branches/exact/src/unitcell.cc

   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 unitcell.cc
   8  * \brief Function implementations for the unitcell class. */
   9
  10 #include <queue>
  11 using namespace std;
  12
  13 #include "unitcell.hh"
  14 #include "cell.hh"
  15
  16 namespace voro {
  17
  18 /** Initializes the unit cell class for a particular non-orthogonal periodic
  19  * geometry, corresponding to a parallelepiped with sides given by three
  20  * vectors. The class constructs the unit Voronoi cell corresponding to this
  21  * geometry.
  22  * \param[in] (bx_) The x coordinate of the first unit vector.
  23  * \param[in] (bxy_,by_) The x and y coordinates of the second unit vector.
  24  * \param[in] (bxz_,byz_,bz_) The x, y, and z coordinates of the third unit
  25  *                            vector. */
  26 unitcell::unitcell(double bx_,double bxy_,double by_,double bxz_,double byz_,double bz_)
  27         : bx(bx_), bxy(bxy_), by(by_), bxz(bxz_), byz(byz_), bz(bz_) {
  28         int i,j,l=1;
  29
  30         // Initialize the Voronoi cell to be a very large rectangular box
  31         const double ucx=max_unit_voro_shells*bx,ucy=max_unit_voro_shells*by,ucz=max_unit_voro_shells*bz;
  32         unit_voro.init(-ucx,ucx,-ucy,ucy,-ucz,ucz);
  33
  34         // Repeatedly cut the cell by shells of periodic image particles
  35         while(l<2*max_unit_voro_shells) {
  36
  37                 // Check to see if any of the planes from the current shell
  38                 // will cut the cell
  39                 if(unit_voro_intersect(l)) {
  40
  41                         // If they do, apply the plane cuts from the current
  42                         // shell
  43                         unit_voro_apply(l,0,0);
  44                         for(i=1;i<l;i++) {
  45                                 unit_voro_apply(l,i,0);
  46                                 unit_voro_apply(-l,i,0);
  47                         }
  48                         for(i=-l;i<=l;i++) unit_voro_apply(i,l,0);
  49                         for(i=1;i<l;i++) for(j=-l+1;j<=l;j++) {
  50                                 unit_voro_apply(l,j,i);
  51                                 unit_voro_apply(-j,l,i);
  52                                 unit_voro_apply(-l,-j,i);
  53                                 unit_voro_apply(j,-l,i);
  54                         }
  55                         for(i=-l;i<=l;i++) for(j=-l;j<=l;j++) unit_voro_apply(i,j,l);
  56                 } else {
  57
  58                         // Calculate a bound on the maximum y and z coordinates
  59                         // that could possibly cut the cell. This is based upon
  60                         // a geometric result that particles with z>l can't cut
  61                         // a cell lying within the paraboloid
  62                         // z<=(l*l-x*x-y*y)/(2*l). It is always a tighter bound
  63                         // than the one based on computing the maximum radius
  64                         // of a Voronoi cell vertex.
  65                         max_uv_y=max_uv_z=0;
  66                         double y,z,q,*pts=unit_voro.pts,*pp=pts;
  67                         while(pp<pts+3*unit_voro.p) {
  68                                 q=*(pp++);y=*(pp++);z=*(pp++);q=sqrt(q*q+y*y+z*z);
  69                                 if(y+q>max_uv_y) max_uv_y=y+q;
  70                                 if(z+q>max_uv_z) max_uv_z=z+q;
  71                         }
  72                         max_uv_z*=0.5;
  73                         max_uv_y*=0.5;
  74                         return;
  75                 }
  76                 l++;
  77         }
  78
  79         // If the routine makes it here, then the unit cell still hasn't been
  80         // completely bounded by the plane cuts. Give the memory error code,
  81         // because this is mainly a case of hitting a safe limit, than any
  82         // inherent problem.
  83         voro_fatal_error("Periodic cell computation failed",VOROPP_MEMORY_ERROR);
  84 }
  85
  86 /** Applies a pair of opposing plane cuts from a periodic image point
  87  * to the unit Voronoi cell.
  88  * \param[in] (i,j,k) the index of the periodic image to consider. */
  89 inline void unitcell::unit_voro_apply(int i,int j,int k) {
  90         double x=i*bx+j*bxy+k*bxz,y=j*by+k*byz,z=k*bz;
  91         unit_voro.plane(x,y,z);
  92         unit_voro.plane(-x,-y,-z);
  93 }
  94
  95 /** Calculates whether the unit Voronoi cell intersects a given periodic image
  96  * of the domain.
  97  * \param[in] (dx,dy,dz) the displacement of the periodic image.
  98  * \param[out] vol the proportion of the unit cell volume within this image,
  99  *                 only computed in the case that the two intersect.
 100  * \return True if they intersect, false otherwise. */
 101 bool unitcell::intersects_image(double dx,double dy,double dz,double &vol) {
 102         const double bxinv=1/bx,byinv=1/by,bzinv=1/bz,ivol=bxinv*byinv*bzinv;
 103         voronoicell c;
 104         c=unit_voro;
 105         dx*=2;dy*=2;dz*=2;
 106         if(!c.plane(0,0,bzinv,dz+1)) return false;
 107         if(!c.plane(0,0,-bzinv,-dz+1)) return false;
 108         if(!c.plane(0,byinv,-byz*byinv*bzinv,dy+1)) return false;
 109         if(!c.plane(0,-byinv,byz*byinv*bzinv,-dy+1)) return false;
 110         if(!c.plane(bxinv,-bxy*bxinv*byinv,(bxy*byz-by*bxz)*ivol,dx+1)) return false;
 111         if(!c.plane(-bxinv,bxy*bxinv*byinv,(-bxy*byz+by*bxz)*ivol,-dx+1)) return false;
 112         vol=c.volume()*ivol;
 113         return true;
 114 }
 115
 116 /** Computes a list of periodic domain images that intersect the unit Voronoi cell.
 117  * \param[out] vi a vector containing triplets (i,j,k) corresponding to domain
 118  *                images that intersect the unit Voronoi cell, when it is
 119  *                centered in the middle of the primary domain.
 120  * \param[out] vd a vector containing the fraction of the Voronoi cell volume
 121  *                within each corresponding image listed in vi. */
 122 void unitcell::images(vector<int> &vi,vector<double> &vd) {
 123         const int ms2=max_unit_voro_shells*2+1,mss=ms2*ms2*ms2;
 124         bool *a=new bool[mss],*ac=a+max_unit_voro_shells*(1+ms2*(1+ms2)),*ap=a;
 125         int i,j,k;
 126         double vol;
 127
 128         // Initialize mask
 129         while(ap<ac) *(ap++)=true;
 130         *(ap++)=false;
 131         while(ap<a+mss) *(ap++)=true;
 132
 133         // Set up the queue and add (0,0,0) image to it
 134         queue<int> q;
 135         q.push(0);q.push(0);q.push(0);
 136
 137         while(!q.empty()) {
 138
 139                 // Read the next entry on the queue
 140                 i=q.front();q.pop();
 141                 j=q.front();q.pop();
 142                 k=q.front();q.pop();
 143
 144                 // Check intersection of this image
 145                 if(intersects_image(i,j,k,vol)) {
 146
 147                         // Add this entry to the output vectors
 148                         vi.push_back(i);
 149                         vi.push_back(j);
 150                         vi.push_back(k);
 151                         vd.push_back(vol);
 152
 153                         // Add neighbors to the queue if they have not been
 154                         // tested
 155                         ap=ac+i+ms2*(j+ms2*k);
 156                         if(k>-max_unit_voro_shells&&*(ap-ms2*ms2)) {q.push(i);q.push(j);q.push(k-1);*(ap-ms2*ms2)=false;}
 157                         if(j>-max_unit_voro_shells&&*(ap-ms2)) {q.push(i);q.push(j-1);q.push(k);*(ap-ms2)=false;}
 158                         if(i>-max_unit_voro_shells&&*(ap-1)) {q.push(i-1);q.push(j);q.push(k);*(ap-1)=false;}
 159                         if(i<max_unit_voro_shells&&*(ap+1)) {q.push(i+1);q.push(j);q.push(k);*(ap+1)=false;}
 160                         if(j<max_unit_voro_shells&&*(ap+ms2)) {q.push(i);q.push(j+1);q.push(k);*(ap+ms2)=false;}
 161                         if(k<max_unit_voro_shells&&*(ap+ms2*ms2)) {q.push(i);q.push(j);q.push(k+1);*(ap+ms2*ms2)=false;}
 162                 }
 163         }
 164
 165         // Remove mask memory
 166         delete [] a;
 167 }
 168
 169 /** Tests to see if a shell of periodic images could possibly cut the periodic
 170  * unit cell.
 171  * \param[in] l the index of the shell to consider.
 172  * \return True if a point in the shell cuts the cell, false otherwise. */
 173 bool unitcell::unit_voro_intersect(int l) {
 174         int i,j;
 175         if(unit_voro_test(l,0,0)) return true;
 176         for(i=1;i<l;i++) {
 177                 if(unit_voro_test(l,i,0)) return true;
 178                 if(unit_voro_test(-l,i,0)) return true;
 179         }
 180         for(i=-l;i<=l;i++) if(unit_voro_test(i,l,0)) return true;
 181         for(i=1;i<l;i++) for(j=-l+1;j<=l;j++) {
 182                 if(unit_voro_test(l,j,i)) return true;
 183                 if(unit_voro_test(-j,l,i)) return true;
 184                 if(unit_voro_test(-l,-j,i)) return true;
 185                 if(unit_voro_test(j,-l,i)) return true;
 186         }
 187         for(i=-l;i<=l;i++) for(j=-l;j<=l;j++) if(unit_voro_test(i,j,l)) return true;
 188         return false;
 189 }
 190
 191 /** Tests to see if a plane cut from a particular periodic image will cut th
 192  * unit Voronoi cell.
 193  * \param[in] (i,j,k) the index of the periodic image to consider.
 194  * \return True if the image cuts the cell, false otherwise. */
 195 inline bool unitcell::unit_voro_test(int i,int j,int k) {
 196         double x=i*bx+j*bxy+k*bxz,y=j*by+k*byz,z=k*bz;
 197         double rsq=x*x+y*y+z*z;
 198         return unit_voro.plane_intersects(x,y,z,rsq);
 199 }
 200
 201 /** Draws the periodic domain in gnuplot format.
 202  * \param[in] fp the file handle to write to. */
 203 void unitcell::draw_domain_gnuplot(FILE *fp) {
 204         fprintf(fp,"0 0 0\n%g 0 0\n%g %g 0\n%g %g 0\n",bx,bx+bxy,by,bxy,by);
 205         fprintf(fp,"%g %g %g\n%g %g %g\n%g %g %g\n%g %g %g\n",bxy+bxz,by+byz,bz,bx+bxy+bxz,by+byz,bz,bx+bxz,byz,bz,bxz,byz,bz);
 206         fprintf(fp,"0 0 0\n%g %g 0\n\n%g %g %g\n%g %g %g\n\n",bxy,by,bxz,byz,bz,bxy+bxz,by+byz,bz);
 207         fprintf(fp,"%g 0 0\n%g %g %g\n\n%g %g 0\n%g %g %g\n\n",bx,bx+bxz,byz,bz,bx+bxy,by,bx+bxy+bxz,by+byz,bz);
 208 }
 209
 210 /** Draws the periodic domain in POV-Ray format.
 211  * \param[in] fp the file handle to write to. */
 212 void unitcell::draw_domain_pov(FILE *fp) {
 213         fprintf(fp,"cylinder{0,0,0>,<%g,0,0>,rr}\n"
 214                    "cylinder{<%g,%g,0>,<%g,%g,0>,rr}\n",bx,bxy,by,bx+bxy,by);
 215         fprintf(fp,"cylinder{<%g,%g,%g>,<%g,%g,%g>,rr}\n"
 216                    "cylinder{<%g,%g,%g>,<%g,%g,%g>,rr}\n",bxz,byz,bz,bx+bxz,byz,bz,bxy+bxz,by+byz,bz,bx+bxy+bxz,by+byz,bz);
 217         fprintf(fp,"cylinder{<0,0,0>,<%g,%g,0>,rr}\n"
 218                    "cylinder{<%g,0,0>,<%g,%g,0>,rr}\n",bxy,by,bx,bx+bxy,by);
 219         fprintf(fp,"cylinder{<%g,%g,%g>,<%g,%g,%g>,rr}\n"
 220                    "cylinder{<%g,%g,%g>,<%g,%g,%g>,rr}\n",bxz,byz,bz,bxy+bxz,by+byz,bz,bx+bxz,byz,bz,bx+bxy+bxz,by+byz,bz);
 221         fprintf(fp,"cylinder{<0,0,0>,<%g,%g,%g>,rr}\n"
 222                    "cylinder{<%g,0,0>,<%g,%g,%g>,rr}\n",bxz,byz,bz,bx,bx+bxz,byz,bz);
 223         fprintf(fp,"cylinder{<%g,%g,0>,<%g,%g,%g>,rr}\n"
 224                    "cylinder{<%g,%g,0>,<%g,%g,%g>,rr}\n",bxy,by,bxy+bxz,by+byz,bz,bx+bxy,by,bx+bxy+bxz,by+byz,bz);
 225         fprintf(fp,"sphere{<0,0,0>,rr}\nsphere{<%g,0,0>,rr}\n"
 226                    "sphere{<%g,%g,0>,rr}\nsphere{<%g,%g,0>,rr}\n",bx,bxy,by,bx+bxy,by);
 227         fprintf(fp,"sphere{<%g,%g,%g>,rr}\nsphere{<%g,%g,%g>,rr}\n"
 228                    "sphere{<%g,%g,%g>,rr}\nsphere{<%g,%g,%g>,rr}\n",bxz,byz,bz,bx+bxz,byz,bz,bxy+bxz,by+byz,bz,bx+bxy+bxz,by+byz,bz);
 229 }
 230
 231 }