container.cc

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// Voro++, a 3D cell-based Voronoi library
//
// Author   : Chris H. Rycroft (LBL / UC Berkeley)
// Email    : chr@alum.mit.edu
// Date     : July 1st 2008

/** \file container.cc
 * \brief Function implementations for the container_base template and related
 * classes. */

#include "cell.hh"
#include "container.hh"

/** Container constructor. The first six arguments set the corners of the box to
 * be (xa,ya,za) and (xb,yb,zb). The box is then divided into an nx by ny by nz
 * grid of blocks, set by the following three arguments. The next three
 * arguments are booleans, which set the periodicity in each direction. The
 * final argument sets the amount of memory allocated to each block. */
template<class r_option>
container_base<r_option>::container_base(fpoint xa,fpoint xb,fpoint ya,fpoint yb,fpoint za,fpoint zb,
                int xn,int yn,int zn,bool xper,bool yper,bool zper,int memi)
        : ax(xa),bx(xb),ay(ya),by(yb),az(za),bz(zb),
        xsp(xn/(xb-xa)),ysp(yn/(yb-ya)),zsp(zn/(zb-za)),
        nx(xn),ny(yn),nz(zn),nxy(xn*yn),nxyz(xn*yn*zn),
        hx(xper?2*xn+1:xn),hy(yper?2*yn+1:yn),hz(zper?2*zn+1:zn),hxy(hx*hy),hxyz(hx*hy*hz),
        xperiodic(xper),yperiodic(yper),zperiodic(zper),
        mv(0),wall_number(0),current_wall_size(init_wall_size),
        radius(this),sz(radius.mem_size) {
        int l;
        co=new int[nxyz];
        for(l=0;l<nxyz;l++) co[l]=0;
        mem=new int[nxyz];
        for(l=0;l<nxyz;l++) mem[l]=memi;
        id=new int*[nxyz];
        for(l=0;l<nxyz;l++) id[l]=new int[memi];
        p=new fpoint*[nxyz];
        for(l=0;l<nxyz;l++) p[l]=new fpoint[sz*memi];
        mask=new unsigned int[hxyz];
        for(l=0;l<hxyz;l++) mask[l]=0;
        s_size=3*(hxy+hz*(hx+hy));if(s_size<18) s_size=18;
        sl=new int[s_size];
        walls=new wall*[current_wall_size];
        mrad=new fpoint[hgridsq*seq_length];
        initialize_radii();
}

/** This function is called during container construction. The routine scans
 * all of the worklists in the wl[] array. For a given worklist of blocks
 * labeled \f$w_1\f$ to \f$w_n\f$, it computes a sequence \f$r_0\f$ to
 * \f$r_n\f$ so that $r_i$ is the minimum distance to all the blocks
 * \f$w_{j}\f$ where \f$j>i\f$ and all blocks outside the worklist. The values
 * of \f$r_n\f$ is calculated first, as the minimum distance to any block in
 * the shell surrounding the worklist. The \f$r_i\f$ are then computed in
 * reverse order by considering the distance to \f$w_{i+1}\f$.
 */
template<class r_option>
void container_base<r_option>::initialize_radii() {
        const unsigned int b1=1<<21,b2=1<<22,b3=1<<24,b4=1<<25,b5=1<<27,b6=1<<28;
        const fpoint xstep=(bx-ax)/nx/fgrid;
        const fpoint ystep=(by-ay)/ny/fgrid;
        const fpoint zstep=(bz-az)/nz/fgrid;
        int i,j,k,lx,ly,lz,l=0,q;
        unsigned int *e=const_cast<unsigned int*> (wl);
        fpoint xlo,ylo,zlo,xhi,yhi,zhi,minr;fpoint *radp=mrad;
        unsigned int f;
        for(zlo=0,zhi=zstep,lz=0;lz<hgrid;zlo=zhi,zhi+=zstep,lz++) {
                for(ylo=0,yhi=ystep,ly=0;ly<hgrid;ylo=yhi,yhi+=ystep,ly++) {
                        for(xlo=0,xhi=xstep,lx=0;lx<hgrid;xlo=xhi,xhi+=xstep,l++,lx++) {
                                minr=large_number;
                                for(q=e[0]+1;q<seq_length;q++) {
                                        f=e[q];
                                        i=(f&127)-64;
                                        j=(f>>7&127)-64;
                                        k=(f>>14&127)-64;
                                        if((f&b2)==b2) {
                                                compute_minimum(minr,xlo,xhi,ylo,yhi,zlo,zhi,i-1,j,k);
                                                if((f&b1)==0) compute_minimum(minr,xlo,xhi,ylo,yhi,zlo,zhi,i+1,j,k);
                                        } else if((f&b1)==b1) compute_minimum(minr,xlo,xhi,ylo,yhi,zlo,zhi,i+1,j,k);
                                        if((f&b4)==b4) {
                                                compute_minimum(minr,xlo,xhi,ylo,yhi,zlo,zhi,i,j-1,k);
                                                if((f&b3)==0) compute_minimum(minr,xlo,xhi,ylo,yhi,zlo,zhi,i,j+1,k);
                                        } else if((f&b3)==b3) compute_minimum(minr,xlo,xhi,ylo,yhi,zlo,zhi,i,j+1,k);
                                        if((f&b6)==b6) {
                                                compute_minimum(minr,xlo,xhi,ylo,yhi,zlo,zhi,i,j,k-1);
                                                if((f&b5)==0) compute_minimum(minr,xlo,xhi,ylo,yhi,zlo,zhi,i,j,k+1);
                                        } else if((f&b5)==b5) compute_minimum(minr,xlo,xhi,ylo,yhi,zlo,zhi,i,j,k+1);
                                }
                                q--;
                                while(q>0) {
                                        radp[q]=minr;
                                        f=e[q];
                                        i=(f&127)-64;
                                        j=(f>>7&127)-64;
                                        k=(f>>14&127)-64;
                                        compute_minimum(minr,xlo,xhi,ylo,yhi,zlo,zhi,i,j,k);
                                        q--;
                                }
                                radp[0]=minr;
                                e+=seq_length;
                                radp+=seq_length;
                        }
                }
        }
}

/** Computes the minimum distance from a subregion to a given block. If this distance
 * is smaller than the value of minr, then it passes
 * \param[in] &minr a pointer to the current minimum distance. If distance
 * computed in this function is smaller, then this distance is set to the new
 * one.
 * \param[in] (&xlo,&ylo,&zlo) the lower coordinates of the subregion being
 * considered.
 * \param[in] (&xhi,&yhi,&zhi) the upper coordinates of the subregion being
 * considered.
 * \param[in] (ti,tj,tk) the coordinates of the block. */
template<class r_option>
inline void container_base<r_option>::compute_minimum(fpoint &minr,fpoint &xlo,fpoint &xhi,fpoint &ylo,fpoint &yhi,fpoint &zlo,fpoint &zhi,int ti,int tj,int tk) {
        const fpoint boxx=(bx-ax)/nx,boxy=(by-ay)/ny,boxz=(bz-az)/nz;
        fpoint radsq,temp;
        if(ti>0) {temp=boxx*ti-xhi;radsq=temp*temp;}
        else if(ti<0) {temp=xlo-boxx*(1+ti);radsq=temp*temp;}
        else radsq=0;
        
        if(tj>0) {temp=boxy*tj-yhi;radsq+=temp*temp;}
        else if(tj<0) {temp=ylo-boxy*(1+tj);radsq+=temp*temp;}

        if(tk>0) {temp=boxz*tk-zhi;radsq+=temp*temp;}
        else if(tk<0) {temp=zlo-boxz*(1+tk);radsq+=temp*temp;}

        if(radsq<minr) minr=radsq;
}

/** Container destructor - free memory. */
template<class r_option>
container_base<r_option>::~container_base() {
        int l;
        for(l=0;l<nxyz;l++) delete [] p[l];
        for(l=0;l<nxyz;l++) delete [] id[l];
        delete [] p;
        delete [] id;
        delete [] mem;
        delete [] co;
        delete [] mask;
        delete [] sl;
        delete [] walls;
        delete [] mrad;
}

/** Dumps all the particle positions and identifies to a file. */
template<class r_option>
void container_base<r_option>::draw_particles(ostream &os) {
        int c,l,i;
        for(l=0;l<nxyz;l++) {
                for(c=0;c<co[l];c++) {
                        os << id[l][c];
                        for(i=sz*c;i<sz*(c+1);i++) os << " " << p[l][i];
                        os << "\n";
                }
        }
}

/** An overloaded version of the draw_particles() routine, that just prints
 * to standard output. */
template<class r_option>
void container_base<r_option>::draw_particles() {
        draw_particles(cin);
}

/** An overloaded version of the draw_particles() routine, that outputs
 * the particle positions to a file.
 * \param[in] filename the file to write to. */
template<class r_option>
void container_base<r_option>::draw_particles(const char *filename) {
        ofstream os;
        os.open(filename,ofstream::out|ofstream::trunc);
        draw_particles(os);
        os.close();
}

/** Dumps all the particle positions in the POV-Ray format. */
template<class r_option>
void container_base<r_option>::draw_particles_pov(ostream &os) {
        int l,c;
        for(l=0;l<nxyz;l++) {
                for(c=0;c<co[l];c++) {
                        os << "// id " << id[l][c] << "\n";
                        os << "sphere{<" << p[l][sz*c] << "," << p[l][sz*c+1] << ","
                           << p[l][sz*c+2] << ">,";
                        radius.rad(os,l,c);
                        os << "}\n";
                }
        }
}

/** An overloaded version of the draw_particles_pov() routine, that just prints
 * to standard output. */
template<class r_option>
void container_base<r_option>::draw_particles_pov() {
        draw_particles_pov(cin);
}

/** An overloaded version of the draw_particles_pov() routine, that outputs
 * the particle positions to a file.
 * \param[in] filename the file to write to. */
template<class r_option>
void container_base<r_option>::draw_particles_pov(const char *filename) {
        ofstream os;
        os.open(filename,ofstream::out|ofstream::trunc);
        draw_particles_pov(os);
        os.close();
}

/** Put a particle into the correct region of the container. */
template<class r_option>
void container_base<r_option>::put(int n,fpoint x,fpoint y,fpoint z) {
        if(x>ax&&y>ay&&z>az) {
                int i,j,k;
                i=int((x-ax)*xsp);j=int((y-ay)*ysp);k=int((z-az)*zsp);
                if(i<nx&&j<ny&&k<nz) {
                        i+=nx*j+nxy*k;
                        if(co[i]==mem[i]) add_particle_memory(i);
                        p[i][sz*co[i]]=x;p[i][sz*co[i]+1]=y;p[i][sz*co[i]+2]=z;
                        radius.store_radius(i,co[i],0.5);
                        id[i][co[i]++]=n;
                }
        }
}

/** Put a particle into the correct region of the container.
 * \param[in] n The numerical ID of the inserted particle.
 * \param[in] (x,y,z) The position vector of the inserted particle.
 * \param[in] r The radius of the particle.*/
template<class r_option>
void container_base<r_option>::put(int n,fpoint x,fpoint y,fpoint z,fpoint r) {
        if(x>ax&&y>ay&&z>az) {
                int i,j,k;
                i=int((x-ax)*xsp);j=int((y-ay)*ysp);k=int((z-az)*zsp);
                if(i<nx&&j<ny&&k<nz) {
                        i+=nx*j+nxy*k;
                        if(co[i]==mem[i]) add_particle_memory(i);
                        p[i][sz*co[i]]=x;p[i][sz*co[i]+1]=y;p[i][sz*co[i]+2]=z;
                        radius.store_radius(i,co[i],r);
                        id[i][co[i]++]=n;
                }
        }
}

/** Increase memory for a particular region. */
template<class r_option>
void container_base<r_option>::add_particle_memory(int i) {
        int *idp;fpoint *pp;
        int l,nmem=2*mem[i];
#if VOROPP_VERBOSE >=3
        cerr << "Particle memory in region " << i << " scaled up to " << nmem << endl;
#endif
        if(nmem>max_particle_memory) throw fatal_error("Absolute maximum memory allocation exceeded");
        idp=new int[nmem];
        for(l=0;l<co[i];l++) idp[l]=id[i][l];
        pp=new fpoint[sz*nmem];
        for(l=0;l<sz*co[i];l++) pp[l]=p[i][l];
        mem[i]=nmem;
        delete [] id[i];id[i]=idp;
        delete [] p[i];p[i]=pp;
}

/** Add list memory. */
template<class r_option>
inline void container_base<r_option>::add_list_memory() {
        int i,j=0,*ps;
        ps=new int[s_size*2];
#if VOROPP_VERBOSE >=2
        cerr << "List memory scaled up to " << s_size*2 << endl;
#endif
        if(s_start<=s_end) {
                for(i=s_start;i<s_end;i++) ps[j++]=sl[i];
        } else {
                for(i=s_start;i<s_size;i++) ps[j++]=sl[i];
                for(i=0;i<s_end;i++) ps[j++]=sl[i];
        }
        s_size*=2;
        s_start=0;s_end=j;
        delete [] sl;sl=ps;
}

/** Import a list of particles from standard input. */
template<class r_option>
void container_base<r_option>::import(istream &is) {
        radius.import(is);
}

/** An overloaded version of the import routine, that reads the standard input.
 */
template<class r_option>
inline void container_base<r_option>::import() {
        import(cin);
}

/** An overloaded version of the import routine, that reads in particles from
 * a particular file.
 * \param[in] filename The name of the file to read from. */
template<class r_option>
inline void container_base<r_option>::import(const char *filename) {
        ifstream is;
        is.open(filename,ifstream::in);
        import(is);
        is.close();
}

/** Outputs the number of particles within each region. */
template<class r_option>
void container_base<r_option>::region_count() {
        int i,j,k,ijk=0;
        for(k=0;k<nz;k++) {
                for(j=0;j<ny;j++) {
                        for(i=0;i<nx;i++) cout << "Region (" << i << "," << j << "," << k << "): " << co[ijk++] << " particles" << endl;
                }
        }
}

/** Clears a container of particles. */
template<class r_option>
void container_base<r_option>::clear() {
        for(int ijk=0;ijk<nxyz;ijk++) co[ijk]=0;
        radius.clear_max();
}

/** Computes the Voronoi cells for all particles within a box with corners
 * (xmin,ymin,zmin) and (xmax,ymax,zmax), and saves the output in a format
 * that can be read by gnuplot. */
template<class r_option>
void container_base<r_option>::draw_cells_gnuplot(const char *filename,fpoint xmin,fpoint xmax,fpoint ymin,fpoint ymax,fpoint zmin,fpoint zmax) {
        fpoint x,y,z,px,py,pz;
        voropp_loop l1(this);
        int q,s;
        voronoicell c;
        ofstream os;
        os.open(filename,ofstream::out|ofstream::trunc);
        s=l1.init(xmin,xmax,ymin,ymax,zmin,zmax,px,py,pz);
        do {
                for(q=0;q<co[s];q++) {
                        x=p[s][sz*q]+px;y=p[s][sz*q+1]+py;z=p[s][sz*q+2]+pz;
                        if(x>xmin&&x<xmax&&y>ymin&&y<ymax&&z>zmin&&z<zmax) {
                                if (compute_cell(c,l1.ip,l1.jp,l1.kp,s,q,x,y,z)) c.draw_gnuplot(os,x,y,z);
                        }
                }
        } while((s=l1.inc(px,py,pz))!=-1);
        os.close();
}

/** If only a filename is supplied to draw_cells_gnuplot(), then assume that we are
 * calculating the entire simulation region. */
template<class r_option>
void container_base<r_option>::draw_cells_gnuplot(const char *filename) {
        draw_cells_gnuplot(filename,ax,bx,ay,by,az,bz);
}

/** Computes the Voronoi cells for all particles within a box with corners
 * (xmin,ymin,zmin) and (xmax,ymax,zmax), and saves the output in a format
 * that can be read by gnuplot.*/
template<class r_option>
void container_base<r_option>::draw_cells_pov(const char *filename,fpoint xmin,fpoint xmax,fpoint ymin,fpoint ymax,fpoint zmin,fpoint zmax) {
        fpoint x,y,z,px,py,pz;
        voropp_loop l1(this);
        int q,s;
        voronoicell c;
        ofstream os;
        os.open(filename,ofstream::out|ofstream::trunc);
        s=l1.init(xmin,xmax,ymin,ymax,zmin,zmax,px,py,pz);
        do {
                for(q=0;q<co[s];q++) {
                        os << "// cell " << id[s][q] << "\n";
                        x=p[s][sz*q]+px;y=p[s][sz*q+1]+py;z=p[s][sz*q+2]+pz;
                        if(x>xmin&&x<xmax&&y>ymin&&y<ymax&&z>zmin&&z<zmax) {
                                if (compute_cell(c,l1.ip,l1.jp,l1.kp,s,q,x,y,z)) c.draw_pov(os,x,y,z);
                        }
                }
        } while((s=l1.inc(px,py,pz))!=-1);
        os.close();
}

/** If only a filename is supplied to draw_cells_pov(), then assume that we are
 * calculating the entire simulation region.*/
template<class r_option>
void container_base<r_option>::draw_cells_pov(const char *filename) {
        draw_cells_pov(filename,ax,bx,ay,by,az,bz);
}

/** This function computes all the cells in the container, but does nothing
 * with the output. It is useful for measuring the pure computation time
 * of the Voronoi algorithm, without any extraneous calculations, such as
 * volume evaluation or cell output. */
template<class r_option>
void container_base<r_option>::compute_all_cells() {
        voronoicell c;
        int i,j,k,ijk=0,q;
        for(k=0;k<nz;k++) for(j=0;j<ny;j++) for(i=0;i<nx;i++,ijk++) {
                for(q=0;q<co[ijk];q++) compute_cell(c,i,j,k,ijk,q);
        }
}


/** Computes the Voronoi volumes for all the particles, and stores the
 * results according to the particle label in the fpoint array bb.*/
template<class r_option>
void container_base<r_option>::store_cell_volumes(fpoint *bb) {
        voronoicell c;
        int i,j,k,ijk=0,q;
        for(k=0;k<nz;k++) for(j=0;j<ny;j++) for(i=0;i<nx;i++,ijk++) {
                for(q=0;q<co[ijk];q++) {
                        if (compute_cell(c,i,j,k,ijk,q)) {
                                bb[id[ijk][q]]=c.volume();
                        } else {
                                bb[id[ijk][q]]=0;
                        }
                }
        }
}

/** Computes the local packing fraction at a point, by summing the volumes
 * of all particles within a test sphere, and dividing by the sum of their
 * Voronoi volumes that were previous computed using the store_cell_volumes()
 * function.
 * \param[in] *bb an array holding the Voronoi volumes of the particles.
 * \param[in] (cx,cy,cz) the center of the test sphere.
 * \param[in] r the radius of the test sphere. */
template<class r_option>
fpoint container_base<r_option>::packing_fraction(fpoint *bb,fpoint cx,fpoint cy,fpoint cz,fpoint r) {
        voropp_loop l1(this);
        fpoint px,py,pz,x,y,z,rsq=r*r,pvol=0,vvol=0;
        int q,s;
        s=l1.init(cx,cy,cz,r,px,py,pz);
        do {
                for(q=0;q<co[s];q++) {
                        x=p[s][sz*q]+px-cx;
                        y=p[s][sz*q+1]+py-cy;
                        z=p[s][sz*q+2]+pz-cz;
                        if (x*x+y*y+z*z<rsq) {
                                pvol+=radius.volume(s,q);
                                vvol+=bb[id[s][q]];
                        }
                }
        } while((s=l1.inc(px,py,pz))!=-1);
        return vvol>tolerance?pvol/vvol*4.1887902047863909846168578443726:0;
}

/** Computes the local packing fraction at a point, by summing the volumes
 * of all particles within test box, and dividing by the sum of their
 * Voronoi volumes that were previous computed using the store_cell_volumes()
 * function.
 * \param[in] *bb an array holding the Voronoi volumes of the particles.
 * \param[in] (xmin,ymin,zmin) the minimum coordinates of the box.
 * \param[in] (xmax,ymax,zmax) the maximum coordinates of the box. */
template<class r_option>
fpoint container_base<r_option>::packing_fraction(fpoint *bb,fpoint xmin,fpoint xmax,fpoint ymin,fpoint ymax,fpoint zmin,fpoint zmax) {
        voropp_loop l1(this);
        fpoint x,y,z,px,py,pz,pvol=0,vvol=0;
        int q,s;
        s=l1.init(xmin,xmax,ymin,ymax,zmin,zmax,px,py,pz);
        do {
                for(q=0;q<co[s];q++) {
                        x=p[s][sz*q]+px;
                        y=p[s][sz*q+1]+py;
                        z=p[s][sz*q+2]+pz;
                        if(x>xmin&&x<xmax&&y>ymin&&y<ymax&&z>zmin&&z<zmax) {
                                pvol+=radius.volume(s,q);
                                vvol+=bb[id[s][q]];
                        }
                }
        } while((s=l1.inc(px,py,pz))!=-1);
        return vvol>tolerance?pvol/vvol*4.1887902047863909846168578443726:0;
}

/** Computes the Voronoi volumes for all the particles, and stores the
 * results according to the particle label in the fpoint array bb.*/
template<class r_option>
fpoint container_base<r_option>::sum_cell_volumes() {
        voronoicell c;
        int i,j,k,ijk=0,q;fpoint vol=0;
        for(k=0;k<nz;k++) for(j=0;j<ny;j++) for(i=0;i<nx;i++,ijk++) {
                for(q=0;q<co[ijk];q++) if (compute_cell(c,i,j,k,ijk,q)) vol+=c.volume();
        }
        return vol;
}

/** Prints a list of all particle labels, positions, and the number of faces to
 * the standard output. */
template<class r_option>
inline void container_base<r_option>::count_all_faces(ostream &os) {
        voronoicell c;
        fpoint x,y,z;
        int i,j,k,ijk=0,q;
        for(k=0;k<nz;k++) for(j=0;j<ny;j++) for(i=0;i<nx;i++,ijk++) {
                for(q=0;q<co[ijk];q++) {
                        x=p[ijk][sz*q];y=p[ijk][sz*q+1];z=p[ijk][sz*q+2];
                        os << id[ijk][q] << " " << x << " " << y << " " << z;
                        radius.print(os,ijk,q);
                        if (compute_cell(c,i,j,k,ijk,q,x,y,z)) {
                                os << " " << c.number_of_faces() << "\n";
                        } else os << " 0\n";
                }
        }
}

/** Prints a list of all particle labels, positions, and the number of faces to
 * the standard output. */
template<class r_option>
void container_base<r_option>::count_all_faces() {
        count_all_faces(cout);
}

/** An overloaded version of count_all_faces(), which outputs the result to a
 * particular file.
 * \param[in] filename The name of the file to write to. */
template<class r_option>
void container_base<r_option>::count_all_faces(const char* filename) {
        ofstream os;
        os.open(filename,ofstream::out|ofstream::trunc);
        count_all_faces(os);
        os.close();     
}

/** Prints a list of all particle labels, positions, and Voronoi volumes to the
 * standard output. */
template<class r_option>
template<class n_option>
inline void container_base<r_option>::print_all(ostream &os,voronoicell_base<n_option> &c) {
        fpoint x,y,z;
        int i,j,k,ijk=0,q;
        for(k=0;k<nz;k++) for(j=0;j<ny;j++) for(i=0;i<nx;i++,ijk++) {
                for(q=0;q<co[ijk];q++) {
                        x=p[ijk][sz*q];y=p[ijk][sz*q+1];z=p[ijk][sz*q+2];
                        os << id[ijk][q] << " " << x << " " << y << " " << z;
                        radius.print(os,ijk,q);
                        if (compute_cell(c,i,j,k,ijk,q,x,y,z)) {
                                os << " " << c.volume();
                                c.neighbors(os);                
                                os << "\n";
                        } else os << " 0\n";
                }
        }
}

/** Prints a list of all particle labels, positions, and Voronoi volumes to the
 * standard output. */
template<class r_option>
void container_base<r_option>::print_all(ostream &os) {
        voronoicell c;
        print_all(os,c);
}

/** An overloaded version of print_all(), which just prints to standard output. */
template<class r_option>
void container_base<r_option>::print_all() {
        voronoicell c;
        print_all(cout,c);
}

/** An overloaded version of print_all(), which outputs the result to a particular
 * file.
 * \param[in] filename The name of the file to write to. */
template<class r_option>
inline void container_base<r_option>::print_all(const char* filename) {
        voronoicell c;
        ofstream os;
        os.open(filename,ofstream::out|ofstream::trunc);
        print_all(os,c);
        os.close();
}

/** Prints a list of all particle labels, positions, Voronoi volumes, and a list
 * of neighboring particles to an output stream.
 * \param[in] os The output stream to print to.*/
template<class r_option>
void container_base<r_option>::print_all_neighbor(ostream &os) {
        voronoicell_neighbor c;
        print_all(os,c);
}

/** An overloaded version of print_all_neighbor(), which just prints to
 * standard output. */
template<class r_option>
void container_base<r_option>::print_all_neighbor() {
        voronoicell_neighbor c;
        print_all(cout,c);
}

/** An overloaded version of print_all_neighbor(), which outputs the result to a
 * particular file
 * \param[in] filename The name of the file to write to. */
template<class r_option>
inline void container_base<r_option>::print_all_neighbor(const char* filename) {
        voronoicell_neighbor c;
        ofstream os;
        os.open(filename,ofstream::out|ofstream::trunc);
        print_all(os,c);
        os.close();
}

/** Initialize the Voronoi cell to be the entire container. For non-periodic
 * coordinates, this is set by the position of the walls. For periodic
 * coordinates, the space is equally divided in either direction from the
 * particle's initial position. That makes sense since those boundaries would
 * be made by the neighboring periodic images of this particle. */
template<class r_option>
template<class n_option>
inline bool container_base<r_option>::initialize_voronoicell(voronoicell_base<n_option> &c,fpoint x,fpoint y,fpoint z) {
        fpoint x1,x2,y1,y2,z1,z2;
        if(xperiodic) x1=-(x2=0.5*(bx-ax));else {x1=ax-x;x2=bx-x;}
        if(yperiodic) y1=-(y2=0.5*(by-ay));else {y1=ay-y;y2=by-y;}
        if(zperiodic) z1=-(z2=0.5*(bz-az));else {z1=az-z;z2=bz-z;}
        c.init(x1,x2,y1,y2,z1,z2);
        for(int j=0;j<wall_number;j++) {
                if (!(walls[j]->cut_cell(c,x,y,z))) return false;
        }
        return true;
}

/** This function tests to see if a given vector lies within the container
 * bounds and any walls.
 * \param[in] (x,y,z) The position vector to be tested.
 * \return True if the point is inside the container, false if the point is
 * outside. */
template<class r_option>
bool container_base<r_option>::point_inside(fpoint x,fpoint y,fpoint z) {
        if(x<ax||x>bx||y<ay||y>by||z<az||z>bz) return false;
        return point_inside_walls(x,y,z);
}

/** This function tests to see if a give vector lies within the walls that have
 * been added to the container, but does not specifically check whether the
 * vector lies within the container bounds.
 * \param[in] (x,y,z) The position vector to be tested.
 * \return True if the point is inside the container, false if the point is
 * outside. */
template<class r_option>
bool container_base<r_option>::point_inside_walls(fpoint x,fpoint y,fpoint z) {
        for(int j=0;j<wall_number;j++) if(!walls[j]->point_inside(x,y,z)) return false;
        return true;
}

/** This routine is a simpler alternative to compute_cell(), that constructs
 * the cell by testing over successively larger spherical shells of particles.
 * For a container that is homogeneously filled with particles, this routine
 * runs as fast as compute_cell(). However, it rapidly becomes inefficient
 * for cases when the particles are not homogeneously distributed, or where
 * parts of the container might not be filled. In that case, the spheres may
 * grow very large before being cut off, leading to poor efficiency.
 * \param[in] &c a reference to a voronoicell object.
 * \param[in] (i,j,k) the coordinates of the block that the test particle is
 * in.
 * \param[in] ijk the index of the block that the test particle is in, set to
 * i+nx*(j+ny*k).
 * \param[in] s the index of the particle within the test block.
 * \param[in] (x,y,z) The coordinates of the particle. */
template<class r_option>
template<class n_option>
bool container_base<r_option>::compute_cell_sphere(voronoicell_base<n_option> &c,int i,int j,int k,int ijk,int s,fpoint x,fpoint y,fpoint z) {

        // This length scale determines how large the spherical shells should
        // be, and it should be set to approximately the particle diameter
        const fpoint length_scale=1;
        fpoint x1,y1,z1,qx,qy,qz,lr=0,lrs=0,ur,urs,rs;
        int q,t;
        voropp_loop l(this);
        if (!initialize_voronoicell(c,x,y,z)) return false;

        // Now the cell is cut by testing neighboring particles in concentric
        // shells. Once the test shell becomes twice as large as the Voronoi
        // cell we can stop testing.
        radius.init(ijk,s);
        while(radius.cutoff(lrs)<c.maxradsq()) {
                ur=lr+0.5*length_scale;urs=ur*ur;
                t=l.init(x,y,z,ur,qx,qy,qz);
                do {
                        for(q=0;q<co[t];q++) {
                                x1=p[t][sz*q]+qx-x;y1=p[t][sz*q+1]+qy-y;z1=p[t][sz*q+2]+qz-z;
                                rs=x1*x1+y1*y1+z1*z1;
                                if(lrs-tolerance<rs&&rs<urs&&(q!=s||ijk!=t)) {
                                        if (!c.nplane(x1,y1,z1,radius.scale(rs,t,q),id[t][q])) return false;
                                }
                        }
                } while((t=l.inc(qx,qy,qz))!=-1);
                lr=ur;lrs=urs;
        }
        return true;
}

/** A overloaded version of compute_cell_sphere(), that sets up the x, y, and z
 * variables.
 * \param[in] &c a reference to a voronoicell object.
 * \param[in] (i,j,k) the coordinates of the block that the test particle is
 * in.
 * \param[in] ijk the index of the block that the test particle is in, set to
 * i+nx*(j+ny*k).
 * \param[in] s the index of the particle within the test block. */
template<class r_option>
template<class n_option>
inline bool container_base<r_option>::compute_cell_sphere(voronoicell_base<n_option> &c,int i,int j,int k,int ijk,int s) {
        fpoint x=p[ijk][sz*s],y=p[ijk][sz*s+1],z=p[ijk][sz*s+2];
        return compute_cell_sphere(c,i,j,k,ijk,s,x,y,z);
}

/** A overloaded version of compute_cell, that sets up the x, y, and z variables.
 * It can be run by the user, and it is also called multiple times by the
 * functions print_all(), store_cell_volumes(), and the output routines.
 * \param[in] &c a reference to a voronoicell object.
 * \param[in] (i,j,k) the coordinates of the block that the test particle is
 * in.
 * \param[in] ijk the index of the block that the test particle is in, set to
 * i+nx*(j+ny*k).
 * \param[in] s the index of the particle within the test block. */
template<class r_option>
template<class n_option>
inline bool container_base<r_option>::compute_cell(voronoicell_base<n_option> &c,int i,int j,int k,int ijk,int s) {
        fpoint x=p[ijk][sz*s],y=p[ijk][sz*s+1],z=p[ijk][sz*s+2];
        return  compute_cell(c,i,j,k,ijk,s,x,y,z);
}

/** This routine computes a Voronoi cell for a single particle in the
 * container. It can be called by the user, but is also forms the core part of
 * several of the main functions, such as store_cell_volumes(), print_all(),
 * and the drawing routines. The algorithm constructs the cell by testing over
 * the neighbors of the particle, working outwards until it reaches those
 * particles which could not possibly intersect the cell. For maximum
 * efficiency, this algorithm is divided into three parts. In the first
 * section, the algorithm tests over the blocks which are in the immediate
 * vicinity of the particle, by making use of one of the precomputed worklists.
 * The code then continues to test blocks on the worklist, but also begins to
 * construct a list of neighboring blocks outside the worklist which may need
 * to be test. In the third section, the routine starts testing these
 * neighboring blocks, evaluating whether or not a particle in them could
 * possibly intersect the cell. For blocks that intersect the cell, it tests
 * the particles in that block, and then adds the block neighbors to the list
 * of potential places to consider.
 * \param[in] &c a reference to a voronoicell object.
 * \param[in] (i,j,k) the coordinates of the block that the test particle is
 * in.
 * \param[in] ijk the index of the block that the test particle is in, set to
 * i+nx*(j+ny*k).
 * \param[in] s the index of the particle within the test block.
 * \param[in] (x,y,z) The coordinates of the particle.
 * \param[in] s the index of the particle within the test block. */
template<class r_option>
template<class n_option>
bool container_base<r_option>::compute_cell(voronoicell_base<n_option> &c,int i,int j,int k,int ijk,int s,fpoint x,fpoint y,fpoint z) {
        const fpoint boxx=(bx-ax)/nx,boxy=(by-ay)/ny,boxz=(bz-az)/nz;
        fpoint x1,y1,z1,qx=0,qy=0,qz=0;
        fpoint xlo,ylo,zlo,xhi,yhi,zhi,rs;
        int ci,cj,ck,di,dj,dk,dijk,ei,ej,ek,eijk,si,sj,sk,sijk;
        fpoint gxs,gys,gzs,*radp;
        int f,g,l;unsigned int q,*e;
        const unsigned int b1=1<<21,b2=1<<22,b3=1<<24,b4=1<<25,b5=1<<27,b6=1<<28;

        radius.init(ijk,s);

        // Initialize the Voronoi cell to fill the entire container
        if (!initialize_voronoicell(c,x,y,z)) return false;
        fpoint crs,mrs;

        int next_count=3,list_index=0,list_size=8;
        int count_list[]={7,11,15,19,26,35,45,59};

        // Test all particles in the particle's local region first
        for(l=0;l<s;l++) {
                x1=p[ijk][sz*l]-x;
                y1=p[ijk][sz*l+1]-y;
                z1=p[ijk][sz*l+2]-z;
                rs=radius.scale(x1*x1+y1*y1+z1*z1,ijk,l);
                if (!c.nplane(x1,y1,z1,rs,id[ijk][l])) return false;
        }
        l++;
        while(l<co[ijk]) {
                x1=p[ijk][sz*l]-x;
                y1=p[ijk][sz*l+1]-y;
                z1=p[ijk][sz*l+2]-z;
                rs=radius.scale(x1*x1+y1*y1+z1*z1,ijk,l);
                if (!c.nplane(x1,y1,z1,rs,id[ijk][l])) return false;
                l++;
        }

        // Now compute the maximum distance squared from the cell
        // center to a vertex. This is used to cut off the calculation
        // since we only need to test out to twice this range.
        mrs=c.maxradsq();

        // Now compute the fractional position of the particle within
        // its region and store it in (fx,fy,fz). We use this to
        // compute an index (si,sj,sk) of which subregion the particle
        // is within.
        unsigned int m1,m2;
        fpoint fx=x-ax-boxx*i,fy=y-ay-boxy*j,fz=z-az-boxz*k;
        si=int(fx*xsp*fgrid);sj=int(fy*ysp*fgrid);sk=int(fz*zsp*fgrid);

        // The indices (si,sj,sk) tell us which worklist to use, to test the
        // blocks in the optimal order. But we only store worklists for the
        // eighth of the region where si, sj, and sk are all less than half the
        // full grid. The rest of the cases are handled by symmetry. In this
        // section, we detect for these cases, by reflecting high values of si,
        // sj, and sk. For these cases, a mask is constructed in m1 and m2
        // which is used to flip the worklist information when it is loaded.
        if(si>=hgrid) {
                gxs=fx;
                m1=127+(3<<21);si=fgrid-1-si;m2=1+(1<<21);
        } else {m1=m2=0;gxs=boxx-fx;}
        if(sj>=hgrid) {
                gys=fy;
                m1|=(127<<7)+(3<<24);sj=fgrid-1-sj;m2|=(1<<7)+(1<<24);
        } else gys=boxy-fy;
        if(sk>=hgrid) {
                gzs=fz;
                m1|=(127<<14)+(3<<27);sk=fgrid-1-sk;m2|=(1<<14)+(1<<27);
        } else gzs=boxz-fz;
        gxs*=gxs;gys*=gys;gzs*=gzs;

        // It's possible that a problem with the int() function could lead to
        // spurious values with particles lying on the boundaries of the regions.
        // In this section we correct for that.
        if(si<0) si=0;if(sj<0) sj=0;if(sk<0) sk=0;

        // Now compute which worklist we are going to use, and set radp and e to
        // point at the right offsets
        sijk=si+hgrid*(sj+hgrid*sk);
        radp=mrad+sijk*seq_length;
        e=(const_cast<unsigned int*> (wl))+sijk*seq_length;
        
        // Read in how many items in the worklist can be tested without having to
        // worry about writing to the mask
        f=e[0];g=0;
        do {

                // At the intervals specified by count_list, we recompute the
                // maximum radius squared
                if(g==next_count) {
                        mrs=c.maxradsq();
                        if(list_index!=list_size) next_count=count_list[list_index++];
                }
                
                // If mrs is less than the minimum distance to any untested
                // block, then we are done.
                if(mrs<radius.cutoff(radp[g])) return true;
                g++;
                
                // Load in a block off the worklist, permute it with the
                // symmetry mask, and decode its position. These are all
                // integer bit operations so they should run very fast.
                q=e[g];q^=m1;q+=m2;
                di=q&127;di-=64;
                dj=(q>>7)&127;dj-=64;
                dk=(q>>14)&127;dk-=64;

                // Check that the worklist position is in range
                if(xperiodic) {if(di<-nx) continue;else if(di>nx) continue;}
                else {if(di<-i) continue;else if(di>=nx-i) continue;}
                if(yperiodic) {if(dj<-ny) continue;else if(dj>ny) continue;}
                else {if(dj<-j) continue;else if(dj>=ny-j) continue;}
                if(zperiodic) {if(dk<-nz) continue;else if(dk>nz) continue;}
                else {if(dk<-k) continue;else if(dk>=nz-k) continue;}
                
                // Call the compute_min_max_radius() function. This returns
                // true if the minimum distance to the block is bigger than the
                // current mrs, in which case we skip this block and move on.
                // Otherwise, it computes the maximum distance to the block and
                // returns it in crs.
                if(compute_min_max_radius(di,dj,dk,fx,fy,fz,gxs,gys,gzs,crs,mrs)) continue;
                
                // Now compute which region we are going to loop over, adding a
                // displacement for the periodic cases.
                di+=i;dj+=j;dk+=k;
                if(xperiodic) {if(di<0) {qx=ax-bx;di+=nx;} else if(di>=nx) {qx=bx-ax;di-=nx;} else qx=0;}
                if(yperiodic) {if(dj<0) {qy=ay-by;dj+=ny;} else if(dj>=ny) {qy=by-ay;dj-=ny;} else qy=0;}
                if(zperiodic) {if(dk<0) {qz=az-bz;dk+=nz;} else if(dk>=nz) {qz=bz-az;dk-=nz;} else qz=0;}
                dijk=di+nx*(dj+ny*dk);

                // If mrs is bigger than the maximum distance to the block,
                // then we have to test all particles in the block for
                // intersections. Otherwise, we do additional checks and skip
                // those particles which can't possibly intersect the block.
                if(mrs>radius.cutoff(crs)) {
                        for(l=0;l<co[dijk];l++) {
                                x1=p[dijk][sz*l]+qx-x;
                                y1=p[dijk][sz*l+1]+qy-y;
                                z1=p[dijk][sz*l+2]+qz-z;
                                rs=radius.scale(x1*x1+y1*y1+z1*z1,dijk,l);
                                if (!c.nplane(x1,y1,z1,rs,id[dijk][l])) return false;
                        }
                } else {
                        for(l=0;l<co[dijk];l++) {
                                x1=p[dijk][sz*l]+qx-x;
                                y1=p[dijk][sz*l+1]+qy-y;
                                z1=p[dijk][sz*l+2]+qz-z;
                                rs=radius.scale(x1*x1+y1*y1+z1*z1,dijk,l);
                                if(rs<mrs) {
                                        if (!c.nplane(x1,y1,z1,rs,id[dijk][l])) return false;
                                }
                        }
                }
        } while(g<f);

        // If we reach here, we were unable to compute the entire cell using
        // the first part of the worklist. This section of the algorithm
        // continues the worklist, but it now starts preparing the mask that we
        // need if we end up going block by block. We do the same as before,
        // but we put a mark down on the mask for every block that's tested.
        // The worklist also contains information about which neighbors of each
        // block are not also on the worklist, and we start storing those
        // points in a list in case we have to go block by block.
        ci=xperiodic?nx:i;
        cj=yperiodic?ny:j;
        ck=zperiodic?nz:k;

        // Update the mask counter, and if it wraps around then reset the
        // whole mask; that will only happen once every 2^32 tries
        mv++;
        if(mv==0) {
                for(l=0;l<hxyz;l++) mask[l]=0;
                mv=1;
        }

        // Reset the block by block counters
        s_start=s_end=0;
        
        while(g<seq_length-1) {

                // At the intervals specified by count_list, we recompute the
                // maximum radius squared
                if(g==next_count) {
                        mrs=c.maxradsq();
                        if(list_index!=list_size) next_count=count_list[list_index++];
                }               
                
                // If mrs is less than the minimum distance to any untested
                // block, then we are done.
                if(mrs<radius.cutoff(radp[g])) return true;
                g++;
                
                // Load in a block off the worklist, permute it with the
                // symmetry mask, and decode its position. These are all
                // integer bit operations so they should run very fast.
                q=e[g];q^=m1;q+=m2;
                di=q&127;di-=64;
                dj=(q>>7)&127;dj-=64;
                dk=(q>>14)&127;dk-=64;
                
                // Compute the position in the mask of the current block. If
                // this lies outside the mask, then skip it. Otherwise, mark
                // it.
                ei=ci+di;
                ej=cj+dj;
                ek=ck+dk;
                if(ei<0) continue;else if(ei>=hx) continue;
                if(ej<0) continue;else if(ej>=hy) continue;
                if(ek<0) continue;else if(ek>=hz) continue;
                eijk=ei+hx*(ej+hy*ek);
                mask[eijk]=mv;
                
                // Call the compute_min_max_radius() function. This returns
                // true if the minimum distance to the block is bigger than the
                // current mrs, in which case we skip this block and move on.
                // Otherwise, it computes the maximum distance to the block and
                // returns it in crs.
                if(compute_min_max_radius(di,dj,dk,fx,fy,fz,gxs,gys,gzs,crs,mrs)) continue;
                
                // Now compute which region we are going to loop over, adding a
                // displacement for the periodic cases.
                di+=i;dj+=j;dk+=k;
                if(xperiodic) {if(di<0) {qx=ax-bx;di+=nx;} else if(di>=nx) {qx=bx-ax;di-=nx;} else qx=0;}
                if(yperiodic) {if(dj<0) {qy=ay-by;dj+=ny;} else if(dj>=ny) {qy=by-ay;dj-=ny;} else qy=0;}
                if(zperiodic) {if(dk<0) {qz=az-bz;dk+=nz;} else if(dk>=nz) {qz=bz-az;dk-=nz;} else qz=0;}
                dijk=di+nx*(dj+ny*dk);

                // If mrs is bigger than the maximum distance to the block,
                // then we have to test all particles in the block for
                // intersections. Otherwise, we do additional checks and skip
                // those particles which can't possibly intersect the block.
                if(mrs>radius.cutoff(crs)) {
                        for(l=0;l<co[dijk];l++) {
                                x1=p[dijk][sz*l]+qx-x;
                                y1=p[dijk][sz*l+1]+qy-y;
                                z1=p[dijk][sz*l+2]+qz-z;
                                rs=radius.scale(x1*x1+y1*y1+z1*z1,dijk,l);
                                if (!c.nplane(x1,y1,z1,rs,id[dijk][l])) return false;
                        }
                } else {
                        for(l=0;l<co[dijk];l++) {
                                x1=p[dijk][sz*l]+qx-x;
                                y1=p[dijk][sz*l+1]+qy-y;
                                z1=p[dijk][sz*l+2]+qz-z;
                                rs=radius.scale(x1*x1+y1*y1+z1*z1,dijk,l);
                                if(rs<mrs) {
                                        if(!c.nplane(x1,y1,z1,rs,id[dijk][l])) return false;
                                }
                        }
                }

                // If there might not be enough memory on the list for these
                // additions, then add more
                if(s_end+18>s_size) add_list_memory();

                // Test the parts of the worklist element which tell us what
                // neighbors of this block are not on the worklist. Store them
                // on the block list, and mark the mask.
                if((q&b2)==b2) {
                        if(ei>0) if(mask[eijk-1]!=mv) {mask[eijk-1]=mv;sl[s_end++]=ei-1;sl[s_end++]=ej;sl[s_end++]=ek;}
                        if((q&b1)==0) if(ei<hx-1) if(mask[eijk+1]!=mv) {mask[eijk+1]=mv;sl[s_end++]=ei+1;sl[s_end++]=ej;sl[s_end++]=ek;}
                } else if((q&b1)==b1) {if(ei<hx-1) if(mask[eijk+1]!=mv) {mask[eijk+1]=mv;sl[s_end++]=ei+1;sl[s_end++]=ej;sl[s_end++]=ek;}}
                if((q&b4)==b4) {if(ej>0) if(mask[eijk-hx]!=mv) {mask[eijk-hx]=mv;sl[s_end++]=ei;sl[s_end++]=ej-1;sl[s_end++]=ek;}
                        if((q&b3)==0) if(ej<hy-1) if(mask[eijk+hx]!=mv) {mask[eijk+hx]=mv;sl[s_end++]=ei;sl[s_end++]=ej+1;sl[s_end++]=ek;}
                } else if((q&b3)==b3) {if(ej<hy-1) if(mask[eijk+hx]!=mv) {mask[eijk+hx]=mv;sl[s_end++]=ei;sl[s_end++]=ej+1;sl[s_end++]=ek;}} 
                if((q&b6)==b6) {if(ek>0) if(mask[eijk-hxy]!=mv) {mask[eijk-hxy]=mv;sl[s_end++]=ei;sl[s_end++]=ej;sl[s_end++]=ek-1;}
                        if((q&b5)==0) if(ek<hz-1) if(mask[eijk+hxy]!=mv) {mask[eijk+hxy]=mv;sl[s_end++]=ei;sl[s_end++]=ej;sl[s_end++]=ek+1;}
                } else if((q&b5)==b5) if(ek<hz-1) if(mask[eijk+hxy]!=mv) {mask[eijk+hxy]=mv;sl[s_end++]=ei;sl[s_end++]=ej;sl[s_end++]=ek+1;}
        }

        // Do a check to see if we've reach the radius cutoff
        if(mrs<radius.cutoff(radp[g])) return true;

        // Update the mask counter, and if it has wrapped around, then
        // reset the mask
        fx+=boxx*ci;fy+=boxy*cj;fz+=boxz*ck;

        // We were unable to completely compute the cell based on the blocks in
        // the worklist, so now we have to go block by block, reading in items
        // off the list
        while(s_start!=s_end) {

                // If we reached the end of the list memory loop back to the start
                if(s_start==s_size) s_start=0;

                // Read in a block off the list, and compute the upper and lower
                // coordinates in each of the three dimensions
                di=sl[s_start++];dj=sl[s_start++];dk=sl[s_start++];
                xlo=di*boxx-fx;xhi=xlo+boxx;
                ylo=dj*boxy-fy;yhi=ylo+boxy;
                zlo=dk*boxz-fz;zhi=zlo+boxz;

                // Carry out plane tests to see if any particle in this block
                // could possibly intersect the cell 
                if(di>ci) {
                        if(dj>cj) {
                                if(dk>ck) {
                                        if(corner_test(c,xlo,ylo,zlo,xhi,yhi,zhi)) continue;
                                } else if(dk<ck) {
                                        if(corner_test(c,xlo,ylo,zhi,xhi,yhi,zlo)) continue;
                                } else {
                                        if(edge_z_test(c,xlo,ylo,zlo,xhi,yhi,zhi)) continue;
                                }
                        } else if(dj<cj) {
                                if(dk>ck) {
                                        if(corner_test(c,xlo,yhi,zlo,xhi,ylo,zhi)) continue;
                                } else if(dk<ck) {
                                        if(corner_test(c,xlo,yhi,zhi,xhi,ylo,zlo)) continue;
                                } else {
                                        if(edge_z_test(c,xlo,yhi,zlo,xhi,ylo,zhi)) continue;
                                }
                        } else {
                                if(dk>ck) {
                                        if(edge_y_test(c,xlo,ylo,zlo,xhi,yhi,zhi)) continue;
                                } else if(dk<ck) {
                                        if(edge_y_test(c,xlo,ylo,zhi,xhi,yhi,zlo)) continue;
                                } else {
                                        if(face_x_test(c,xlo,ylo,zlo,yhi,zhi)) continue;
                                }
                        }
                } else if(di<ci) {
                        if(dj>cj) {
                                if(dk>ck) {
                                        if(corner_test(c,xhi,ylo,zlo,xlo,yhi,zhi)) continue;
                                } else if(dk<ck) {
                                        if(corner_test(c,xhi,ylo,zhi,xlo,yhi,zlo)) continue;
                                } else {
                                        if(edge_z_test(c,xhi,ylo,zlo,xlo,yhi,zhi)) continue;
                                }
                        } else if(dj<cj) {
                                if(dk>ck) {
                                        if(corner_test(c,xhi,yhi,zlo,xlo,ylo,zhi)) continue;
                                } else if(dk<ck) {
                                        if(corner_test(c,xhi,yhi,zhi,xlo,ylo,zlo)) continue;
                                } else {
                                        if(edge_z_test(c,xhi,yhi,zlo,xlo,ylo,zhi)) continue;
                                }
                        } else {
                                if(dk>ck) {
                                        if(edge_y_test(c,xhi,ylo,zlo,xlo,yhi,zhi)) continue;
                                } else if(dk<ck) {
                                        if(edge_y_test(c,xhi,ylo,zhi,xlo,yhi,zlo)) continue;
                                } else {
                                        if(face_x_test(c,xhi,ylo,zlo,yhi,zhi)) continue;
                                }
                        }
                } else {
                        if(dj>cj) {
                                if(dk>ck) {
                                        if(edge_x_test(c,xlo,ylo,zlo,xhi,yhi,zhi)) continue;
                                } else if(dk<ck) {
                                        if(edge_x_test(c,xlo,ylo,zhi,xhi,yhi,zlo)) continue;
                                } else {
                                        if(face_y_test(c,xlo,ylo,zlo,xhi,zhi)) continue;
                                }
                        } else if(dj<cj) {
                                if(dk>ck) {
                                        if(edge_x_test(c,xlo,yhi,zlo,xhi,ylo,zhi)) continue;
                                } else if(dk<ck) {
                                        if(edge_x_test(c,xlo,yhi,zhi,xhi,ylo,zlo)) continue;
                                } else {
                                        if(face_y_test(c,xlo,yhi,zlo,xhi,zhi)) continue;
                                }
                        } else {
                                if(dk>ck) {
                                        if(face_z_test(c,xlo,ylo,zlo,xhi,yhi)) continue;
                                } else if(dk<ck) {
                                        if(face_z_test(c,xlo,ylo,zhi,xhi,yhi)) continue;
                                } else {
                                        cout << "Can't happen ... happened\n";
                                }
                        }
                }

                // Now compute the region that we are going to test over, and
                // set a displacement vector for the periodic cases.
                if(xperiodic) {ei=i+di-nx;if(ei<0) {qx=ax-bx;ei+=nx;} else if(ei>=nx) {qx=bx-ax;ei-=nx;} else qx=0;} else ei=di;
                if(yperiodic) {ej=j+dj-ny;if(ej<0) {qy=ay-by;ej+=ny;} else if(ej>=ny) {qy=by-ay;ej-=ny;} else qy=0;} else ej=dj;
                if(zperiodic) {ek=k+dk-nz;if(ek<0) {qz=az-bz;ek+=nz;} else if(ek>=nz) {qz=bz-az;ek-=nz;} else qz=0;} else ek=dk;
                eijk=ei+nx*(ej+ny*ek);

                // Loop over all the elements in the block to test for cuts.
                // It would be possible to exclude some of these cases by testing
                // against mrs, but I am not convinced that this will save time.
                for(l=0;l<co[eijk];l++) {
                        x1=p[eijk][sz*l]+qx-x;
                        y1=p[eijk][sz*l+1]+qy-y;
                        z1=p[eijk][sz*l+2]+qz-z;
                        rs=radius.scale(x1*x1+y1*y1+z1*z1,eijk,l);
                        if (!c.nplane(x1,y1,z1,rs,id[eijk][l])) return false;
                }

                // If there's not much memory on the block list then add more
                if((s_start<=s_end?s_size-s_end+s_start:s_end-s_start)<18) add_list_memory();

                // Test the neighbors of the current block, and add them to the
                // block list if they haven't already been tested.
                dijk=di+hx*(dj+hy*dk);
                if(di>0) if(mask[dijk-1]!=mv) {if(s_end==s_size) s_end=0;mask[dijk-1]=mv;sl[s_end++]=di-1;sl[s_end++]=dj;sl[s_end++]=dk;}
                if(dj>0) if(mask[dijk-hx]!=mv) {if(s_end==s_size) s_end=0;mask[dijk-hx]=mv;sl[s_end++]=di;sl[s_end++]=dj-1;sl[s_end++]=dk;}
                if(dk>0) if(mask[dijk-hxy]!=mv) {if(s_end==s_size) s_end=0;mask[dijk-hxy]=mv;sl[s_end++]=di;sl[s_end++]=dj;sl[s_end++]=dk-1;}
                if(di<hx-1) if(mask[dijk+1]!=mv) {if(s_end==s_size) s_end=0;mask[dijk+1]=mv;sl[s_end++]=di+1;sl[s_end++]=dj;sl[s_end++]=dk;}
                if(dj<hy-1) if(mask[dijk+hx]!=mv) {if(s_end==s_size) s_end=0;mask[dijk+hx]=mv;sl[s_end++]=di;sl[s_end++]=dj+1;sl[s_end++]=dk;}
                if(dk<hz-1) if(mask[dijk+hxy]!=mv) {if(s_end==s_size) s_end=0;mask[dijk+hxy]=mv;sl[s_end++]=di;sl[s_end++]=dj;sl[s_end++]=dk+1;}
        }

        return true;
}

/** This function checks to see whether a particular block can possibly have
 * any intersection with a Voronoi cell, for the case when the closest point
 * from the cell center to the block is at a corner.
 * \param[in] &c a reference to a Voronoi cell.
 * \param[in] (xl,yl,zl) the relative coordinates of the corner of the block closest to
 * the cell center.
 * \param[in] (xh,yh,zh) the relative coordinates of the corner of the block furthest
 * away from the cell center.
 * \return false if the block may intersect, true if does not. */
template<class r_option>
template<class n_option>
inline bool container_base<r_option>::corner_test(voronoicell_base<n_option> &c,fpoint xl,fpoint yl,fpoint zl,fpoint xh,fpoint yh,fpoint zh) {
        if(c.plane_intersects_guess(xh,yl,zl,radius.cutoff(xl*xh+yl*yl+zl*zl))) return false;
        if(c.plane_intersects(xh,yh,zl,radius.cutoff(xl*xh+yl*yh+zl*zl))) return false;
        if(c.plane_intersects(xl,yh,zl,radius.cutoff(xl*xl+yl*yh+zl*zl))) return false;
        if(c.plane_intersects(xl,yh,zh,radius.cutoff(xl*xl+yl*yh+zl*zh))) return false;
        if(c.plane_intersects(xl,yl,zh,radius.cutoff(xl*xl+yl*yl+zl*zh))) return false;
        if(c.plane_intersects(xh,yl,zh,radius.cutoff(xl*xh+yl*yl+zl*zh))) return false;
        return true;
}

/** This function checks to see whether a particular block can possibly have
 * any intersection with a Voronoi cell, for the case when the closest point
 * from the cell center to the block is on an edge which points along the x
 * direction.
 * \param[in] &c a reference to a Voronoi cell.
 * \param[in] (x0,x1) the minimum and maximum relative x coordinates of the block.
 * \param[in] (yl,zl) the relative y and z coordinates of the corner of the block closest to
 * the cell center.
 * \param[in] (yh,zh) the relative y and z coordinates of the corner of the block furthest
 * away from the cell center.
 * \return false if the block may intersect, true if does not. */
template<class r_option>
template<class n_option>
inline bool container_base<r_option>::edge_x_test(voronoicell_base<n_option> &c,fpoint x0,fpoint yl,fpoint zl,fpoint x1,fpoint yh,fpoint zh) {
        if(c.plane_intersects_guess(x0,yl,zh,radius.cutoff(yl*yl+zl*zh))) return false;
        if(c.plane_intersects(x1,yl,zh,radius.cutoff(yl*yl+zl*zh))) return false;
        if(c.plane_intersects(x1,yl,zl,radius.cutoff(yl*yl+zl*zl))) return false;
        if(c.plane_intersects(x0,yl,zl,radius.cutoff(yl*yl+zl*zl))) return false;
        if(c.plane_intersects(x0,yh,zl,radius.cutoff(yl*yh+zl*zl))) return false;
        if(c.plane_intersects(x1,yh,zl,radius.cutoff(yl*yh+zl*zl))) return false;
        return true;
}

/** This function checks to see whether a particular block can possibly have
 * any intersection with a Voronoi cell, for the case when the closest point
 * from the cell center to the block is on an edge which points along the y
 * direction.
 * \param[in] &c a reference to a Voronoi cell.
 * \param[in] (y0,y1) the minimum and maximum relative y coordinates of the block.
 * \param[in] (xl,zl) the relative x and z coordinates of the corner of the block closest to
 * the cell center.
 * \param[in] (xh,zh) the relative x and z coordinates of the corner of the block furthest
 * away from the cell center.
 * \return false if the block may intersect, true if does not. */
template<class r_option>
template<class n_option>
inline bool container_base<r_option>::edge_y_test(voronoicell_base<n_option> &c,fpoint xl,fpoint y0,fpoint zl,fpoint xh,fpoint y1,fpoint zh) {
        if(c.plane_intersects_guess(xl,y0,zh,radius.cutoff(xl*xl+zl*zh))) return false;
        if(c.plane_intersects(xl,y1,zh,radius.cutoff(xl*xl+zl*zh))) return false;
        if(c.plane_intersects(xl,y1,zl,radius.cutoff(xl*xl+zl*zl))) return false;
        if(c.plane_intersects(xl,y0,zl,radius.cutoff(xl*xl+zl*zl))) return false;
        if(c.plane_intersects(xh,y0,zl,radius.cutoff(xl*xh+zl*zl))) return false;
        if(c.plane_intersects(xh,y1,zl,radius.cutoff(xl*xh+zl*zl))) return false;
        return true;
}

/** This function checks to see whether a particular block can possibly have
 * any intersection with a Voronoi cell, for the case when the closest point
 * from the cell center to the block is on an edge which points along the z
 * direction.
 * \param[in] &c a reference to a Voronoi cell.
 * \param[in] (z0,z1) the minimum and maximum relative z coordinates of the block.
 * \param[in] (xl,yl) the relative x and y coordinates of the corner of the block closest to
 * the cell center.
 * \param[in] (xh,yh) the relative x and y coordinates of the corner of the block furthest
 * away from the cell center.
 * \return false if the block may intersect, true if does not. */
template<class r_option>
template<class n_option>
inline bool container_base<r_option>::edge_z_test(voronoicell_base<n_option> &c,fpoint xl,fpoint yl,fpoint z0,fpoint xh,fpoint yh,fpoint z1) {
        if(c.plane_intersects_guess(xl,yh,z0,radius.cutoff(xl*xl+yl*yh))) return false;
        if(c.plane_intersects(xl,yh,z1,radius.cutoff(xl*xl+yl*yh))) return false;
        if(c.plane_intersects(xl,yl,z1,radius.cutoff(xl*xl+yl*yl))) return false;
        if(c.plane_intersects(xl,yl,z0,radius.cutoff(xl*xl+yl*yl))) return false;
        if(c.plane_intersects(xh,yl,z0,radius.cutoff(xl*xh+yl*yl))) return false;
        if(c.plane_intersects(xh,yl,z1,radius.cutoff(xl*xh+yl*yl))) return false;
        return true;
}

/** This function checks to see whether a particular block can possibly have
 * any intersection with a Voronoi cell, for the case when the closest point
 * from the cell center to the block is on a face aligned with the x direction.
 * \param[in] &c a reference to a Voronoi cell.
 * \param[in] xl the minimum distance from the cell center to the face.
 * \param[in] (y0,y1) the minimum and maximum relative y coordinates of the block.
 * \param[in] (z0,z1) the minimum and maximum relative z coordinates of the block.
 * \return false if the block may intersect, true if does not. */
template<class r_option>
template<class n_option>
inline bool container_base<r_option>::face_x_test(voronoicell_base<n_option> &c,fpoint xl,fpoint y0,fpoint z0,fpoint y1,fpoint z1) {
        if(c.plane_intersects_guess(xl,y0,z0,radius.cutoff(xl*xl))) return false;
        if(c.plane_intersects(xl,y0,z1,radius.cutoff(xl*xl))) return false;
        if(c.plane_intersects(xl,y1,z1,radius.cutoff(xl*xl))) return false;
        if(c.plane_intersects(xl,y1,z0,radius.cutoff(xl*xl))) return false;
        return true;
}

/** This function checks to see whether a particular block can possibly have
 * any intersection with a Voronoi cell, for the case when the closest point
 * from the cell center to the block is on a face aligned with the y direction.
 * \param[in] &c a reference to a Voronoi cell.
 * \param[in] yl the minimum distance from the cell center to the face.
 * \param[in] (x0,x1) the minimum and maximum relative x coordinates of the block.
 * \param[in] (z0,z1) the minimum and maximum relative z coordinates of the block.
 * \return false if the block may intersect, true if does not. */
template<class r_option>
template<class n_option>
inline bool container_base<r_option>::face_y_test(voronoicell_base<n_option> &c,fpoint x0,fpoint yl,fpoint z0,fpoint x1,fpoint z1) {
        if(c.plane_intersects_guess(x0,yl,z0,radius.cutoff(yl*yl))) return false;
        if(c.plane_intersects(x0,yl,z1,radius.cutoff(yl*yl))) return false;
        if(c.plane_intersects(x1,yl,z1,radius.cutoff(yl*yl))) return false;
        if(c.plane_intersects(x1,yl,z0,radius.cutoff(yl*yl))) return false;
        return true;
}

/** This function checks to see whether a particular block can possibly have
 * any intersection with a Voronoi cell, for the case when the closest point
 * from the cell center to the block is on a face aligned with the z direction.
 * \param[in] &c a reference to a Voronoi cell.
 * \param[in] zl the minimum distance from the cell center to the face.
 * \param[in] (x0,x1) the minimum and maximum relative x coordinates of the block.
 * \param[in] (y0,y1) the minimum and maximum relative y coordinates of the block.
 * \return false if the block may intersect, true if does not. */
template<class r_option>
template<class n_option>
inline bool container_base<r_option>::face_z_test(voronoicell_base<n_option> &c,fpoint x0,fpoint y0,fpoint zl,fpoint x1,fpoint y1) {
        if(c.plane_intersects_guess(x0,y0,zl,radius.cutoff(zl*zl))) return false;
        if(c.plane_intersects(x0,y1,zl,radius.cutoff(zl*zl))) return false;
        if(c.plane_intersects(x1,y1,zl,radius.cutoff(zl*zl))) return false;
        if(c.plane_intersects(x1,y0,zl,radius.cutoff(zl*zl))) return false;
        return true;
}

/** Creates a voropp_loop object, by pulling the necessary constants about the container
 * geometry from a pointer to the current container class. */
template<class r_option>
voropp_loop::voropp_loop(container_base<r_option> *q) : sx(q->bx-q->ax), sy(q->by-q->ay), sz(q->bz-q->az),
        xsp(q->xsp),ysp(q->ysp),zsp(q->zsp),
        ax(q->ax),ay(q->ay),az(q->az),
        nx(q->nx),ny(q->ny),nz(q->nz),nxy(q->nxy),nxyz(q->nxyz),
        xperiodic(q->xperiodic),yperiodic(q->yperiodic),zperiodic(q->zperiodic) {}

/** Initializes a voropp_loop object, by finding all blocks which are within a distance
 * r of the vector (vx,vy,vz). It returns the first block which is to be
 * tested, and sets the periodic displacement vector (px,py,pz) accordingly. */
inline int voropp_loop::init(fpoint vx,fpoint vy,fpoint vz,fpoint r,fpoint &px,fpoint &py,fpoint &pz) {
        ai=step_int((vx-ax-r)*xsp);
        bi=step_int((vx-ax+r)*xsp);
        if(!xperiodic) {
                if(ai<0) {ai=0;if(bi<0) bi=0;}
                if(bi>=nx) {bi=nx-1;if(ai>=nx) ai=nx-1;} 
        }
        aj=step_int((vy-ay-r)*ysp);
        bj=step_int((vy-ay+r)*ysp);
        if(!yperiodic) {
                if(aj<0) {aj=0;if(bj<0) bj=0;}
                if(bj>=ny) {bj=ny-1;if(aj>=ny) aj=ny-1;} 
        }
        ak=step_int((vz-az-r)*zsp);
        bk=step_int((vz-az+r)*zsp);
        if(!zperiodic) {
                if(ak<0) {ak=0;if(bk<0) bk=0;}
                if(bk>=nz) {bk=nz-1;if(ak>=nz) ak=nz-1;} 
        }
        i=ai;j=aj;k=ak;
        aip=ip=step_mod(i,nx);apx=px=step_div(i,nx)*sx;
        ajp=jp=step_mod(j,ny);apy=py=step_div(j,ny)*sy;
        akp=kp=step_mod(k,nz);apz=pz=step_div(k,nz)*sz;
        inc1=aip-step_mod(bi,nx);
        inc2=nx*(ny+ajp-step_mod(bj,ny))+inc1;
        inc1+=nx;
        s=aip+nx*(ajp+ny*akp);
        return s;
}

/** Initializes a voropp_loop object, by finding all blocks which overlap the box with
 * corners (xmin,ymin,zmin) and (xmax,ymax,zmax). It returns the first block
 * which is to be tested, and sets the periodic displacement vector (px,py,pz)
 * accordingly. */
inline int voropp_loop::init(fpoint xmin,fpoint xmax,fpoint ymin,fpoint ymax,fpoint zmin,fpoint zmax,fpoint &px,fpoint &py,fpoint &pz) {
        ai=step_int((xmin-ax)*xsp);
        bi=step_int((xmax-ax)*xsp);
        if(!xperiodic) {
                if(ai<0) {ai=0;if(bi<0) bi=0;}
                if(bi>=nx) {bi=nx-1;if(ai>=nx) ai=nx-1;} 
        }
        aj=step_int((ymin-ay)*ysp);
        bj=step_int((ymax-ay)*ysp);
        if(!yperiodic) {
                if(aj<0) {aj=0;if(bj<0) bj=0;}
                if(bj>=ny) {bj=ny-1;if(aj>=ny) aj=ny-1;} 
        }
        ak=step_int((zmin-az)*zsp);
        bk=step_int((zmax-az)*zsp);
        if(!zperiodic) {
                if(ak<0) {ak=0;if(bk<0) bk=0;}
                if(bk>=nz) {bk=nz-1;if(ak>=nz) ak=nz-1;} 
        }
        i=ai;j=aj;k=ak;
        aip=ip=step_mod(i,nx);apx=px=step_div(i,nx)*sx;
        ajp=jp=step_mod(j,ny);apy=py=step_div(j,ny)*sy;
        akp=kp=step_mod(k,nz);apz=pz=step_div(k,nz)*sz;
        inc1=aip-step_mod(bi,nx);
        inc2=nx*(ny+ajp-step_mod(bj,ny))+inc1;
        inc1+=nx;
        s=aip+nx*(ajp+ny*akp);
        return s;
}

/** Returns the next block to be tested in a loop, and updates the periodicity
 * vector if necessary. */
inline int voropp_loop::inc(fpoint &px,fpoint &py,fpoint &pz) {
        if(i<bi) {
                i++;
                if(ip<nx-1) {ip++;s++;} else {ip=0;s+=1-nx;px+=sx;}
                return s;
        } else if(j<bj) {
                i=ai;ip=aip;px=apx;j++;
                if(jp<ny-1) {jp++;s+=inc1;} else {jp=0;s+=inc1-nxy;py+=sy;}
                return s;
        } else if(k<bk) {
                i=ai;ip=aip;j=aj;jp=ajp;px=apx;py=apy;k++;
                if(kp<nz-1) {kp++;s+=inc2;} else {kp=0;s+=inc2-nxyz;pz+=sz;}
                return s;
        } else return -1;
}

/** Custom int function, that gives consistent stepping for negative numbers.
 * With normal int, we have (-1.5,-0.5,0.5,1.5) -> (-1,0,0,1).
 * With this routine, we have (-1.5,-0.5,0.5,1.5) -> (-2,-1,0,1).*/
inline int voropp_loop::step_int(fpoint a) {
        return a<0?int(a)-1:int(a);
}

/** Custom mod function, that gives consistent stepping for negative numbers. */
inline int voropp_loop::step_mod(int a,int b) {
        return a>=0?a%b:b-1-(b-1-a)%b;
}

/** Custom div function, that gives consistent stepping for negative numbers. */
inline int voropp_loop::step_div(int a,int b) {
        return a>=0?a/b:-1+(a+1)/b;
}

/** Adds a wall to the container.
 * \param[in] &w a wall object to be added.*/
template<class r_option>
void container_base<r_option>::add_wall(wall& w) {
        if(wall_number==current_wall_size) {
                current_wall_size*=2;
                if(current_wall_size>max_wall_size) throw fatal_error("Wall memory allocation exceeded absolute maximum");
                wall **pwall;
                pwall=new wall*[current_wall_size];
                for(int i=0;i<wall_number;i++) pwall[i]=walls[i];
                delete [] walls;walls=pwall;            
        }
        walls[wall_number++]=&w;
}

/** Sets the radius of the jth particle in region i to r, and updates the maximum particle radius.
 * \param[in] i the region of the particle to consider.
 * \param[in] j the number of the particle within the region.
 * \param[in] r the radius to set. */
inline void radius_poly::store_radius(int i,int j,fpoint r) {
        cc->p[i][4*j+3]=r;
        if(r>max_radius) max_radius=r;
}

/** Clears the stored maximum radius. */
inline void radius_poly::clear_max() {
        max_radius=0;
}

/** Imports a list of particles from an input stream for the monodisperse case
 * where no radius information is expected.
 * \param[in] &is an input stream to read from. */
inline void radius_mono::import(istream &is) {
        int n;fpoint x,y,z;
        is >> n >> x >> y >> z;
        while(!is.eof()) {
                cc->put(n,x,y,z);
                is >> n >> x >> y >> z;
        }
}

/** Imports a list of particles from an input stream for the polydisperse case,
 * where both positions and particle radii are both stored.
 * \param[in] &is an input stream to read from. */
inline void radius_poly::import(istream &is) {
        int n;fpoint x,y,z,r;
        is >> n >> x >> y >> z >> r;
        while(!is.eof()) {
                cc->put(n,x,y,z,r);
                is >> n >> x >> y >> z >> r;
        }
}

/** Initializes the radius_poly class for a new Voronoi cell calculation,
 * by computing the radial cut-off value, based on the current particle's
 * radius and the maximum radius of any particle in the packing.
 * \param[in] ijk the region to consider.
 * \param[in] s the number of the particle within the region. */
inline void radius_poly::init(int ijk,int s) {
        crad=cc->p[ijk][4*s+3];
        mul=1+(crad*crad-max_radius*max_radius)/((max_radius+crad)*(max_radius+crad));
        crad*=crad;
}

/** This routine is called when deciding when to terminate the computation
 * of a Voronoi cell. For the Voronoi radical tessellation for a polydisperse
 * case, this routine multiplies the cutoff value by the scaling factor that
 * was precomputed in the init() routine.
 * \param[in] lrs a cutoff radius for the cell computation.
 * \return The value scaled by the factor mul. */
inline fpoint radius_poly::cutoff(fpoint lrs) {
        return mul*lrs;
}

/** This routine is called when deciding when to terminate the computation
 * of a Voronoi cell. For the monodisperse case, this routine just returns
 * the same value that is passed to it.
 * \param[in] lrs a cutoff radius for the cell computation.
 * \return The same value passed to it. */
inline fpoint radius_mono::cutoff(fpoint lrs) {
        return lrs;
}

/** Prints the radius of particle, by just supplying a generic value of "s".
 * \param[in] &os the output stream to write to.
 * \param[in] l the region to consider.
 * \param[in] c the number of the particle within the region. */
inline void radius_mono::rad(ostream &os,int l,int c) {
        os << "s";
}

/** Prints the radius of a particle to an open output stream.
 * \param[in] &os the output stream to write to.
 * \param[in] l the region to consider.
 * \param[in] c the number of the particle within the region. */
inline void radius_poly::rad(ostream &os,int l,int c) {
        os << cc->p[l][4*c+3];
}

/** Returns the scaled volume of a particle, which is always set
 * to 0.125 for the monodisperse case where particles are taken
 * to have unit diameter.
 * \param[in] ijk the region to consider.
 * \param[in] s the number of the particle within the region.
 * \return The cube of the radius of the particle, which is 0.125
 * in this case. */
inline fpoint radius_mono::volume(int ijk,int s) {
        return 0.125;
}

/** Returns the scaled volume of a particle.
 * \param[in] ijk the region to consider.
 * \param[in] s the number of the particle within the region.
 * \return The cube of the radius of the particle. */
inline fpoint radius_poly::volume(int ijk,int s) {
        fpoint a=cc->p[ijk][4*s+3];
        return a*a*a;
}

/** Scales the position of a plane according to the relative sizes
 * of the particle radii.
 * \param[in] rs the distance between the Voronoi cell and the cutting plane.
 * \param[in] t the region to consider
 * \param[in] q the number of the particle within the region.
 * \return The scaled position. */
inline fpoint radius_poly::scale(fpoint rs,int t,int q) {
        return rs+crad-cc->p[t][4*q+3]*cc->p[t][4*q+3];
}

/** Applies a blank scaling to the position of a cutting plane.
 * \param[in] rs the distance between the Voronoi cell and the cutting plane.
 * \param[in] t the region to consider
 * \param[in] q the number of the particle within the region.
 * \return The scaled position, which for this case, is equal to rs. */
inline fpoint radius_mono::scale(fpoint rs,int t,int q) {
        return rs;
}

/** Prints the radius of a particle to an open file stream.
 * \param[in] &os an open file stream.
 * \param[in] ijk the region to consider.
 * \param[in] q the number of the particle within the region. */
inline void radius_poly::print(ostream &os,int ijk,int q) {
        os << " " << cc->p[ijk][4*q+3];
}

/** This routine checks to see whether a point is within a particular distance
 * of a nearby region. If the point is within the distance of the region, then
 * the routine returns true, and computes the maximum distance from the point
 * to the region. Otherwise, the routine returns false.
 * \param[in] (di,dj,dk) The position of the nearby region to be tested,
 * relative to the region that the point is in. 
 * \param[in] (fx,fy,fz) The displacement of the point within its region.
 * \param[in] (gxs,gys,gzs) The minimum squared distances from the point to the
 * sides of its region.
 * \param[in] &crs A reference in which to return the maximum distance to the
 * region (only computed if the routine returns positive).
 * \param[in] mrs The distance to be tested.
 * \return False if the region is further away than mrs, true if the region in within mrs.*/
template<class r_option>
inline bool container_base<r_option>::compute_min_max_radius(int di,int dj,int dk,fpoint fx,fpoint fy,fpoint fz,fpoint gxs,fpoint gys,fpoint gzs,fpoint &crs,fpoint mrs) {
        fpoint xlo,ylo,zlo;
        const fpoint boxx=(bx-ax)/nx,boxy=(by-ay)/ny,boxz=(bz-az)/nz;
        const fpoint bxsq=boxx*boxx+boxy*boxy+boxz*boxz;
        if(di>0) {
                xlo=di*boxx-fx;
                crs=xlo*xlo;
                if(dj>0) {
                        ylo=dj*boxy-fy;
                        crs+=ylo*ylo;
                        if(dk>0) {
                                zlo=dk*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=bxsq+2*(boxx*xlo+boxy*ylo+boxz*zlo);
                        } else if(dk<0) {
                                zlo=(dk+1)*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=bxsq+2*(boxx*xlo+boxy*ylo-boxz*zlo);
                        } else {
                                if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxx*(2*xlo+boxx)+boxy*(2*ylo+boxy)+gzs;
                        }
                } else if(dj<0) {
                        ylo=(dj+1)*boxy-fy;
                        crs+=ylo*ylo;
                        if(dk>0) {
                                zlo=dk*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=bxsq+2*(boxx*xlo-boxy*ylo+boxz*zlo);
                        } else if(dk<0) {
                                zlo=(dk+1)*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=bxsq+2*(boxx*xlo-boxy*ylo-boxz*zlo);
                        } else {
                                if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxx*(2*xlo+boxx)+boxy*(-2*ylo+boxy)+gzs;
                        }
                } else {
                        if(dk>0) {
                                zlo=dk*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxz*(2*zlo+boxz);
                        } else if(dk<0) {
                                zlo=(dk+1)*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxz*(-2*zlo+boxz);
                        } else {
                                if(radius.cutoff(crs)>mrs) return true;
                                crs+=gzs;
                        }
                        crs+=gys+boxx*(2*xlo+boxx);
                }
        } else if(di<0) {
                xlo=(di+1)*boxx-fx;
                crs=xlo*xlo;
                if(dj>0) {
                        ylo=dj*boxy-fy;
                        crs+=ylo*ylo;
                        if(dk>0) {
                                zlo=dk*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=bxsq+2*(-boxx*xlo+boxy*ylo+boxz*zlo);
                        } else if(dk<0) {
                                zlo=(dk+1)*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=bxsq+2*(-boxx*xlo+boxy*ylo-boxz*zlo);
                        } else {
                                if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxx*(-2*xlo+boxx)+boxy*(2*ylo+boxy)+gzs;
                        }
                } else if(dj<0) {
                        ylo=(dj+1)*boxy-fy;
                        crs+=ylo*ylo;
                        if(dk>0) {
                                zlo=dk*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=bxsq+2*(-boxx*xlo-boxy*ylo+boxz*zlo);
                        } else if(dk<0) {
                                zlo=(dk+1)*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=bxsq+2*(-boxx*xlo-boxy*ylo-boxz*zlo);
                        } else {
                                if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxx*(-2*xlo+boxx)+boxy*(-2*ylo+boxy)+gzs;
                        }
                } else {
                        if(dk>0) {
                                zlo=dk*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxz*(2*zlo+boxz);
                        } else if(dk<0) {
                                zlo=(dk+1)*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxz*(-2*zlo+boxz);
                        } else {
                                if(radius.cutoff(crs)>mrs) return true;
                                crs+=gzs;
                        }
                        crs+=gys+boxx*(-2*xlo+boxx);
                }
        } else {
                if(dj>0) {
                        ylo=dj*boxy-fy;
                        crs=ylo*ylo;
                        if(dk>0) {
                                zlo=dk*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxz*(2*zlo+boxz);
                        } else if(dk<0) {
                                zlo=(dk+1)*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxz*(-2*zlo+boxz);
                        } else {
                                if(radius.cutoff(crs)>mrs) return true;
                                crs+=gzs;
                        }
                        crs+=boxy*(2*ylo+boxy);
                } else if(dj<0) {
                        ylo=(dj+1)*boxy-fy;
                        crs=ylo*ylo;
                        if(dk>0) {
                                zlo=dk*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxz*(2*zlo+boxz);
                        } else if(dk<0) {
                                zlo=(dk+1)*boxz-fz;
                                crs+=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxz*(-2*zlo+boxz);
                        } else {
                                if(radius.cutoff(crs)>mrs) return true;
                                crs+=gzs;
                        }
                        crs+=boxy*(-2*ylo+boxy);
                } else {
                        if(dk>0) {
                                zlo=dk*boxz-fz;crs=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxz*(2*zlo+boxz);
                        } else if(dk<0) {
                                zlo=(dk+1)*boxz-fz;crs=zlo*zlo;if(radius.cutoff(crs)>mrs) return true;
                                crs+=boxz*(-2*zlo+boxz);
                        } else {
                                crs=0;
                                cout << "Can't happen ... happened\n";
                        }
                        crs+=gys;
                }
                crs+=gxs;
        }
        return false;
}

#include "worklist.cc"

---