> v;face_orders(v);
 157                         voro_print_vector(v,fp);
 158                 }
 159                 void face_freq_table(vector<int> &v);
 160                 /** Outputs a */
 161                 inline void output_face_freq_table(FILE *fp=stdout) {
 162                         vector<int> v;face_freq_table(v);
 163                         voro_print_vector(v,fp);
 164                 }
 165                 void face_vertices(vector<int> &v);
 166                 /** Outputs the */
 167                 inline void output_face_vertices(FILE *fp=stdout) {
 168                         vector<int> v;face_vertices(v);
 169                         voro_print_face_vertices(v,fp);
 170                 }
 171                 void face_perimeters(vector<double> &v);
 172                 /** Outputs a list of the perimeters of each face.
 173                  * \param[in] fp the file handle to write to. */
 174                 inline void output_face_perimeters(FILE *fp=stdout) {
 175                         vector<double> v;face_perimeters(v);
 176                         voro_print_vector(v,fp);
 177                 }
 178                 void normals(vector<double> &v);
 179                 /** Outputs a list of the perimeters of each face.
 180                  * \param[in] fp the file handle to write to. */
 181                 inline void output_normals(FILE *fp=stdout) {
 182                         vector<double> v;normals(v);
 183                         voro_print_positions(v,fp);
 184                 }
 185                 /** Outputs a custom string of information about the Voronoi
 186                  * cell to a file. It assumes the cell is at (0,0,0) and has a
 187                  * the default_radius associated with it.
 188                  * \param[in] format the custom format string to use.
 189                  * \param[in] fp the file handle to write to. */
 190                 inline void output_custom(const char *format,FILE *fp=stdout) {output_custom(format,0,0,0,0,default_radius,fp);}
 191                 void output_custom(const char *format,int i,double x,double y,double z,double r,FILE *fp=stdout);
 192                 template<class vc_class>
 193                 bool nplane(vc_class &vc,double x,double y,double z,double rs,int p_id);
 194                 bool plane_intersects(double x,double y,double z,double rs);
 195                 bool plane_intersects_guess(double x,double y,double z,double rs);
 196                 void construct_relations();
 197                 void check_relations();
 198                 void check_duplicates();
 199                 void print_edges();
 200                 /** Returns a list of IDs of neighboring particles
 201                  * corresponding to each face.
 202                  * \param[out] v a reference to a vector in which to return the
 203                  *               results. If no neighbor information is
 204                  *               available, a blank vector is returned. */
 205                 virtual void neighbors(vector<int> &v) {v.clear();}
 206                 /** This is a virtual function that is overridden by a routine
 207                  * to print a list of IDs of neighboring particles
 208                  * corresponding to each face. By default, when no neighbor
 209                  * information is available, the routine does nothing.
 210                  * \param[in] fp the file handle to write to. */
 211                 virtual void output_neighbors(FILE *fp=stdout) {}
 212                 /** This a virtual function that is overridden by a routine to
 213                  * print the neighboring particle IDs for a given vertex. By
 214                  * default, when no neighbor information is available, the
 215                  * routine does nothing.
 216                  * \param[in] i the vertex to consider. */
 217                 virtual void print_edges_neighbors(int i) {};
 218                 /** This is a simple inline function for picking out the index
 219                  * of the next edge counterclockwise at the current vertex.
 220                  * \param[in] a the index of an edge of the current vertex.
 221                  * \param[in] p the number of the vertex.
 222                  * \return 0 if a=nu[p]-1, or a+1 otherwise. */
 223                 inline int cycle_up(int a,int p) {return a==nu[p]-1?0:a+1;}
 224                 /** This is a simple inline function for picking out the index
 225                  * of the next edge clockwise from the current vertex.
 226                  * \param[in] a the index of an edge of the current vertex.
 227                  * \param[in] p the number of the vertex.
 228                  * \return nu[p]-1 if a=0, or a-1 otherwise. */
 229                 inline int cycle_down(int a,int p) {return a==0?nu[p]-1:a-1;}
 230         protected:
 231                 /** This a one dimensional array that holds the current sizes
 232                  * of the memory allocations for them mep array.*/
 233                 int *mem;
 234                 /** This is a one dimensional array that holds the current
 235                  * number of vertices of order p that are stored in the mep[p]
 236                  * array. */
 237                 int *mec;
 238                 /** This is a two dimensional array for holding the information
 239                  * about the edges of the Voronoi cell. mep[p] is a
 240                  * one-dimensional array for holding the edge information about
 241                  * all vertices of order p, with each vertex holding 2*p+1
 242                  * integers of information. The total number of vertices held
 243                  * on mep[p] is stored in mem[p]. If the space runs out, the
 244                  * code allocates more using the add_memory() routine. */
 245                 int **mep;
 246                 inline void reset_edges();
 247                 template<class vc_class>
 248                 void check_memory_for_copy(vc_class &vc,voronoicell_base* vb);
 249                 void copy(voronoicell_base* vb);
 250         private:
 251                 /** This is the delete stack, used to store the vertices which
 252                  * are going to be deleted during the plane cutting procedure.
 253                  */
 254                 int *ds,*stacke;
 255                 /** This is the auxiliary delete stack, which has size set by
 256                  * current_delete2_size. */
 257                 int *ds2,*stacke2;
 258                 /** This stores the current memory allocation for the marginal
 259                  * cases. */
 260                 int current_marginal;
 261                 /** This stores the total number of marginal points which are
 262                  * currently in the buffer. */
 263                 int n_marg;
 264                 /** This array contains a list of the marginal points, and also
 265                  * the outcomes of the marginal tests. */
 266                 int *marg;
 267                 /** The x coordinate of the normal vector to the test plane. */
 268                 mpq_class px;
 269                 /** The y coordinate of the normal vector to the test plane. */
 270                 mpq_class py;
 271                 /** The z coordinate of the normal vector to the test plane. */
 272                 mpq_class pz;
 273                 /** The magnitude of the normal vector to the test plane. */
 274                 mpq_class prsq;
 275                 template<class vc_class>
 276                 void add_memory(vc_class &vc,int i,int *stackp2);
 277                 template<class vc_class>
 278                 void add_memory_vertices(vc_class &vc);
 279                 template<class vc_class>
 280                 void add_memory_vorder(vc_class &vc);
 281                 void add_memory_ds(int *&stackp);
 282                 void add_memory_ds2(int *&stackp2);
 283                 template<class vc_class>
 284                 inline bool collapse_order1(vc_class &vc);
 285                 template<class vc_class>
 286                 inline bool collapse_order2(vc_class &vc);
 287                 template<class vc_class>
 288                 inline bool delete_connection(vc_class &vc,int j,int k,bool hand);
 289                 inline bool plane_intersects_track(mpq_class x,mpq_class y,mpq_class z,mpq_class rs,mpq_class g);
 290                 inline void normals_search(vector<double> &v,int i,int j,int k);
 291                 inline bool search_edge(int l,int &m,int &k);
 292                 inline int m_test(int n,mpq_class &ans);
 293                 friend class voronoicell;
 294                 friend class voronoicell_neighbor;
 295 };
 296
 297 /** \brief Extension of the voronoicell_base class to represent a Voronoi
 298  * cell without neighbor information.
 299  *
 300  * This class is an extension of the voronoicell_base class, in cases when
 301  * is not necessary to track the IDs of neighboring particles associated
 302  * with each face of the Voronoi cell. */
 303 class voronoicell : public voronoicell_base {
 304         public:
 305                 using voronoicell_base::nplane;
 306                 /** Copies the information from another voronoicell class into
 307                  * this class, extending memory allocation if necessary.
 308                  * \param[in] c the class to copy. */
 309                 inline void operator=(voronoicell &c) {
 310                         voronoicell_base* vb((voronoicell_base*) &c);
 311                         check_memory_for_copy(*this,vb);copy(vb);
 312                 }
 313                 /** Cuts a Voronoi cell using by the plane corresponding to the
 314                  * perpendicular bisector of a particle.
 315                  * \param[in] (x,y,z) the position of the particle.
 316                  * \param[in] rsq the modulus squared of the vector.
 317                  * \param[in] p_id the plane ID, ignored for this case where no
 318                  *                 neighbor tracking is enabled.
 319                  * \return False if the plane cut deleted the cell entirely,
 320                  *         true otherwise. */
 321                 inline bool nplane(double x,double y,double z,double rsq,int p_id) {
 322                         return nplane(*this,x,y,z,rsq,0);
 323                 }
 324                 /** Cuts a Voronoi cell using by the plane corresponding to the
 325                  * perpendicular bisector of a particle.
 326                  * \param[in] (x,y,z) the position of the particle.
 327                  * \param[in] p_id the plane ID, ignored for this case where no
 328                  *                 neighbor tracking is enabled.
 329                  * \return False if the plane cut deleted the cell entirely,
 330                  *         true otherwise. */
 331                 inline bool nplane(double x,double y,double z,int p_id) {
 332                         double rsq=x*x+y*y+z*z;
 333                         return nplane(*this,x,y,z,rsq,0);
 334                 }
 335                 /** Cuts a Voronoi cell using by the plane corresponding to the
 336                  * perpendicular bisector of a particle.
 337                  * \param[in] (x,y,z) the position of the particle.
 338                  * \param[in] rsq the modulus squared of the vector.
 339                  * \return False if the plane cut deleted the cell entirely,
 340                  *         true otherwise. */
 341                 inline bool plane(double x,double y,double z,double rsq) {
 342                         return nplane(*this,x,y,z,rsq,0);
 343                 }
 344                 /** Cuts a Voronoi cell using by the plane corresponding to the
 345                  * perpendicular bisector of a particle.
 346                  * \param[in] (x,y,z) the position of the particle.
 347                  * \return False if the plane cut deleted the cell entirely,
 348                  *         true otherwise. */
 349                 inline bool plane(double x,double y,double z) {
 350                         double rsq=x*x+y*y+z*z;
 351                         return nplane(*this,x,y,z,rsq,0);
 352                 }
 353                 /** Initializes the Voronoi cell to be rectangular box with the
 354                  * given dimensions.
 355                  * \param[in] (xmin,xmax) the minimum and maximum x coordinates.
 356                  * \param[in] (ymin,ymax) the minimum and maximum y coordinates.
 357                  * \param[in] (zmin,zmax) the minimum and maximum z coordinates. */
 358                 inline void init(double xmin,double xmax,double ymin,double ymax,double zmin,double zmax) {
 359                         init_base(xmin,xmax,ymin,ymax,zmin,zmax);
 360                 }
 361                 /** Initializes the cell to be an octahedron with vertices at
 362                  * (l,0,0), (-l,0,0), (0,l,0), (0,-l,0), (0,0,l), and (0,0,-l).
 363                  * \param[in] l a parameter setting the size of the octahedron.
 364                  */
 365                 inline void init_octahedron(double l) {
 366                         init_octahedron_base(l);
 367                 }
 368                 /** Initializes the cell to be a tetrahedron.
 369                  * \param[in] (x0,y0,z0) the coordinates of the first vertex.
 370                  * \param[in] (x1,y1,z1) the coordinates of the second vertex.
 371                  * \param[in] (x2,y2,z2) the coordinates of the third vertex.
 372                  * \param[in] (x3,y3,z3) the coordinates of the fourth vertex.
 373                  */
 374                 inline 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) {
 375                         init_tetrahedron_base(x0,y0,z0,x1,y1,z1,x2,y2,z2,x3,y3,z3);
 376                 }
 377         private:
 378                 inline void n_allocate(int i,int m) {};
 379                 inline void n_add_memory_vertices(int i) {};
 380                 inline void n_add_memory_vorder(int i) {};
 381                 inline void n_set_pointer(int p,int n) {};
 382                 inline void n_copy(int a,int b,int c,int d) {};
 383                 inline void n_set(int a,int b,int c) {};
 384                 inline void n_set_aux1(int k) {};
 385                 inline void n_copy_aux1(int a,int b) {};
 386                 inline void n_copy_aux1_shift(int a,int b) {};
 387                 inline void n_set_aux2_copy(int a,int b) {};
 388                 inline void n_copy_pointer(int a,int b) {};
 389                 inline void n_set_to_aux1(int j) {};
 390                 inline void n_set_to_aux2(int j) {};
 391                 inline void n_allocate_aux1(int i) {};
 392                 inline void n_switch_to_aux1(int i) {};
 393                 inline void n_copy_to_aux1(int i,int m) {};
 394                 inline void n_set_to_aux1_offset(int k,int m) {};
 395                 inline void n_neighbors(vector<int> &v) {v.clear();};
 396                 friend class voronoicell_base;
 397 };
 398
 399 /** \brief Extension of the voronoicell_base class to represent a Voronoi cell
 400  * with neighbor information.
 401  *
 402  * This class is an extension of the voronoicell_base class, in cases when the
 403  * IDs of neighboring particles associated with each face of the Voronoi cell.
 404  * It contains additional data structures mne and ne for storing this
 405  * information. */
 406 class voronoicell_neighbor : public voronoicell_base {
 407         public:
 408                 using voronoicell_base::nplane;
 409                 /** This two dimensional array holds the neighbor information
 410                  * associated with each vertex. mne[p] is a one dimensional
 411                  * array which holds all of the neighbor information for
 412                  * vertices of order p. */
 413                 int **mne;
 414                 /** This is a two dimensional array that holds the neighbor
 415                  * information associated with each vertex. ne[i] points to a
 416                  * one-dimensional array in mne[nu[i]]. ne[i][j] holds the
 417                  * neighbor information associated with the jth edge of vertex
 418                  * i. It is set to the ID number of the plane that made the
 419                  * face that is clockwise from the jth edge. */
 420                 int **ne;
 421                 voronoicell_neighbor();
 422                 ~voronoicell_neighbor();
 423                 void operator=(voronoicell &c);
 424                 void operator=(voronoicell_neighbor &c);
 425                 /** Cuts the Voronoi cell by a particle whose center is at a
 426                  * separation of (x,y,z) from the cell center. The value of rsq
 427                  * should be initially set to \f$x^2+y^2+z^2\f$.
 428                  * \param[in] (x,y,z) the normal vector to the plane.
 429                  * \param[in] rsq the distance along this vector of the plane.
 430                  * \param[in] p_id the plane ID (for neighbor tracking only).
 431                  * \return False if the plane cut deleted the cell entirely,
 432                  * true otherwise. */
 433                 inline bool nplane(double x,double y,double z,double rsq,int p_id) {
 434                         return nplane(*this,x,y,z,rsq,p_id);
 435                 }
 436                 /** This routine calculates the modulus squared of the vector
 437                  * before passing it to the main nplane() routine with full
 438                  * arguments.
 439                  * \param[in] (x,y,z) the vector to cut the cell by.
 440                  * \param[in] p_id the plane ID (for neighbor tracking only).
 441                  * \return False if the plane cut deleted the cell entirely,
 442                  *         true otherwise. */
 443                 inline bool nplane(double x,double y,double z,int p_id) {
 444                         double rsq=x*x+y*y+z*z;
 445                         return nplane(*this,x,y,z,rsq,p_id);
 446                 }
 447                 /** This version of the plane routine just makes up the plane
 448                  * ID to be zero. It will only be referenced if neighbor
 449                  * tracking is enabled.
 450                  * \param[in] (x,y,z) the vector to cut the cell by.
 451                  * \param[in] rsq the modulus squared of the vector.
 452                  * \return False if the plane cut deleted the cell entirely,
 453                  *         true otherwise. */
 454                 inline bool plane(double x,double y,double z,double rsq) {
 455                         return nplane(*this,x,y,z,rsq,0);
 456                 }
 457                 /** Cuts a Voronoi cell using the influence of a particle at
 458                  * (x,y,z), first calculating the modulus squared of this
 459                  * vector before passing it to the main nplane() routine. Zero
 460                  * is supplied as the plane ID, which will be ignored unless
 461                  * neighbor tracking is enabled.
 462                  * \param[in] (x,y,z) the vector to cut the cell by.
 463                  * \return False if the plane cut deleted the cell entirely,
 464                  *         true otherwise. */
 465                 inline bool plane(double x,double y,double z) {
 466                         double rsq=x*x+y*y+z*z;
 467                         return nplane(*this,x,y,z,rsq,0);
 468                 }
 469                 void init(double xmin,double xmax,double ymin,double ymax,double zmin,double zmax);
 470                 void init_octahedron(double l);
 471                 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);
 472                 void check_facets();
 473                 virtual void neighbors(vector<int> &v);
 474                 virtual void print_edges_neighbors(int i);
 475                 virtual void output_neighbors(FILE *fp=stdout) {
 476                         vector<int> v;neighbors(v);
 477                         voro_print_vector(v,fp);
 478                 }
 479         private:
 480                 int *paux1;
 481                 int *paux2;
 482                 inline void n_allocate(int i,int m) {mne[i]=new int[m*i];}
 483                 inline void n_add_memory_vertices(int i) {
 484                         int **pp=new int*[i];
 485                         for(int j=0;j<current_vertices;j++) pp[j]=ne[j];
 486                         delete [] ne;ne=pp;
 487                 }
 488                 inline void n_add_memory_vorder(int i) {
 489                         int **p2=new int*[i];
 490                         for(int j=0;j<current_vertex_order;j++) p2[j]=mne[j];
 491                         delete [] mne;mne=p2;
 492                 }
 493                 inline void n_set_pointer(int p,int n) {
 494                         ne[p]=mne[n]+n*mec[n];
 495                 }
 496                 inline void n_copy(int a,int b,int c,int d) {ne[a][b]=ne[c][d];}
 497                 inline void n_set(int a,int b,int c) {ne[a][b]=c;}
 498                 inline void n_set_aux1(int k) {paux1=mne[k]+k*mec[k];}
 499                 inline void n_copy_aux1(int a,int b) {paux1[b]=ne[a][b];}
 500                 inline void n_copy_aux1_shift(int a,int b) {paux1[b]=ne[a][b+1];}
 501                 inline void n_set_aux2_copy(int a,int b) {
 502                         paux2=mne[b]+b*mec[b];
 503                         for(int i=0;i<b;i++) ne[a][i]=paux2[i];
 504                 }
 505                 inline void n_copy_pointer(int a,int b) {ne[a]=ne[b];}
 506                 inline void n_set_to_aux1(int j) {ne[j]=paux1;}
 507                 inline void n_set_to_aux2(int j) {ne[j]=paux2;}
 508                 inline void n_allocate_aux1(int i) {paux1=new int[i*mem[i]];}
 509                 inline void n_switch_to_aux1(int i) {delete [] mne[i];mne[i]=paux1;}
 510                 inline void n_copy_to_aux1(int i,int m) {paux1[m]=mne[i][m];}
 511                 inline void n_set_to_aux1_offset(int k,int m) {ne[k]=paux1+m;}
 512                 friend class voronoicell_base;
 513 };
 514
 515 }
 516
 517 #endif