Voro++
unitcell.cc
Go to the documentation of this file.
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 <cmath>
11 #include <queue>
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.
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(std::vector<int> &vi,std::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
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  std::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
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. */
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. */
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 }
const double bz
Definition: unitcell.hh:41
const double bx
Definition: unitcell.hh:26
bool plane_intersects(double x, double y, double z, double rsq)
Definition: cell.cc:1920
#define VOROPP_MEMORY_ERROR
Definition: config.hh:113
bool plane(double x, double y, double z, double rsq)
Definition: cell.hh:338
const double byz
Definition: unitcell.hh:38
voronoicell unit_voro
Definition: unitcell.hh:44
Header file for the voronoicell and related classes.
void images(std::vector< int > &vi, std::vector< double > &vd)
Definition: unitcell.cc:122
unitcell(double bx_, double bxy_, double by_, double bxz_, double byz_, double bz_)
Definition: unitcell.cc:26
Header file for the unitcell class.
void draw_domain_pov(const char *filename)
Definition: unitcell.hh:56
double max_uv_y
Definition: unitcell.hh:67
const double by
Definition: unitcell.hh:32
bool intersects_image(double dx, double dy, double dz, double &vol)
Definition: unitcell.cc:101
double max_uv_z
Definition: unitcell.hh:70
const double bxy
Definition: unitcell.hh:29
Extension of the voronoicell_base class to represent a Voronoi cell without neighbor information...
Definition: cell.hh:300
const double bxz
Definition: unitcell.hh:35
void draw_domain_gnuplot(const char *filename)
Definition: unitcell.hh:48
void init(double xmin, double xmax, double ymin, double ymax, double zmin, double zmax)
Definition: cell.hh:355