cell.cc

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// Voro++, a 3D cell-based Voronoi library
//
// Author   : Chris H. Rycroft (LBL / UC Berkeley)
// Email    : [email protected]
// Date     : July 1st 2008

/** \file cell.cc
 * \brief Function implementations for the voronoicell_base template and
 * related classes. */

#include "cell.hh"

/** Constructs a Voronoi cell and sets up the initial memory. */
template<class n_option>
voronoicell_base<n_option>::voronoicell_base() :
        current_vertices(init_vertices), current_vertex_order(init_vertex_order),
        current_delete_size(init_delete_size), current_delete2_size(init_delete2_size),
        ed(new int*[current_vertices]), nu(new int[current_vertices]),
        pts(new fpoint[3*current_vertices]), mem(new int[current_vertex_order]),
        mec(new int[current_vertex_order]), mep(new int*[current_vertex_order]),
        ds(new int[current_delete_size]), ds2(new int[current_delete2_size]), neighbor(this) {
        int i;
        sure.p=pts;
        for(i=0;i<3;i++) {
                mem[i]=init_n_vertices;mec[i]=0;
                mep[i]=new int[init_n_vertices*(2*i+1)];
        }
        mem[3]=init_3_vertices;mec[3]=0;
        mep[3]=new int[init_3_vertices*7];
        for(i=4;i<current_vertex_order;i++) {
                mem[i]=init_n_vertices;mec[i]=0;
                mep[i]=new int[init_n_vertices*(2*i+1)];
        }
}

/** The voronoicell destructor deallocates all the dynamic memory. */
template<class n_option>
voronoicell_base<n_option>::~voronoicell_base() {
        delete [] ds;
        delete [] ds2;
        for(int i=0;i<current_vertex_order;i++) if(mem[i]>0) delete [] mep[i];
        delete [] mem;
        delete [] mec;
        delete [] mep;
        delete [] ed;
        delete [] nu;
        delete [] pts;
}

/** Increases the memory storage for a particular vertex order, by increasing
 * the size of the of the corresponding mep array. If the arrays already exist,
 * their size is doubled; if they don't exist, then new ones of size
 * init_n_vertices are allocated. The routine also ensures that the pointers in
 * the ed array are updated, by making use of the back pointers. For the cases
 * where the back pointer has been temporarily overwritten in the marginal
 * vertex code, the auxiliary delete stack is scanned to find out how to update
 * the ed value. If the template has been instantiated with the neighbor
 * tracking turned on, then the routine also reallocates the corresponding mne
 * array.
 * \param[in] i the order of the vertex memory to be increased. */
template<class n_option>
void voronoicell_base<n_option>::add_memory(int i) {
        int s=2*i+1;
        if(mem[i]==0) {
                neighbor.allocate(i,init_n_vertices);
                mep[i]=new int[init_n_vertices*s];
                mem[i]=init_n_vertices;
#if VOROPP_VERBOSE >=2
                cerr << "Order " << i << " vertex memory created " << endl;
#endif
        } else {
                int j=0,k,*l;
                mem[i]*=2;
                if(mem[i]>max_n_vertices) voropp_fatal_error("Point memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
#if VOROPP_VERBOSE >=2
                cerr << "Order " << i << " vertex memory scaled up to " << mem[i] << endl;
#endif
                l=new int[s*mem[i]];
                int m=0;
                neighbor.allocate_aux1(i);
                while(j<s*mec[i]) {
                        k=mep[i][j+2*i];
                        if(k>=0) {
                                ed[k]=l+j;
                                neighbor.set_to_aux1_offset(k,m);
                        } else {
                                int o;
                                for(o=0;o<stack2;o++) {
                                        if(ed[ds2[o]]==mep[i]+j) {
                                                ed[ds2[o]]=l+j;
                                                neighbor.set_to_aux1_offset(ds2[o],m);
                                                break;
                                        }
                                }
                                if(o==stack2) voropp_fatal_error("Couldn't relocate dangling pointer",VOROPP_INTERNAL_ERROR);
#if VOROPP_VERBOSE >=3
                                cerr << "Relocated dangling pointer" << endl;
#endif
                        }
                        for(k=0;k<s;k++,j++) l[j]=mep[i][j];
                        for(k=0;k<i;k++,m++) neighbor.copy_to_aux1(i,m);
                }
                delete [] mep[i];
                mep[i]=l;
                neighbor.switch_to_aux1(i);
        }
}

/** Doubles the maximum number of vertices allowed, by reallocating the ed, nu,
 * and pts arrays. If the allocation exceeds the absolute maximum set in
 * max_vertices, then the routine exits with a fatal error. If the template has
 * been instantiated with the neighbor tracking turned on, then the routine
 * also reallocates the ne array. */
template<class n_option>
void voronoicell_base<n_option>::add_memory_vertices() {
        int i=2*current_vertices,j,**pp,*pnu;
        if(i>max_vertices) voropp_fatal_error("Vertex memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
#if VOROPP_VERBOSE >=2
        cerr << "Vertex memory scaled up to " << i << endl;
#endif
        fpoint *ppts;
        pp=new int*[i];
        for(j=0;j<current_vertices;j++) pp[j]=ed[j];
        delete [] ed;ed=pp;
        neighbor.add_memory_vertices(i);
        pnu=new int[i];
        for(j=0;j<current_vertices;j++) pnu[j]=nu[j];
        delete [] nu;nu=pnu;
        ppts=new fpoint[3*i];
        for(j=0;j<3*current_vertices;j++) ppts[j]=pts[j];
        delete [] pts;sure.p=pts=ppts;
        current_vertices=i;
}

/** Doubles the maximum allowed vertex order, by reallocating mem, mep, and mec
 * arrays. If the allocation exceeds the absolute maximum set in
 * max_vertex_order, then the routine causes a fatal error. If the template has
 * been instantiated with the neighbor tracking turned on, then the routine
 * also reallocates the mne array. */
template<class n_option>
void voronoicell_base<n_option>::add_memory_vorder() {
        int i=2*current_vertex_order,j,*p1,**p2;
        if(i>max_vertex_order) voropp_fatal_error("Vertex order memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
#if VOROPP_VERBOSE >=2
        cerr << "Vertex order memory scaled up to " << i << endl;
#endif
        p1=new int[i];
        for(j=0;j<current_vertex_order;j++) p1[j]=mem[j];while(j<i) p1[j++]=0;
        delete [] mem;mem=p1;
        p2=new int*[i];
        for(j=0;j<current_vertex_order;j++) p2[j]=mep[j];
        delete [] mep;mep=p2;
        p1=new int[i];
        for(j=0;j<current_vertex_order;j++) p1[j]=mec[j];while(j<i) p1[j++]=0;
        delete [] mec;mec=p1;
        neighbor.add_memory_vorder(i);
        current_vertex_order=i;
}

/** Doubles the size allocation of the main delete stack. If the allocation
 * exceeds the absolute maximum set in max_delete_size, then routine causes a
 * fatal error. */
template<class n_option>
void voronoicell_base<n_option>::add_memory_ds() {
        int i=2*current_delete_size,j,*pds;
        if(i>max_delete_size) voropp_fatal_error("Delete stack 1 memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
#if VOROPP_VERBOSE >=2
        cerr << "Delete stack 1 memory scaled up to " << i << endl;
#endif
        pds=new int[i];
        for(j=0;j<current_delete_size;j++) pds[j]=ds[j];
        delete [] ds;ds=pds;
        current_delete_size=i;
}

/** Doubles the size allocation of the auxiliary delete stack. If the
 * allocation exceeds the absolute maximum set in max_delete2_size, then the
 * routine causes a fatal error. */
template<class n_option>
void voronoicell_base<n_option>::add_memory_ds2() {
        int i=2*current_delete2_size,j,*pds2;
        if(i>max_delete2_size) voropp_fatal_error("Delete stack 2 memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
#if VOROPP_VERBOSE >=2
        cerr << "Delete stack 2 memory scaled up to " << i << endl;
#endif
        pds2=new int[i];
        for(j=0;j<current_delete2_size;j++) pds2[j]=ds2[j];
        delete [] ds2;ds2=pds2;
        current_delete2_size=i;
}

/** Initializes a Voronoi cell as a rectangular box with the given dimensions.
 * \param[in] (xmin,xmax) the minimum and maximum x coordinates.
 * \param[in] (ymin,ymax) the minimum and maximum y coordinates.
 * \param[in] (zmin,zmax) the minimum and maximum z coordinates. */
template<class n_option>
void voronoicell_base<n_option>::init(fpoint xmin,fpoint xmax,fpoint ymin,fpoint ymax,fpoint zmin,fpoint zmax) {
        for(int i=0;i<current_vertex_order;i++) mec[i]=0;up=0;
        mec[3]=p=8;xmin*=2;xmax*=2;ymin*=2;ymax*=2;zmin*=2;zmax*=2;
        pts[0]=xmin;pts[1]=ymin;pts[2]=zmin;
        pts[3]=xmax;pts[4]=ymin;pts[5]=zmin;
        pts[6]=xmin;pts[7]=ymax;pts[8]=zmin;
        pts[9]=xmax;pts[10]=ymax;pts[11]=zmin;
        pts[12]=xmin;pts[13]=ymin;pts[14]=zmax;
        pts[15]=xmax;pts[16]=ymin;pts[17]=zmax;
        pts[18]=xmin;pts[19]=ymax;pts[20]=zmax;
        pts[21]=xmax;pts[22]=ymax;pts[23]=zmax;
        int *q=mep[3];
        q[0]=1;q[1]=4;q[2]=2;q[3]=2;q[4]=1;q[5]=0;q[6]=0;
        q[7]=3;q[8]=5;q[9]=0;q[10]=2;q[11]=1;q[12]=0;q[13]=1;
        q[14]=0;q[15]=6;q[16]=3;q[17]=2;q[18]=1;q[19]=0;q[20]=2;
        q[21]=2;q[22]=7;q[23]=1;q[24]=2;q[25]=1;q[26]=0;q[27]=3;
        q[28]=6;q[29]=0;q[30]=5;q[31]=2;q[32]=1;q[33]=0;q[34]=4;
        q[35]=4;q[36]=1;q[37]=7;q[38]=2;q[39]=1;q[40]=0;q[41]=5;
        q[42]=7;q[43]=2;q[44]=4;q[45]=2;q[46]=1;q[47]=0;q[48]=6;
        q[49]=5;q[50]=3;q[51]=6;q[52]=2;q[53]=1;q[54]=0;q[55]=7;
        ed[0]=q;ed[1]=q+7;ed[2]=q+14;ed[3]=q+21;
        ed[4]=q+28;ed[5]=q+35;ed[6]=q+42;ed[7]=q+49;
        neighbor.init();
        nu[0]=nu[1]=nu[2]=nu[3]=nu[4]=nu[5]=nu[6]=nu[7]=3;
}

/** Initializes a Voronoi cell as a regular octahedron.
 * \param[in] l The distance from the octahedron center to a vertex. Six
 *              vertices are initialized at (-l,0,0), (l,0,0), (0,-l,0),
 *              (0,l,0), (0,0,-l), and (0,0,l). */
template<class n_option>
inline void voronoicell_base<n_option>::init_octahedron(fpoint l) {
        for(int i=0;i<current_vertex_order;i++) mec[i]=0;up=0;
        mec[4]=p=6;l*=2;
        pts[0]=-l;pts[1]=0;pts[2]=0;
        pts[3]=l;pts[4]=0;pts[5]=0;
        pts[6]=0;pts[7]=-l;pts[8]=0;
        pts[9]=0;pts[10]=l;pts[11]=0;
        pts[12]=0;pts[13]=0;pts[14]=-l;
        pts[15]=0;pts[16]=0;pts[17]=l;
        int *q=mep[4];
        q[0]=2;q[1]=5;q[2]=3;q[3]=4;q[4]=0;q[5]=0;q[6]=0;q[7]=0;q[8]=0;
        q[9]=2;q[10]=4;q[11]=3;q[12]=5;q[13]=2;q[14]=2;q[15]=2;q[16]=2;q[17]=1;
        q[18]=0;q[19]=4;q[20]=1;q[21]=5;q[22]=0;q[23]=3;q[24]=0;q[25]=1;q[26]=2;
        q[27]=0;q[28]=5;q[29]=1;q[30]=4;q[31]=2;q[32]=3;q[33]=2;q[34]=1;q[35]=3;
        q[36]=0;q[37]=3;q[38]=1;q[39]=2;q[40]=3;q[41]=3;q[42]=1;q[43]=1;q[44]=4;
        q[45]=0;q[46]=2;q[47]=1;q[48]=3;q[49]=1;q[50]=3;q[51]=3;q[52]=1;q[53]=5;
        ed[0]=q;ed[1]=q+9;ed[2]=q+18;ed[3]=q+27;ed[4]=q+36;ed[5]=q+45;
        neighbor.init_octahedron();
        nu[0]=nu[1]=nu[2]=nu[3]=nu[4]=nu[5]=4;
}

/** Initializes a Voronoi cell as a tetrahedron. It assumes that the normal to
 * the face for the first three vertices points inside.
 * \param (x0,y0,z0) a position vector for the first vertex.
 * \param (x1,y1,z1) a position vector for the second vertex.
 * \param (x2,y2,z2) a position vector for the third vertex.
 * \param (x3,y3,z3) a position vector for the fourth vertex. */
template<class n_option>
inline void voronoicell_base<n_option>::init_tetrahedron(fpoint x0,fpoint y0,fpoint z0,fpoint x1,fpoint y1,fpoint z1,fpoint x2,fpoint y2,fpoint z2,fpoint x3,fpoint y3,fpoint z3) {
        for(int i=0;i<current_vertex_order;i++) mec[i]=0;up=0;
        mec[3]=p=4;
        pts[0]=x0*2;pts[1]=y0*2;pts[2]=z0*2;
        pts[3]=x1*2;pts[4]=y1*2;pts[5]=z1*2;
        pts[6]=x2*2;pts[7]=y2*2;pts[8]=z2*2;
        pts[9]=x3*2;pts[10]=y3*2;pts[11]=z3*2;
        int *q=mep[3];
        q[0]=1;q[1]=3;q[2]=2;q[3]=0;q[4]=0;q[5]=0;q[6]=0;
        q[7]=0;q[8]=2;q[9]=3;q[10]=0;q[11]=2;q[12]=1;q[13]=1;
        q[14]=0;q[15]=3;q[16]=1;q[17]=2;q[18]=2;q[19]=1;q[20]=2;
        q[21]=0;q[22]=1;q[23]=2;q[24]=1;q[25]=2;q[26]=1;q[27]=3;
        ed[0]=q;ed[1]=q+7;ed[2]=q+14;ed[3]=q+21;
        neighbor.init_tetrahedron();
        nu[0]=nu[1]=nu[2]=nu[3]=3;
}

/** Initializes an arbitrary test object using the add_vertex() and
 * construct_relations() routines. See the source code for information about
 * the specific objects.
 * \param[in] n the number of the test object (from 0 to 9). */
template<class n_option>
inline void voronoicell_base<n_option>::init_test(int n) {
        for(int i=0;i<current_vertex_order;i++) mec[i]=0;up=p=0;
        switch(n) {
                case 0:
                        // A peaked object, with a high vertex 6, and a ridge
                        // at z=0 from vertex 1 to 2. This can be used to test
                        // the order 1 vertex collapse routine.
                        add_vertex(1,-2,-1,3,1,5);
                        add_vertex(0,-1,1,5,0,2);
                        add_vertex(0,1,0,1,3,6,4);
                        add_vertex(1,4,-1,4,6,2,0);
                        add_vertex(-1,4,-1,3,5,2,6);
                        add_vertex(-1,-2,-1,4,0,1);
                        add_vertex(0,3,0,4,2,3);
                        break;
                case 1:
                        // A truncated pyramid shape, with vertex 4 in the z=0
                        // plane. This can be used to test order 4 vertex
                        // generation.
                        add_vertex(-2,2,-1,3,4,1);
                        add_vertex(2,2,-1,0,5,2);
                        add_vertex(2,-2,-1,1,6,3);
                        add_vertex(-2,-2,-1,2,7,0);
                        add_vertex(-1,1,0,0,7,5);
                        add_vertex(1,1,1,1,4,6);
                        add_vertex(1,-1,1,7,2,5);
                        add_vertex(-1,-1,1,4,3,6);
                        break;
                case 2:
                        // An object with two peaks at vertices 4 and 6,
                        // connected with a trough at vertex 5. It can be used
                        // to test the part of the routine that deals with
                        // augmenting existing vertices.
                        add_vertex(1,-2,-1,1,3,4);
                        add_vertex(-1,-2,-1,2,0,4,5);
                        add_vertex(-1,2,-1,1,6,3);
                        add_vertex(1,2,-1,2,6,5,0);
                        add_vertex(0,-1,1,5,1,0);
                        add_vertex(0,0,0,1,4,3,6);
                        add_vertex(0,1,1,2,5,3);
                        break;
                case 3:
                        // A box with a pyramid on top of it. This a good
                        // test object to make sure that the code can handle
                        // object with vertices of different orders.
                        add_vertex(-1,-1,-1,4,3,1);
                        add_vertex(1,-1,-1,0,2,5);
                        add_vertex(1,1,-1,6,1,3);
                        add_vertex(-1,1,-1,2,0,7);
                        add_vertex(-1,-1,1,7,0,5,8);
                        add_vertex(1,-1,1,4,1,6,8);
                        add_vertex(1,1,1,5,2,7,8);
                        add_vertex(-1,1,1,6,3,4,8);
                        add_vertex(0,0,2,7,4,5,6);
                        break;
                case 4:
                        // A shape with two peaks (vertices 6 and 9) connected
                        // with a trough (vertices 7 and 8). It can be used as
                        // a basic test of the double edge skipping in the plane
                        // generation routine, whereby an edge is omitted if
                        // the routine is tracing along a part it has already
                        // been down.
                        add_vertex(1,-3,-1,5,6,1);
                        add_vertex(-1,-3,-1,0,6,2);
                        add_vertex(-3,0,-1,1,7,8,3);
                        add_vertex(-1,3,-1,2,9,4);
                        add_vertex(1,3,-1,3,9,5);
                        add_vertex(3,0,-1,4,8,7,0);
                        add_vertex(0,-2,1,7,1,0);
                        add_vertex(0,-1,0,8,2,6,5);
                        add_vertex(0,1,0,9,2,7,5);
                        add_vertex(0,2,1,3,8,4);
                        break;
                case 5:
                        // An object with four peaks (vertices 8 to 11)
                        // connected by a trough (vertex 16). It can be used to
                        // the test multiple augmentation of edges of a
                        // particular vertex.
                        add_vertex(-1,-3,-1,7,1,8,12);
                        add_vertex(1,-3,-1,2,12,8,0);
                        add_vertex(3,-1,-1,3,9,13,1);
                        add_vertex(3,1,-1,4,13,9,2);
                        add_vertex(1,3,-1,5,10,14,3);
                        add_vertex(-1,3,-1,6,14,10,4);
                        add_vertex(-3,1,-1,7,11,15,5);
                        add_vertex(-3,-1,-1,0,15,11,6);
                        add_vertex(0,-2,1,0,1,12);
                        add_vertex(2,0,1,2,3,13);
                        add_vertex(0,2,1,14,4,5);
                        add_vertex(-2,0,1,7,15,6);
                        add_vertex(0,-1,0.5,0,8,1,16);
                        add_vertex(1,0,0.5,2,9,3,16);
                        add_vertex(0,1,0.5,4,10,5,16);
                        add_vertex(-1,0,0.5,6,11,7,16);
                        add_vertex(0,0,0,15,12,13,14);
                        break;
                case 6:
                        // An object with four peaks (vertices 8 to 11)
                        // connected by a sequence of ridges. It can be used to
                        // the test multiple cases of double edge skipping
                        // on the same vertex.
                        add_vertex(-1,-3,-1,7,1,8,12);
                        add_vertex(1,-3,-1,2,12,8,0);
                        add_vertex(3,-1,-1,3,9,13,1);
                        add_vertex(3,1,-1,4,13,9,2);
                        add_vertex(1,3,-1,5,10,14,3);
                        add_vertex(-1,3,-1,6,14,10,4);
                        add_vertex(-3,1,-1,7,11,15,5);
                        add_vertex(-3,-1,-1,0,15,11,6);
                        add_vertex(0,-2,1,0,1,12);
                        add_vertex(2,0,1,2,3,13);
                        add_vertex(0,2,1,14,4,5);
                        add_vertex(-2,0,1,7,15,6);
                        add_vertex(0,-1,0,0,8,1,16);
                        add_vertex(1,0,0,2,9,3,16);
                        add_vertex(0,1,0,4,10,5,16);
                        add_vertex(-1,0,0,6,11,7,16);
                        add_vertex(0,0,0,15,12,13,14);
                        break;
                case 7:
                        // A variation on the zeroth test shape, with a peak
                        // (vertices 7 and 8) connected to a ridge at z=0
                        // (vertices 4 and 5)
                        add_vertex(2,-3,-1,3,4,1);
                        add_vertex(-2,-3,-1,0,4,2);
                        add_vertex(-2,3,-1,1,7,3);
                        add_vertex(2,3,-1,2,6,0);
                        add_vertex(0,-2,0,0,5,1);
                        add_vertex(0,1,0,4,6,7);
                        add_vertex(1,2,1,7,5,3);
                        add_vertex(-1,2,1,5,6,2);
                        break;
                case 8:
                        // A triangular object with a skewed peak, that can be used to
                        // test the order two vertex removal routine
                        add_vertex(3,-2,-1,2,3,1);
                        add_vertex(-3,-2,-1,0,4,2);
                        add_vertex(0,4,-1,1,5,0);
                        add_vertex(1.5,-1,0,7,0,6);
                        add_vertex(-1.5,-1,0,1,7,8);
                        add_vertex(0,2,0,8,6,2);
                        add_vertex(0.75,0.5,0,9,3,5);
                        add_vertex(0,-1,0,4,3,9);
                        add_vertex(-0.75,0.5,0,4,9,5);
                        add_vertex(0,0,1,8,7,6);
                        break;
                case 9:
                        // This a tetrahedron with some low-order extraneous edges, and can
                        // be used to test the order 1 and order 2 removal routines
                        add_vertex(0,0,0,3,1,2);
                        add_vertex(1,0,1,3,2,0);
                        add_vertex(1,1,0,3,0,1);
                        add_vertex(2,0,0,6,4,2,1,0);
                        add_vertex(3,1,0,3,6,8,5);
                        add_vertex(3,2,0,4);
                        add_vertex(4,0,0,4,3,7,8);
                        add_vertex(5,0,0,6);
                        add_vertex(4,1,0,6,4);
        }

        construct_relations();
        neighbor.label_facets();
}

/** Adds an order one vertex to the memory structure, and specifies its edge.
 * \param[in] (x,y,z) are the coordinates of the vertex.
 * \param[in] a is the first and only edge of this vertex. */
template<class n_option>
void voronoicell_base<n_option>::add_vertex(fpoint x,fpoint y,fpoint z,int a) {
        pts[3*p]=x;pts[3*p+1]=y;pts[3*p+2]=z;nu[p]=1;
        if(mem[1]==mec[1]) add_memory(1);
        neighbor.set_pointer(p,1);
        int *q=mep[1]+3*mec[1]++;ed[p]=q;
        q[0]=a;q[2]=p++;
}

/** Adds an order 2 vertex to the memory structure, and specifies its edges.
 * \param[in] (x,y,z) are the coordinates of the vertex.
 * \param[in] (a,b) are the edges of this vertex. */
template<class n_option>
void voronoicell_base<n_option>::add_vertex(fpoint x,fpoint y,fpoint z,int a,int b) {
        pts[3*p]=x;pts[3*p+1]=y;pts[3*p+2]=z;nu[p]=2;
        if(mem[2]==mec[2]) add_memory(2);
        neighbor.set_pointer(p,2);
        int *q=mep[2]+5*mec[2]++;ed[p]=q;
        q[0]=a;q[1]=b;q[4]=p++;
}

/** Adds an order 3 vertex to the memory structure, and specifies its edges.
 * \param[in] (x,y,z) are the coordinates of the vertex.
 * \param[in] (a,b,c) are the edges of this vertex. */
template<class n_option>
void voronoicell_base<n_option>::add_vertex(fpoint x,fpoint y,fpoint z,int a,int b,int c) {
        pts[3*p]=x;pts[3*p+1]=y;pts[3*p+2]=z;nu[p]=3;
        if(mem[3]==mec[3]) add_memory(3);
        neighbor.set_pointer(p,3);
        int *q=mep[3]+7*mec[3]++;ed[p]=q;
        q[0]=a;q[1]=b;q[2]=c;q[6]=p++;
}

/** Adds an order 4 vertex to the memory structure, and specifies its edges.
 * \param[in] (x,y,z) are the coordinates of the vertex.
 * \param[in] (a,b,c,d) are the edges of this vertex. */
template<class n_option>
void voronoicell_base<n_option>::add_vertex(fpoint x,fpoint y,fpoint z,int a,int b,int c,int d) {
        pts[3*p]=x;pts[3*p+1]=y;pts[3*p+2]=z;nu[p]=4;
        if(mem[4]==mec[4]) add_memory(4);
        neighbor.set_pointer(p,4);
        int *q=mep[4]+9*mec[4]++;ed[p]=q;
        q[0]=a;q[1]=b;q[2]=c;q[3]=d;q[8]=p++;
}

/** Adds an order 5 vertex to the memory structure, and specifies its edges.
 * \param[in] (x,y,z) are the coordinates of the vertex.
 * \param[in] (a,b,c,d,e) are the edges of this vertex. */
template<class n_option>
void voronoicell_base<n_option>::add_vertex(fpoint x,fpoint y,fpoint z,int a,int b,int c,int d,int e) {
        pts[3*p]=x;pts[3*p+1]=y;pts[3*p+2]=z;nu[p]=5;
        if(mem[5]==mec[5]) add_memory(5);
        neighbor.set_pointer(p,5);
        int *q=mep[5]+11*mec[5]++;ed[p]=q;
        q[0]=a;q[1]=b;q[2]=c;q[3]=d;q[4]=e;q[10]=p++;
}

/** Checks that the relational table of the Voronoi cell is accurate, and
 * prints out any errors. This algorithm is O(p), so running it every time the
 * plane routine is called will result in a significant slowdown. */
template<class n_option>
void voronoicell_base<n_option>::check_relations() {
        int i,j;
        for(i=0;i<p;i++) for(j=0;j<nu[i];j++) if(ed[ed[i][j]][ed[i][nu[i]+j]]!=i)
                cout << "Relational error at point " << i << ", edge " << j << "." << endl;
}

/** This routine checks for any two vertices that are connected by more than
 * one edge. The plane algorithm is designed so that this should not happen, so
 * any occurrences are most likely errors. Note that the routine is O(p), so
 * running it every time the plane routine is called will result in a
 * significant slowdown. */
template<class n_option>
void voronoicell_base<n_option>::check_duplicates() {
        int i,j,k;
        for(i=0;i<p;i++) for(j=1;j<nu[i];j++) for(k=0;k<j;k++) if(ed[i][j]==ed[i][k])
                cout << "Duplicate edges: (" << i << "," << j << ") and (" << i << "," << k << ") [" << ed[i][j] << "]" << endl;
}

/** Constructs the relational table if the edges have been specified. */
template<class n_option>
void voronoicell_base<n_option>::construct_relations() {
        int i,j,k,l;
        for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                l=0;
                while(ed[k][l]!=i) {
                        l++;
                        if(l==nu[k]) voropp_fatal_error("Relation table construction failed",VOROPP_INTERNAL_ERROR);
                }
                ed[i][nu[i]+j]=l;
        }
}

/** Cuts the Voronoi cell by a particle whose center is at a separation of
 * (x,y,z) from the cell center. The value of rsq should be initially set to
 * \f$x^2+y^2+z^2\f$.
 * \param[in] (x,y,z) the normal vector to the plane.
 * \param[in] rsq the distance along this vector of the plane.
 * \param[in] p_id the plane ID (for neighbor tracking only).
 * \return False if the plane cut deleted the cell entirely, true otherwise. */
template<class n_option>
bool voronoicell_base<n_option>::nplane(fpoint x,fpoint y,fpoint z,fpoint rsq,int p_id) {
        int count=0,i,j,k,lp=up,cp,qp,rp,stack=0;stack2=0;
        int us=0,ls=0,qs,iqs,cs,uw,qw,lw;
        int *edp,*edd;
        fpoint u,l,r,q;bool complicated_setup=false,new_double_edge=false,double_edge=false;

        //Initialize the safe testing routine
        sure.init(x,y,z,rsq);

        //Test approximately sqrt(n)/4 points for their proximity to the plane
        //and keep the one which is closest
        uw=sure.test(up,u);

        // Starting from an initial guess, we now move from vertex to vertex,
        // to try and find an edge which intersects the cutting plane,
        // or a vertex which is on the plane
        try {
                if(uw==1) {

                        // The test point is inside the cutting plane.
                        us=0;
                        do {
                                lp=ed[up][us];
                                lw=sure.test(lp,l);
                                if(l<u) break;
                                us++;
                        } while (us<nu[up]);

                        if(us==nu[up]) {
                                return false;
                        }

                        ls=ed[up][nu[up]+us];
                        while(lw==1) {
                                if(++count>=p) throw true;
                                u=l;up=lp;
                                for(us=0;us<ls;us++) {
                                        lp=ed[up][us];
                                        lw=sure.test(lp,l);
                                        if(l<u) break;
                                }
                                if(us==ls) {
                                        us++;
                                        while(us<nu[up]) {
                                                lp=ed[up][us];
                                                lw=sure.test(lp,l);
                                                if(l<u) break;
                                                us++;
                                        }
                                        if(us==nu[up]) {
                                                return false;
                                        }
                                }
                                ls=ed[up][nu[up]+us];
                        }

                        // If the last point in the iteration is within the
                        // plane, we need to do the complicated setup
                        // routine. Otherwise, we use the regular iteration.
                        if(lw==0) {
                                up=lp;
                                complicated_setup=true;
                        } else complicated_setup=false;
                } else if(uw==-1) {
                        us=0;
                        do {
                                qp=ed[up][us];
                                qw=sure.test(qp,q);
                                if(u<q) break;
                                us++;
                        } while (us<nu[up]);
                        if(us==nu[up]) return true;

                        while(qw==-1) {
                                qs=ed[up][nu[up]+us];
                                if(++count>=p) throw true;
                                u=q;up=qp;
                                for(us=0;us<qs;us++) {
                                        qp=ed[up][us];
                                        qw=sure.test(qp,q);
                                        if(u<q) break;
                                }
                                if(us==qs) {
                                        us++;
                                        while(us<nu[up]) {
                                                qp=ed[up][us];
                                                qw=sure.test(qp,q);
                                                if(u<q) break;
                                                us++;
                                        }
                                        if(us==nu[up]) return true;
                                }
                        }
                        if(qw==1) {
                                lp=up;ls=us;l=u;
                                up=qp;us=ed[lp][nu[lp]+ls];u=q;
                                complicated_setup=false;
                        } else {
                                up=qp;
                                complicated_setup=true;
                        }
                } else {

                        // Our original test point was on the plane, so we
                        // automatically head for the complicated setup
                        // routine
                        complicated_setup=true;
                }
        }
        catch(bool except) {
                // This routine is a fall-back, in case floating point errors
                // cause the usual search routine to fail. In the fall-back
                // routine, we just test every edge to find one straddling
                // the plane.
#if VOROPP_VERBOSE >=1
                cerr << "Bailed out of convex calculation\n";
#endif
                qw=1;lw=0;
                for(qp=0;qp<p;qp++) {
                        qw=sure.test(qp,q);
                        if(qw==1) {

                                // The point is inside the cutting space. Now
                                // see if we can find a neighbor which isn't.
                                for(us=0;us<nu[qp];us++) {
                                        lp=ed[qp][us];
                                        if(lp<qp) {
                                                lw=sure.test(lp,l);
                                                if(lw!=1) break;
                                        }
                                }
                                if(us<nu[qp]) {
                                        up=qp;
                                        if(lw==0) {
                                                complicated_setup=true;
                                        } else {
                                                complicated_setup=false;
                                                u=q;
                                                ls=ed[up][nu[up]+us];
                                        }
                                        break;
                                }
                        } else if(qw==-1) {

                                // The point is outside the cutting space. See
                                // if we can find a neighbor which isn't.
                                for(ls=0;ls<nu[qp];ls++) {
                                        up=ed[qp][ls];
                                        if(up<qp) {
                                                uw=sure.test(up,u);
                                                if(uw!=-1) break;
                                        }
                                }
                                if(ls<nu[qp]) {
                                        if(uw==0) {
                                                up=qp;
                                                complicated_setup=true;
                                        } else {
                                                complicated_setup=false;
                                                lp=qp;l=q;
                                                us=ed[lp][nu[lp]+ls];
                                        }
                                        break;
                                }
                        } else {

                                // The point is in the plane, so we just
                                // proceed with the complicated setup routine
                                up=qp;
                                complicated_setup=true;
                                break;
                        }
                }
                if(qp==p) return qw==-1?true:false;
        }

        // We're about to add the first point of the new facet. In either
        // routine, we have to add a point, so first check there's space for
        // it.
        if(p==current_vertices) add_memory_vertices();

        if(complicated_setup) {
                // The search algorithm found a point which is on the cutting
                // plane. We leave that point in place, and create a new one at
                // the same location.
                pts[3*p]=pts[3*up];
                pts[3*p+1]=pts[3*up+1];
                pts[3*p+2]=pts[3*up+2];

                // Search for a collection of edges of the test vertex which
                // are outside of the cutting space. Begin by testing the
                // zeroth edge.
                i=0;
                lp=ed[up][0];
                lw=sure.test(lp,l);
                if(lw!=-1) {

                        // The first edge is either inside the cutting space,
                        // or lies within the cutting plane. Test the edges
                        // sequentially until we find one that is outside.
                        rp=lw;
                        do {
                                i++;

                                // If we reached the last edge with no luck
                                // then all of the vertices are inside
                                // or on the plane, so the cell is completely
                                // deleted
                                if(i==nu[up]) return false;
                                lp=ed[up][i];
                                lw=sure.test(lp,l);
                        } while (lw!=-1);
                        j=i+1;

                        // We found an edge outside the cutting space. Keep
                        // moving through these edges until we find one that's
                        // inside or on the plane.
                        while(j<nu[up]) {
                                lp=ed[up][j];
                                lw=sure.test(lp,l);
                                if(lw!=-1) break;
                                j++;
                        }

                        // Compute the number of edges for the new vertex. In
                        // general it will be the number of outside edges
                        // found, plus two. But we need to recognize the
                        // special case when all but one edge is outside, and
                        // the remaining one is on the plane. For that case we
                        // have to reduce the edge count by one to prevent
                        // doubling up.
                        if(j==nu[up]&&i==1&&rp==0) {
                                nu[p]=nu[up];
                                double_edge=true;
                        } else nu[p]=j-i+2;
                        k=1;

                        // Add memory for the new vertex if needed, and
                        // initialize
                        while (nu[p]>=current_vertex_order) add_memory_vorder();
                        if(mec[nu[p]]==mem[nu[p]]) add_memory(nu[p]);
                        neighbor.set_pointer(p,nu[p]);
                        ed[p]=mep[nu[p]]+(2*nu[p]+1)*mec[nu[p]]++;
                        ed[p][2*nu[p]]=p;

                        // Copy the edges of the original vertex into the new
                        // one. Delete the edges of the original vertex, and
                        // update the relational table.
                        us=cycle_down(i,up);
                        while(i<j) {
                                qp=ed[up][i];
                                qs=ed[up][nu[up]+i];
                                neighbor.copy(p,k,up,i);
                                ed[p][k]=qp;
                                ed[p][nu[p]+k]=qs;
                                ed[qp][qs]=p;
                                ed[qp][nu[qp]+qs]=k;
                                ed[up][i]=-1;
                                i++;k++;
                        }
                        qs=i==nu[up]?0:i;
                } else {

                        // In this case, the zeroth edge is outside the cutting
                        // plane. Begin by searching backwards from the last
                        // edge until we find an edge which isn't outside.
                        i=nu[up]-1;
                        lp=ed[up][i];
                        lw=sure.test(lp,l);
                        while(lw==-1) {
                                i--;

                                // If i reaches zero, then we have a point in
                                // the plane all of whose edges are outside
                                // the cutting space, so we just exit
                                if(i==0) return true;
                                lp=ed[up][i];
                                lw=sure.test(lp,l);
                        }

                        // Now search forwards from zero
                        j=1;
                        qp=ed[up][j];
                        qw=sure.test(qp,q);
                        while(qw==-1) {
                                j++;
                                qp=ed[up][j];
                                qw=sure.test(qp,l);
                        }

                        // Compute the number of edges for the new vertex. In
                        // general it will be the number of outside edges
                        // found, plus two. But we need to recognize the
                        // special case when all but one edge is outside, and
                        // the remaining one is on the plane. For that case we
                        // have to reduce the edge count by one to prevent
                        // doubling up.
                        if(i==j&&qw==0) {
                                double_edge=true;
                                nu[p]=nu[up];
                        } else {
                                nu[p]=nu[up]-i+j+1;
                        }

                        // Add memory to store the vertex if it doesn't exist
                        // already
                        k=1;
                        while(nu[p]>=current_vertex_order) add_memory_vorder();
                        if(mec[nu[p]]==mem[nu[p]]) add_memory(nu[p]);

                        // Copy the edges of the original vertex into the new
                        // one. Delete the edges of the original vertex, and
                        // update the relational table.
                        neighbor.set_pointer(p,nu[p]);
                        ed[p]=mep[nu[p]]+(2*nu[p]+1)*mec[nu[p]]++;
                        ed[p][2*nu[p]]=p;
                        us=i++;
                        while(i<nu[up]) {
                                qp=ed[up][i];
                                qs=ed[up][nu[up]+i];
                                neighbor.copy(p,k,up,i);
                                ed[p][k]=qp;
                                ed[p][nu[p]+k]=qs;
                                ed[qp][qs]=p;
                                ed[qp][nu[qp]+qs]=k;
                                ed[up][i]=-1;
                                i++;k++;
                        }
                        i=0;
                        while(i<j) {
                                qp=ed[up][i];
                                qs=ed[up][nu[up]+i];
                                neighbor.copy(p,k,up,i);
                                ed[p][k]=qp;
                                ed[p][nu[p]+k]=qs;
                                ed[qp][qs]=p;
                                ed[qp][nu[qp]+qs]=k;
                                ed[up][i]=-1;
                                i++;k++;
                        }
                        qs=j;
                }
                if(!double_edge) {
                        neighbor.copy(p,k,up,qs);
                        neighbor.set(p,0,p_id);
                } else neighbor.copy(p,0,up,qs);

                // Add this point to the auxiliary delete stack
                if(stack2==current_delete2_size) add_memory_ds2();
                ds2[stack2++]=up;

                // Look at the edges on either side of the group that was
                // detected. We're going to commence facet computation by
                // moving along one of them. We are going to end up coming back
                // along the other one.
                cs=k;
                qp=up;q=u;
                i=ed[up][us];
                us=ed[up][nu[up]+us];
                up=i;
                ed[qp][2*nu[qp]]=-p;

        } else {

                // The search algorithm found an intersected edge between the
                // points lp and up. Create a new vertex between them which
                // lies on the cutting plane. Since u and l differ by at least
                // the tolerance, this division should never screw up.
                if(stack==current_delete_size) add_memory_ds();
                ds[stack++]=up;
                r=1/(u-l);
                pts[3*p]=(pts[3*lp]*u-pts[3*up]*l)*r;
                pts[3*p+1]=(pts[3*lp+1]*u-pts[3*up+1]*l)*r;
                pts[3*p+2]=(pts[3*lp+2]*u-pts[3*up+2]*l)*r;

                // This point will always have three edges. Connect one of them
                // to lp.
                nu[p]=3;
                if(mec[3]==mem[3]) add_memory(3);
                neighbor.set_pointer(p,3);
                neighbor.set(p,0,p_id);
                neighbor.copy(p,1,up,us);
                neighbor.copy(p,2,lp,ls);
                ed[p]=mep[3]+7*mec[3]++;
                ed[p][6]=p;
                ed[up][us]=-1;
                ed[lp][ls]=p;
                ed[lp][nu[lp]+ls]=1;
                ed[p][1]=lp;
                ed[p][nu[p]+1]=ls;
                cs=2;

                // Set the direction to move in
                qs=cycle_up(us,up);
                qp=up;q=u;
        }

        // When the code reaches here, we have initialized the first point, and
        // we have a direction for moving it to construct the rest of the facet
        cp=p;rp=p;p++;
        while(qp!=up||qs!=us) {

                // We're currently tracing round an intersected facet. Keep
                // moving around it until we find a point or edge which
                // intersects the plane.
                lp=ed[qp][qs];
                lw=sure.test(lp,l);

                if(lw==1) {

                        // The point is still in the cutting space. Just add it
                        // to the delete stack and keep moving.
                        if(stack==current_delete_size) add_memory_ds();
                        qs=cycle_up(ed[qp][nu[qp]+qs],lp);
                        qp=lp;
                        q=l;
                        ds[stack++]=qp;

                } else if(lw==-1) {

                        // The point is outside of the cutting space, so we've
                        // found an intersected edge. Introduce a regular point
                        // at the point of intersection. Connect it to the
                        // point we just tested. Also connect it to the previous
                        // new point in the facet we're constructing.
                        if(p==current_vertices) add_memory_vertices();
                        r=1/(q-l);
                        pts[3*p]=(pts[3*lp]*q-pts[3*qp]*l)*r;
                        pts[3*p+1]=(pts[3*lp+1]*q-pts[3*qp+1]*l)*r;
                        pts[3*p+2]=(pts[3*lp+2]*q-pts[3*qp+2]*l)*r;
                        nu[p]=3;
                        if(mec[3]==mem[3]) add_memory(3);
                        ls=ed[qp][qs+nu[qp]];
                        neighbor.set_pointer(p,3);
                        neighbor.set(p,0,p_id);
                        neighbor.copy(p,1,qp,qs);
                        neighbor.copy(p,2,lp,ls);
                        ed[p]=mep[3]+7*mec[3]++;
                        ed[p][6]=p;
                        ed[lp][ls]=p;
                        ed[lp][nu[lp]+ls]=1;
                        ed[p][1]=lp;
                        ed[p][0]=cp;
                        ed[p][nu[p]+1]=ls;
                        ed[p][nu[p]]=cs;
                        ed[cp][cs]=p;
                        ed[cp][nu[cp]+cs]=0;
                        ed[qp][qs]=-1;
                        qs=cycle_up(qs,qp);
                        cp=p++;
                        cs=2;
                } else {

                        // We've found a point which is on the cutting plane.
                        // We're going to introduce a new point right here, but
                        // first we need to figure out the number of edges it
                        // has.
                        if(p==current_vertices) add_memory_vertices();

                        // If the previous vertex detected a double edge, our
                        // new vertex will have one less edge.
                        k=double_edge?0:1;
                        qs=ed[qp][nu[qp]+qs];
                        qp=lp;
                        iqs=qs;

                        // Start testing the edges of the current point until
                        // we find one which isn't outside the cutting space
                        do {
                                k++;
                                qs=cycle_up(qs,qp);
                                lp=ed[qp][qs];
                                lw=sure.test(lp,l);
                        } while (lw==-1);

                        // Now we need to find out whether this marginal vertex
                        // we are on has been visited before, because if that's
                        // the case, we need to add vertices to the existing
                        // new vertex, rather than creating a fresh one. We also
                        // need to figure out whether we're in a case where we
                        // might be creating a duplicate edge.
                        j=-ed[qp][2*nu[qp]];
                        if(qp==up&&qs==us) {

                                // If we're heading into the final part of the
                                // new facet, then we never worry about the
                                // duplicate edge calculation.
                                new_double_edge=false;
                                if(j>0) k+=nu[j];
                        } else {
                                if(j>0) {

                                        // This vertex was visited before, so
                                        // count those vertices to the ones we
                                        // already have.
                                        k+=nu[j];

                                        // The only time when we might make a
                                        // duplicate edge is if the point we're
                                        // going to move to next is also a
                                        // marginal point, so test for that
                                        // first.
                                        if(lw==0) {

                                                // Now see whether this marginal point
                                                // has been visited before.
                                                i=-ed[lp][2*nu[lp]];
                                                if(i>0) {

                                                        // Now see if the last edge of that other
                                                        // marginal point actually ends up here.
                                                        if(ed[i][nu[i]-1]==j) {
                                                                new_double_edge=true;
                                                                k-=1;
                                                        } else new_double_edge=false;
                                                } else {

                                                        // That marginal point hasn't been visited
                                                        // before, so we probably don't have to worry
                                                        // about duplicate edges, except in the
                                                        // case when that's the way into the end
                                                        // of the facet, because that way always creates
                                                        // an edge.
                                                        if(j==rp&&lp==up&&ed[qp][nu[qp]+qs]==us) {
                                                                new_double_edge=true;
                                                                k-=1;
                                                        } else new_double_edge=false;
                                                }
                                        } else new_double_edge=false;
                                } else {

                                        // The vertex hasn't been visited
                                        // before, but let's see if it's
                                        // marginal
                                        if(lw==0) {

                                                // If it is, we need to check
                                                // for the case that it's a
                                                // small branch, and that we're
                                                // heading right back to where
                                                // we came from
                                                i=-ed[lp][2*nu[lp]];
                                                if(i==cp) {
                                                        new_double_edge=true;
                                                        k-=1;
                                                } else new_double_edge=false;
                                        } else new_double_edge=false;
                                }
                        }

                        // k now holds the number of edges of the new vertex
                        // we are forming. Add memory for it if it doesn't exist
                        // already.
                        while(k>=current_vertex_order) add_memory_vorder();
                        if(mec[k]==mem[k]) add_memory(k);

                        // Now create a new vertex with order k, or augment
                        // the existing one
                        if(j>0) {

                                // If we're augmenting a vertex but we don't
                                // actually need any more edges, just skip this
                                // routine to avoid memory confusion
                                if(nu[j]!=k) {
                                        // Allocate memory and copy the edges
                                        // of the previous instance into it
                                        neighbor.set_aux1(k);
                                        edp=mep[k]+(2*k+1)*mec[k]++;
                                        i=0;
                                        while(i<nu[j]) {
                                                neighbor.copy_aux1(j,i);
                                                edp[i]=ed[j][i];
                                                edp[k+i]=ed[j][nu[j]+i];
                                                i++;
                                        }
                                        edp[2*k]=j;

                                        // Remove the previous instance with
                                        // fewer vertices from the memory
                                        // structure
                                        edd=mep[nu[j]]+(2*nu[j]+1)*--mec[nu[j]];
                                        if(edd!=ed[j]) {
                                                for(lw=0;lw<=2*nu[j];lw++) ed[j][lw]=edd[lw];
                                                neighbor.set_aux2_copy(j,nu[j]);
                                                neighbor.copy_pointer(edd[2*nu[j]],j);
                                                ed[edd[2*nu[j]]]=ed[j];
                                        }
                                        neighbor.set_to_aux1(j);
                                        ed[j]=edp;
                                } else i=nu[j];
                        } else {

                                // Allocate a new vertex of order k
                                neighbor.set_pointer(p,k);
                                ed[p]=mep[k]+(2*k+1)*mec[k]++;
                                ed[p][2*k]=p;
                                if(stack2==current_delete2_size) add_memory_ds2();
                                ds2[stack2++]=qp;
                                pts[3*p]=pts[3*qp];
                                pts[3*p+1]=pts[3*qp+1];
                                pts[3*p+2]=pts[3*qp+2];
                                ed[qp][2*nu[qp]]=-p;
                                j=p++;
                                i=0;
                        }
                        nu[j]=k;

                        // Unless the previous case was a double edge, connect
                        // the first available edge of the new vertex to the
                        // last one in the facet
                        if(!double_edge) {
                                ed[j][i]=cp;
                                ed[j][nu[j]+i]=cs;
                                neighbor.set(j,i,p_id);
                                ed[cp][cs]=j;
                                ed[cp][nu[cp]+cs]=i;
                                i++;
                        }

                        // Copy in the edges of the underlying vertex,
                        // and do one less if this was a double edge
                        qs=iqs;
                        while(i<(new_double_edge?k:k-1)) {
                                qs=cycle_up(qs,qp);
                                lp=ed[qp][qs];ls=ed[qp][nu[qp]+qs];
                                neighbor.copy(j,i,qp,qs);
                                ed[j][i]=lp;
                                ed[j][nu[j]+i]=ls;
                                ed[lp][ls]=j;
                                ed[lp][nu[lp]+ls]=i;
                                ed[qp][qs]=-1;
                                i++;
                        }
                        qs=cycle_up(qs,qp);
                        cs=i;
                        cp=j;
                        neighbor.copy(j,new_double_edge?0:cs,qp,qs);

                        // Update the double_edge flag, to pass it
                        // to the next instance of this routine
                        double_edge=new_double_edge;
                }
        }

        // Connect the final created vertex to the initial one
        ed[cp][cs]=rp;
        ed[rp][0]=cp;
        ed[cp][nu[cp]+cs]=0;
        ed[rp][nu[rp]+0]=cs;

        // Delete points: first, remove any duplicates
        i=0;
        while(i<stack) {
                j=ds[i];
                if(ed[j][nu[j]]!=-1) {
                        ed[j][nu[j]]=-1;
                        i++;
                } else ds[i]=ds[--stack];
        }

        // Add the points in the auxiliary delete stack,
        // and reset their back pointers
        for(i=0;i<stack2;i++) {
                j=ds2[i];
                ed[j][2*nu[j]]=j;
                if(ed[j][nu[j]]!=-1) {
                        ed[j][nu[j]]=-1;
                        if(stack==current_delete_size) add_memory_ds();
                        ds[stack++]=j;
                }
        }

        // Scan connections and add in extras
        for(i=0;i<stack;i++) {
                cp=ds[i];
                for(j=0;j<nu[cp];j++) {
                        qp=ed[cp][j];
                        if(qp!=-1) {
                                if(ed[qp][nu[qp]]!=-1) {
                                        if(stack==current_delete_size) add_memory_ds();
                                        ds[stack++]=qp;
                                        ed[qp][nu[qp]]=-1;
                                }
                        }
                }
        }
        up=0;

        // Delete them from the array structure
        while(stack>0) {
                while(ed[--p][nu[p]]==-1) {
                        j=nu[p];
                        mec[j]--;
                        for(i=0;i<=2*j;i++) ed[p][i]=(mep[j]+(2*j+1)*mec[j])[i];
                        neighbor.set_aux2_copy(p,j);
                        neighbor.copy_pointer(ed[p][2*j],p);
                        ed[ed[p][2*j]]=ed[p];
                }
                up=ds[--stack];
                if(up<p) {

                        // Vertex management
                        pts[3*up]=pts[3*p];
                        pts[3*up+1]=pts[3*p+1];
                        pts[3*up+2]=pts[3*p+2];

                        // Memory management
                        j=nu[up];
                        mec[j]--;
                        for(i=0;i<=2*j;i++) ed[up][i]=(mep[j]+(2*j+1)*mec[j])[i];
                        neighbor.set_aux2_copy(up,j);
                        neighbor.copy_pointer(ed[up][2*j],up);
                        neighbor.copy_pointer(up,p);
                        ed[ed[up][2*j]]=ed[up];

                        // Edge management
                        ed[up]=ed[p];
                        nu[up]=nu[p];
                        for(i=0;i<nu[up];i++) {
                                if(ed[up][i]==-1)
                                        voropp_fatal_error("Dangling edge found",VOROPP_INTERNAL_ERROR);
                                ed[ed[up][i]][ed[up][nu[up]+i]]=up;
                        }
                        ed[up][2*nu[up]]=up;
                } else up=p++;
        }

        // Check for any vertices of zero order
        if(mec[0]>0) voropp_fatal_error("Zero order vertex formed",VOROPP_INTERNAL_ERROR);

        // Collapse any order 2 vertices and exit
        return collapse_order2();
}

/** During the creation of a new facet in the plane routine, it is possible
 * that some order two vertices may arise. This routine removes them.
 * Suppose an order two vertex joins c and d. If there's a edge between
 * c and d already, then the order two vertex is just removed; otherwise,
 * the order two vertex is removed and c and d are joined together directly.
 * It is possible this process will create order two or order one vertices,
 * and the routine is continually run until all of them are removed.
 * \return False if the vertex removal was unsuccessful, indicative of the cell
 *         reducing to zero volume and disappearing; true if the vertex removal
 *         was successful. */
template<class n_option>
inline bool voronoicell_base<n_option>::collapse_order2() {
        if(!collapse_order1()) return false;
        int a,b,i,j,k,l;
        while(mec[2]>0) {

                // Pick a order 2 vertex and read in its edges
                i=--mec[2];
                j=mep[2][5*i];k=mep[2][5*i+1];
                if(j==k) {
#if VOROPP_VERBOSE >=1
                        cerr << "Order two vertex joins itself" << endl;
#endif
                        return false;
                }

                // Scan the edges of j to see if joins k
                for(l=0;l<nu[j];l++) {
                        if(ed[j][l]==k) break;
                }

                // If j doesn't already join k, join them together.
                // Otherwise delete the connection to the current
                // vertex from j and k.
                a=mep[2][5*i+2];b=mep[2][5*i+3];i=mep[2][5*i+4];
                if(l==nu[j]) {
                        ed[j][a]=k;
                        ed[k][b]=j;
                        ed[j][nu[j]+a]=b;
                        ed[k][nu[k]+b]=a;
                } else {
                        if(!delete_connection(j,a,false)) return false;
                        if(!delete_connection(k,b,true)) return false;
                }

                // Compact the memory
                --p;
                if(up==i) up=0;
                if(p!=i) {
                        if(up==p) up=i;
                        pts[3*i]=pts[3*p];
                        pts[3*i+1]=pts[3*p+1];
                        pts[3*i+2]=pts[3*p+2];
                        for(k=0;k<nu[p];k++) ed[ed[p][k]][ed[p][nu[p]+k]]=i;
                        neighbor.copy_pointer(i,p);
                        ed[i]=ed[p];
                        nu[i]=nu[p];
                        ed[i][2*nu[i]]=i;
                }

                // Collapse any order 1 vertices if they were created
                if(!collapse_order1()) return false;
        }
        return true;
}

/** Order one vertices can potentially be created during the order two collapse
 * routine. This routine keeps removing them until there are none left.
 * \return False if the vertex removal was unsuccessful, indicative of the cell
 *         having zero volume and disappearing; true if the vertex removal was
 *         successful. */
template<class n_option>
inline bool voronoicell_base<n_option>::collapse_order1() {
        int i,j,k;
        while(mec[1]>0) {
                up=0;
#if VOROPP_VERBOSE >=1
                cerr << "Order one collapse" << endl;
#endif
                i=--mec[1];
                j=mep[1][3*i];k=mep[1][3*i+1];
                i=mep[1][3*i+2];
                if(!delete_connection(j,k,false)) return false;
                --p;
                if(up==i) up=0;
                if(p!=i) {
                        if(up==p) up=i;
                        pts[3*i]=pts[3*p];
                        pts[3*i+1]=pts[3*p+1];
                        pts[3*i+2]=pts[3*p+2];
                        for(k=0;k<nu[p];k++) ed[ed[p][k]][ed[p][nu[p]+k]]=i;
                        neighbor.copy_pointer(i,p);
                        ed[i]=ed[p];
                        nu[i]=nu[p];
                        ed[i][2*nu[i]]=i;
                }
        }
        return true;
}

/** This routine deletes the kth edge of vertex j and reorganizes the memory.
 * If the neighbor computation is enabled, we also have to supply an handedness
 * flag to decide whether to preserve the plane on the left or right of the
 * connection.
 * \return False if a zero order vertex was formed, indicative of the cell
 *         disappearing; true if the vertex removal was successful. */
template<class n_option>
inline bool voronoicell_base<n_option>::delete_connection(int j,int k,bool hand) {
        int q=hand?k:cycle_up(k,j);
        int i=nu[j]-1,l,*edp,*edd,m;
        if(i<1) {
                cout << "Zero order vertex formed" << endl;
                return false;
        }
        if(mec[i]==mem[i]) add_memory(i);
        neighbor.set_aux1(i);
        for(l=0;l<q;l++) neighbor.copy_aux1(j,l);
        while(l<i) {
                neighbor.copy_aux1_shift(j,l);
                l++;
        }
        edp=mep[i]+(2*i+1)*mec[i]++;
        edp[2*i]=j;
        for(l=0;l<k;l++) {
                edp[l]=ed[j][l];
                edp[l+i]=ed[j][l+nu[j]];
        }
        while(l<i) {
                m=ed[j][l+1];
                edp[l]=m;
                k=ed[j][l+nu[j]+1];
                edp[l+i]=k;
                ed[m][nu[m]+k]--;
                l++;
        }

        edd=mep[nu[j]]+(2*nu[j]+1)*--mec[nu[j]];
        for(l=0;l<=2*nu[j];l++) ed[j][l]=edd[l];
        neighbor.set_aux2_copy(j,nu[j]);
        neighbor.set_to_aux2(edd[2*nu[j]]);
        neighbor.set_to_aux1(j);
        ed[edd[2*nu[j]]]=edd;
        ed[j]=edp;
        nu[j]=i;
        return true;
}

/** Cuts a Voronoi cell using the influence of a particle at (x,y,z), first
 * calculating the modulus squared of this vector before passing it to the
 * main nplane() routine. Zero is supplied as the plane ID, which will be
 * ignored unless neighbor tracking is enabled.
 * \param[in] (x,y,z) the vector to cut the cell by.
 * \return False if the plane cut deleted the cell entirely, true otherwise. */
template<class n_option>
inline bool voronoicell_base<n_option>::plane(fpoint x,fpoint y,fpoint z) {
        fpoint rsq=x*x+y*y+z*z;
        return nplane(x,y,z,rsq,0);
}

/** This version of the plane routine just makes up the plane ID to be zero. It
 * will only be referenced if neighbor tracking is enabled.
 * \param[in] (x,y,z) the vector to cut the cell by.
 * \param[in] rsq the modulus squared of the vector.
 * \return False if the plane cut deleted the cell entirely, true otherwise. */
template<class n_option>
inline bool voronoicell_base<n_option>::plane(fpoint x,fpoint y,fpoint z,fpoint rsq) {
        return nplane(x,y,z,rsq,0);
}

/** This routine calculates the modulus squared of the vector before passing it
 * to the main nplane() routine with full arguments.
 * \param[in] (x,y,z) the vector to cut the cell by.
 * \param[in] p_id the plane ID (for neighbor tracking only).
 * \return False if the plane cut deleted the cell entirely, true otherwise. */
template<class n_option>
inline bool voronoicell_base<n_option>::nplane(fpoint x,fpoint y,fpoint z,int p_id) {
        fpoint rsq=x*x+y*y+z*z;
        return nplane(x,y,z,rsq,p_id);
}

/** This is a simple inline function for picking out the index of the next edge
 * counterclockwise at the current vertex.
 * \param[in] a the index of an edge of the current vertex.
 * \param[in] p the number of the vertex.
 * \return 0 if a=nu[p]-1, or a+1 otherwise. */
template<class n_option>
inline int voronoicell_base<n_option>::cycle_up(int a,int p) {
        return a==nu[p]-1?0:a+1;
}

/** This is a simple inline function for picking out the index of the next edge
 * clockwise from the current vertex.
 * \param[in] a the index of an edge of the current vertex.
 * \param[in] p the number of the vertex.
 * \return nu[p]-1 if a=0, or a-1 otherwise. */
template<class n_option>
inline int voronoicell_base<n_option>::cycle_down(int a,int p) {
        return a==0?nu[p]-1:a-1;
}

/** Calculates the volume of the Voronoi cell, by decomposing the cell into
 * tetrahedra extending outward from the zeroth vertex, whose volumes are
 * evaluated using a scalar triple product.
 * \return A floating point number holding the calculated volume. */
template<class n_option>
fpoint voronoicell_base<n_option>::volume() {
        const fpoint fe=1/48.0;
        fpoint vol=0;
        int i,j,k,l,m,n;
        fpoint ux,uy,uz,vx,vy,vz,wx,wy,wz;
        for(i=1;i<p;i++) {
                ux=pts[0]-pts[3*i];
                uy=pts[1]-pts[3*i+1];
                uz=pts[2]-pts[3*i+2];
                for(j=0;j<nu[i];j++) {
                        k=ed[i][j];
                        if(k>=0) {
                                ed[i][j]=-1-k;
                                l=cycle_up(ed[i][nu[i]+j],k);
                                vx=pts[3*k]-pts[0];
                                vy=pts[3*k+1]-pts[1];
                                vz=pts[3*k+2]-pts[2];
                                m=ed[k][l];ed[k][l]=-1-m;
                                while(m!=i) {
                                        n=cycle_up(ed[k][nu[k]+l],m);
                                        wx=pts[3*m]-pts[0];
                                        wy=pts[3*m+1]-pts[1];
                                        wz=pts[3*m+2]-pts[2];
                                        vol+=ux*vy*wz+uy*vz*wx+uz*vx*wy-uz*vy*wx-uy*vx*wz-ux*vz*wy;
                                        k=m;l=n;vx=wx;vy=wy;vz=wz;
                                        m=ed[k][l];ed[k][l]=-1-m;
                                }
                        }
                }
        }
        reset_edges();
        return vol*fe;
}

/** Calculates the areas of each face of the Voronoi cell and prints the
 * results to an output stream.
 * \param[in] os an output stream to write to. */
template<class n_option>
void voronoicell_base<n_option>::output_face_areas(ostream &os) {
        bool later=false;
        fpoint area;
        int i,j,k,l,m,n;
        fpoint ux,uy,uz,vx,vy,vz,wx,wy,wz;
        for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                if(k>=0) {
                        area=0;
                        ed[i][j]=-1-k;
                        l=cycle_up(ed[i][nu[i]+j],k);
                        m=ed[k][l];ed[k][l]=-1-m;
                        while(m!=i) {
                                n=cycle_up(ed[k][nu[k]+l],m);
                                ux=pts[3*k]-pts[3*i];
                                uy=pts[3*k+1]-pts[3*i+1];
                                uz=pts[3*k+2]-pts[3*i+2];
                                vx=pts[3*m]-pts[3*i];
                                vy=pts[3*m+1]-pts[3*i+1];
                                vz=pts[3*m+2]-pts[3*i+2];
                                wx=uy*vz-uz*vy;
                                wy=uz*vx-ux*vz;
                                wz=ux*vy-uy*vx;
                                area+=sqrt(wx*wx+wy*wy+wz*wz);
                                k=m;l=n;
                                m=ed[k][l];ed[k][l]=-1-m;
                        }
                        if(later) os << " ";else later=true;
                        os << 0.125*area;
                }
        }
        reset_edges();
}


/** Calculates the total surface area of the Voronoi cell.
 * \return The computed area. */
template<class n_option>
fpoint voronoicell_base<n_option>::surface_area() {
        fpoint area=0;
        int i,j,k,l,m,n;
        fpoint ux,uy,uz,vx,vy,vz,wx,wy,wz;
        for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                if(k>=0) {
                        ed[i][j]=-1-k;
                        l=cycle_up(ed[i][nu[i]+j],k);
                        m=ed[k][l];ed[k][l]=-1-m;
                        while(m!=i) {
                                n=cycle_up(ed[k][nu[k]+l],m);
                                ux=pts[3*k]-pts[3*i];
                                uy=pts[3*k+1]-pts[3*i+1];
                                uz=pts[3*k+2]-pts[3*i+2];
                                vx=pts[3*m]-pts[3*i];
                                vy=pts[3*m+1]-pts[3*i+1];
                                vz=pts[3*m+2]-pts[3*i+2];
                                wx=uy*vz-uz*vy;
                                wy=uz*vx-ux*vz;
                                wz=ux*vy-uy*vx;
                                area+=sqrt(wx*wx+wy*wy+wz*wz);
                                k=m;l=n;
                                m=ed[k][l];ed[k][l]=-1-m;
                        }
                }
        }
        reset_edges();
        return 0.125*area;
}


/** Calculates the centroid of the Voronoi cell, by decomposing the cell into
 * tetrahedra extending outward from the zeroth vertex.
 * \param[out] (cx,cy,cz) references to floating point numbers in which to
 *                        pass back the centroid vector. */
template<class n_option>
void voronoicell_base<n_option>::centroid(fpoint &cx,fpoint &cy,fpoint &cz) {
        fpoint tvol,vol=0;cx=cy=cz=0;
        int i,j,k,l,m,n;
        fpoint ux,uy,uz,vx,vy,vz,wx,wy,wz;
        for(i=1;i<p;i++) {
                ux=pts[0]-pts[3*i];
                uy=pts[1]-pts[3*i+1];
                uz=pts[2]-pts[3*i+2];
                for(j=0;j<nu[i];j++) {
                        k=ed[i][j];
                        if(k>=0) {
                                ed[i][j]=-1-k;
                                l=cycle_up(ed[i][nu[i]+j],k);
                                vx=pts[3*k]-pts[0];
                                vy=pts[3*k+1]-pts[1];
                                vz=pts[3*k+2]-pts[2];
                                m=ed[k][l];ed[k][l]=-1-m;
                                while(m!=i) {
                                        n=cycle_up(ed[k][nu[k]+l],m);
                                        wx=pts[3*m]-pts[0];
                                        wy=pts[3*m+1]-pts[1];
                                        wz=pts[3*m+2]-pts[2];
                                        tvol=ux*vy*wz+uy*vz*wx+uz*vx*wy-uz*vy*wx-uy*vx*wz-ux*vz*wy;
                                        vol+=tvol;
                                        cx+=(wx+vx-ux)*tvol;
                                        cy+=(wy+vy-uy)*tvol;
                                        cz+=(wz+vz-uz)*tvol;
                                        k=m;l=n;vx=wx;vy=wy;vz=wz;
                                        m=ed[k][l];ed[k][l]=-1-m;
                                }
                        }
                }
        }
        reset_edges();
        if(vol>tolerance_sq) {
                vol=0.125/vol;
                cx=cx*vol+0.5*pts[0];
                cy=cy*vol+0.5*pts[1];
                cz=cz*vol+0.5*pts[2];
        } else cx=cy=cz=0;
}

/** Computes the maximum radius squared of a vertex from the center of the
 * cell. It can be used to determine when enough particles have been testing an
 * all planes that could cut the cell have been considered.
 * \return The maximum radius squared of a vertex.*/
template<class n_option>
fpoint voronoicell_base<n_option>::max_radius_squared() {
        int i;fpoint r,s;
        r=pts[0]*pts[0]+pts[1]*pts[1]+pts[2]*pts[2];
        for(i=3;i<3*p;i+=3) {
                s=pts[i]*pts[i]+pts[i+1]*pts[i+1]+pts[i+2]*pts[i+2];
                if(s>r) r=s;
        }
        return r;
}

/** Calculates the total edge distance of the Voronoi cell.
 * \return A floating point number holding the calculated distance. */
template<class n_option>
fpoint voronoicell_base<n_option>::total_edge_distance() {
        int i,j,k;
        fpoint dis=0,dx,dy,dz;
        for(i=0;i<p-1;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                if(k>i) {
                        dx=pts[3*k]-pts[3*i];
                        dy=pts[3*k+1]-pts[3*i+1];
                        dz=pts[3*k+2]-pts[3*i+2];
                        dis+=sqrt(dx*dx+dy*dy+dz*dz);
                }
        }
        return 0.5*dis;
}

/** Outputs the edges of the Voronoi cell in POV-Ray format to an open file
 * stream, displacing the cell by given vector.
 * \param[in] os a output stream to write to.
 * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
 */
template<class n_option>
void voronoicell_base<n_option>::draw_pov(ostream &os,fpoint x,fpoint y,fpoint z) {
        int i,j,k;fpoint ux,uy,uz;
        for(i=0;i<p;i++) {
                ux=x+0.5*pts[3*i];uy=y+0.5*pts[3*i+1];uz=z+0.5*pts[3*i+2];
                os << "sphere{<" << ux << "," << uy << "," << uz << ">,r}\n";
                for(j=0;j<nu[i];j++) {
                        k=ed[i][j];
                        if(k<i) os << "cylinder{<" << ux << "," << uy << "," << uz << ">,<" << x+0.5*pts[3*k] << "," << y+0.5*pts[3*k+1] << "," << z+0.5*pts[3*k+2] << ">,r}\n";
                }
        }
}

/** An overloaded version of the draw_pov routine, that outputs the edges of
 * the Voronoi cell in POV-Ray format to a file.
 * \param[in] filename the file to write to.
 * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
 */
template<class n_option>
inline void voronoicell_base<n_option>::draw_pov(const char *filename,fpoint x,fpoint y,fpoint z) {
        ofstream os;
        os.open(filename,ofstream::out|ofstream::trunc);
        draw_pov(os,x,y,z);
        os.close();
}

/** An overloaded version of the draw_pov routine, that outputs the edges of the
 * Voronoi cell (in POV-Ray format) to standard output.
 * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
 */
template<class n_option>
inline void voronoicell_base<n_option>::draw_pov(fpoint x,fpoint y,fpoint z) {
        draw_pov(cout,x,y,z);
}

/** Outputs the edges of the Voronoi cell in gnuplot format to an output stream.
 * \param[in] os a reference to an output stream to write to.
 * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
 */
template<class n_option>
void voronoicell_base<n_option>::draw_gnuplot(ostream &os,fpoint x,fpoint y,fpoint z) {
        int i,j,k;fpoint ux,uy,uz;
        for(i=0;i<p;i++) {
                ux=x+0.5*pts[3*i];uy=y+0.5*pts[3*i+1];uz=z+0.5*pts[3*i+2];
                for(j=0;j<nu[i];j++) {
                        k=ed[i][j];
                        if(ed[i][j]<i) os << ux << " " << uy << " " << uz << "\n" << x+0.5*pts[3*k] << " " << y+0.5*pts[3*k+1] << " " << z+0.5*pts[3*k+2] << "\n\n\n";
                }
        }
}

/** An overloaded version of the draw_gnuplot routine that writes directly to
 * a file.
 * \param[in] filename The name of the file to write to.
 * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
 */
template<class n_option>
inline void voronoicell_base<n_option>::draw_gnuplot(const char *filename,fpoint x,fpoint y,fpoint z) {
        ofstream os;
        os.open(filename,ofstream::out|ofstream::trunc);
        draw_gnuplot(os,x,y,z);
        os.close();
}

/** An overloaded version of the draw_gnuplot routine, that prints to the
 * standard output.
 * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
 */
template<class n_option>
inline void voronoicell_base<n_option>::draw_gnuplot(fpoint x,fpoint y,fpoint z) {
        draw_gnuplot(cout,x,y,z);
}

/** Outputs the Voronoi cell in the POV mesh2 format, described in section
 * 1.3.2.2 of the POV-Ray documentation. The mesh2 output consists of a list of
 * vertex vectors, followed by a list of triangular faces. The routine also
 * makes use of the optional inside_vector specification, which makes the mesh
 * object solid, so the the POV-Ray Constructive Solid Geometry (CSG) can be
 * applied.
 * \param[in] os an output stream to write to.
 * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
 */
template<class n_option>
inline void voronoicell_base<n_option>::draw_pov_mesh(ostream &os,fpoint x,fpoint y,fpoint z) {
        int i,j,k,l,m,n;
        os << "mesh2 {\nvertex_vectors {\n" << p << ",\n";
        for(i=0;i<p;i++) {
                os << "<" << x+0.5*pts[3*i] << "," << y+0.5*pts[3*i+1] << "," << z+0.5*pts[3*i+2] << ">,\n";
        }
        os << "}\nface_indices {\n" << 2*(p-2) << ",\n";
        for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                if(k>=0) {
                        ed[i][j]=-1-k;
                        l=cycle_up(ed[i][nu[i]+j],k);
                        m=ed[k][l];ed[k][l]=-1-m;
                        while(m!=i) {
                                n=cycle_up(ed[k][nu[k]+l],m);
                                os << "<" << i << "," << k << "," << m << ">\n";
                                k=m;l=n;
                                m=ed[k][l];ed[k][l]=-1-m;
                        }
                }
        }
        reset_edges();
        os << "}\ninside_vector <0,0,1>\n}\n";
}

/** Several routines in the class that gather cell-based statistics internally
 * track their progress by flipping edges to negative so that they know what
 * parts of the cell have already been tested. This function resets them back
 * to positive. When it is called, it assumes that every edge in the routine
 * should have already been flipped to negative, and it bails out with an
 * internal error if it encounters a positive edge. */
template<class n_option>
inline void voronoicell_base<n_option>::reset_edges() {
        int i,j;
        for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
                if(ed[i][j]>=0) voropp_fatal_error("Edge reset routine found a previously untested edge",VOROPP_INTERNAL_ERROR);
                ed[i][j]=-1-ed[i][j];
        }
}

/** An overloaded version of the draw_pov_mesh routine, that writes directly to a
 * file.
 * \param[in] filename a filename to write to.
 * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
 */
template<class n_option>
inline void voronoicell_base<n_option>::draw_pov_mesh(const char *filename,fpoint x,fpoint y,fpoint z) {
        ofstream os;
        os.open(filename,ofstream::out|ofstream::trunc);
        draw_pov_mesh(os,x,y,z);
        os.close();
}

/** An overloaded version of the draw_pov_mesh routine, that prints to the
 * standard output.
 * \param[in] (x,y,z) a displacement vector to be added to the cell's position.
 */
template<class n_option>
inline void voronoicell_base<n_option>::draw_pov_mesh(fpoint x,fpoint y,fpoint z) {
        draw_pov_mesh(cout,x,y,z);
}

/** Randomly perturbs the points in the Voronoi cell by an amount r.
 * \param[in] r the amount to perturb each coordinate by. */
template<class n_option>
inline void voronoicell_base<n_option>::perturb(fpoint r) {
        for(int i=0;i<3*p;i++) pts[i]+=(2*fpoint(rand())/RAND_MAX-1)*r;
}

/** Initializes the suretest class and creates a buffer for marginal points. */
suretest::suretest() : current_marginal(init_marginal) {
        sn=new int[2*current_marginal];
}

/** Suretest destructor that deallocates memory for the marginal cases. */
suretest::~suretest() {
        delete [] sn;
}

/** Sets up the suretest class with a particular test plane, and removes any
 * special cases from the table.
 * \param[in] (x,y,z) the normal vector to the plane.
 * \param[in] rsq the distance along this vector of the plane. */
inline void suretest::init(fpoint x,fpoint y,fpoint z,fpoint rsq) {
        sc=0;px=x;py=y;pz=z;prsq=rsq;
}

/** Checks to see if a given vertex is inside, outside or within the test
 * plane. If the point is far away from the test plane, the routine immediately
 * returns whether it is inside or outside. If the routine is close the the
 * plane and within the specified tolerance, then the special check_marginal()
 * routine is called.
 * \param[in] n the vertex to test.
 * \param[out] ans the result of the scalar product used in evaluating the
 *                 location of the point.
 * \return -1 if the point is inside the plane, 1 if the point is outside the
 *         plane, or 0 if the point is within the plane. */
inline int suretest::test(int n,fpoint &ans) {
        ans=px*p[3*n]+py*p[3*n+1]+pz*p[3*n+2]-prsq;
        if(ans<-tolerance2) {
                return -1;
        } else if(ans>tolerance2) {
                return 1;
        }
        return check_marginal(n,ans);
}

/** Checks to see if a given vertex is inside, outside or within the test
 * plane, for the case when the point has been detected to be very close to the
 * plane. The routine ensures that the returned results are always consistent
 * with previous tests, by keeping a table of any marginal results. The routine
 * first sees if the vertex is in the table, and if it finds a previously
 * computed result it uses that. Otherwise, it computes a result for this
 * vertex and adds it the table.
 * \param[in] n the vertex to test.
 * \param[in] ans the result of the scalar product used in evaluating
 *                the location of the point.
 * \return -1 if the point is inside the plane, 1 if the point is outside the
 *         plane, or 0 if the point is within the plane. */
int suretest::check_marginal(int n,fpoint &ans) {
        int i;
        for(i=0;i<sc;i+=2) if(sn[i]==n) return sn[i+1];
        if(sc==2*current_marginal) {
                i=2*current_marginal;
                if(i>max_marginal) voropp_fatal_error("Marginal case buffer allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
#if VOROPP_VERBOSE >=2
                cerr << "Marginal cases buffer scaled up to " << i << endl;
#endif
                int *psn=new int[2*i];
                for(int j=0;j<2*current_marginal;j++) psn[j]=sn[j];
                delete [] sn;sn=psn;
        }
        sn[sc++]=n;
        sn[sc++]=ans>tolerance?1:(ans<-tolerance?-1:0);
        return sn[sc-1];
}

/** Prints the vertices, their edges, the relation table, and also notifies if
 * any memory errors are visible. */
template<class n_option>
void voronoicell_base<n_option>::print_edges() {
        int j;
        for(int i=0;i<p;i++) {
                cout << i << " " << nu[i] << "  ";
                for(j=0;j<nu[i];j++) cout << " " << ed[i][j];
                cout << "   ";
                while(j<2*nu[i]) cout << " " << ed[i][j++];
                cout << "    " << ed[i][j];
                neighbor.print_edges(i);
                cout << "    " << pts[3*i] << " " << pts[3*i+1] << " " << pts[3*i+2];
                cout << " " << ed[i];
                if(ed[i]>=mep[nu[i]]+mec[nu[i]]*(2*nu[i]+1)) cout << " Memory error";
                cout << endl;
        }
}

/** For each face of the Voronoi cell, this routine prints the out the normal
 * vector of the face, and scales it to the distance from the cell center to
 * that plane.
 * \param[in] os an output stream to write to. */
template<class n_option>
void voronoicell_base<n_option>::output_normals(ostream &os) {
        int i,j,k;bool later=false;
        for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                if(k>=0) {
                        if(later) os << " ";
                        else later=true;
                        output_normals_search(os,i,j,k);
                }
        }
        reset_edges();
}

/** This inline routine is called by output_normals(). It attempts to construct
 * a single normal vector that is associated with a particular face. It first
 * traces around the face, trying to find two vectors along the face edges
 * whose vector product is above the numerical tolerance. It then constructs
 * the normal vector using this product. If the face is too small, and the none
 * of the vector products are large enough, the routine may return (0,0,0) as
 * the normal vector.
 * \param[in] os an output stream to write to.
 * \param[in] i the initial vertex of the face to test.
 * \param[in] j the index of an edge of the vertex.
 * \param[in] k the neighboring vertex of i, set to ed[i][j]. */
template<class n_option>
inline void voronoicell_base<n_option>::output_normals_search(ostream &os,int i,int j,int k) {
        ed[i][j]=-1-k;
        int l=cycle_up(ed[i][nu[i]+j],k),m;
        fpoint ux,uy,uz,vx,vy,vz,wx,wy,wz,wmag;
        do {
                m=ed[k][l];ed[k][l]=-1-m;
                ux=pts[3*m]-pts[3*k];
                uy=pts[3*m+1]-pts[3*k+1];
                uz=pts[3*m+2]-pts[3*k+2];

                // Test to see if the length of this edge is above the tolerance
                if(ux*ux+uy*uy+uz*uz>tolerance_sq) {
                        while(m!=i) {
                                l=cycle_up(ed[k][nu[k]+l],m);
                                k=m;m=ed[k][l];ed[k][l]=-1-m;
                                vx=pts[3*m]-pts[3*k];
                                vy=pts[3*m+1]-pts[3*k+1];
                                vz=pts[3*m+2]-pts[3*k+2];

                                // Construct the vector product of this edge with
                                // the previous one
                                wx=uz*vy-uy*vz;
                                wy=ux*vz-uz*vx;
                                wz=uy*vx-ux*vy;
                                wmag=wx*wx+wy*wy+wz*wz;

                                // Test to see if this vector product of the
                                // two edges is above the tolerance
                                if(wmag>tolerance_sq) {

                                        // Construct the normal vector and print it
                                        wmag=1/sqrt(wmag);
                                        os << "(" << wx*wmag << "," << wy*wmag << "," << wz*wmag << ")";

                                        // Mark all of the remaining edges of this
                                        // face and exit
                                        while(m!=i) {
                                                l=cycle_up(ed[k][nu[k]+l],m);
                                                k=m;m=ed[k][l];ed[k][l]=-1-m;
                                        }
                                        return;
                                }
                        }
                        os << "(0,0,0)";
                        return;
                }
                l=cycle_up(ed[k][nu[k]+l],m);
                k=m;
        } while (k!=i);
        os << "(0,0,0)";
}


/** Returns the number of faces of a computed Voronoi cell.
 * \return The number of faces. */
template<class n_option>
int voronoicell_base<n_option>::number_of_faces() {
        int i,j,k,l,m,s=0;
        for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                if(k>=0) {
                        s++;
                        ed[i][j]=-1-k;
                        l=cycle_up(ed[i][nu[i]+j],k);
                        do {
                                m=ed[k][l];
                                ed[k][l]=-1-m;
                                l=cycle_up(ed[k][nu[k]+l],m);
                                k=m;
                        } while (k!=i);

                }
        }
        reset_edges();
        return s;
}

/** Outputs the vertex orders to an open output stream.
 * \param[in] os the output stream to write to. */
template<class n_option>
void voronoicell_base<n_option>::output_vertex_orders(ostream &os) {
        if(p==0) return;
        os << nu[0];
        for(int i=1;i<p;i++) os << " " << nu[i];
}

/** Outputs the vertex vectors to an open output stream using the local
 * coordinate system.
 * \param[in] os the output stream to write to. */
template<class n_option>
void voronoicell_base<n_option>::output_vertices(ostream &os) {
        if(p==0) return;
        os << "(" << pts[0]*0.5 << "," << pts[1]*0.5 << "," << pts[2]*0.5 << ")";
        for(int i=3;i<3*p;i+=3) os << " (" << pts[i]*0.5 << "," << pts[i+1]*0.5 << "," << pts[i+2]*0.5 << ")";
}


/** Outputs the vertex vectors to an open output stream using the global
 * coordinate system.
 * \param[in] os the output stream to write to.
 * \param[in] (x,y,z) the position vector of the particle in the global
 *                    coordinate system. */
template<class n_option>
void voronoicell_base<n_option>::output_vertices(ostream &os,fpoint x,fpoint y,fpoint z) {
        if(p==0) return;
        os << "(" << x+pts[0]*0.5 << "," << y+pts[1]*0.5 << "," << z+pts[2]*0.5 << ")";
        for(int i=3;i<3*p;i+=3) os << " (" << x+pts[i]*0.5 << "," << y+pts[i+1]*0.5 << "," << z+pts[i+2]*0.5 << ")";
}

/** This routine outputs the perimeters of each face.
 * \param[in] os an open output stream to write to. */
template<class n_option>
void voronoicell_base<n_option>::output_face_perimeters(ostream &os) {
        int i,j,k,l,m;bool later=false;
        fpoint dx,dy,dz,perim;
        for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                if(k>=0) {
                        dx=pts[3*k]-pts[3*i];
                        dy=pts[3*k+1]-pts[3*i+1];
                        dz=pts[3*k+2]-pts[3*i+2];
                        perim=sqrt(dx*dx+dy*dy+dz*dz);
                        ed[i][j]=-1-k;
                        l=cycle_up(ed[i][nu[i]+j],k);
                        do {
                                m=ed[k][l];
                                dx=pts[3*m]-pts[3*k];
                                dy=pts[3*m+1]-pts[3*k+1];
                                dz=pts[3*m+2]-pts[3*k+2];
                                perim+=sqrt(dx*dx+dy*dy+dz*dz);
                                ed[k][l]=-1-m;
                                l=cycle_up(ed[k][nu[k]+l],m);
                                k=m;
                        } while (k!=i);
                        if(later) os << " ";else later=true;
                        os << 0.5*perim;
                }
        }
        reset_edges();
}

/** For each face, this routine outputs a bracketed sequence of numbers
 * containing a list of all the vertices that make up that face.
 * \param[in] os an open output stream to write to. */
template<class n_option>
void voronoicell_base<n_option>::output_face_vertices(ostream &os) {
        int i,j,k,l,m;bool later=false;
        for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                if(k>=0) {
                        if(later) os << " ";else later=true;
                        os << "(" << i;
                        ed[i][j]=-1-k;
                        l=cycle_up(ed[i][nu[i]+j],k);
                        do {
                                os << "," << k;
                                m=ed[k][l];
                                ed[k][l]=-1-m;
                                l=cycle_up(ed[k][nu[k]+l],m);
                                k=m;
                        } while (k!=i);
                        os << ")";
                }
        }
        reset_edges();
}

/** Outputs a list of the number of edges in each face.
 * \param[in] os an open output stream to write to. */
template<class n_option>
void voronoicell_base<n_option>::output_face_orders(ostream &os) {
        int i,j,k,l,m,q;bool later=false;
        for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                if(k>=0) {
                        q=1;
                        ed[i][j]=-1-k;
                        l=cycle_up(ed[i][nu[i]+j],k);
                        do {
                                q++;
                                m=ed[k][l];
                                ed[k][l]=-1-m;
                                l=cycle_up(ed[k][nu[k]+l],m);
                                k=m;
                        } while (k!=i);
                        if(later) os << " ";else later=true;
                        os << q;
                }
        }
        reset_edges();
}

/** Computes the number of edges that each face has and outputs a frequency
 * table of the results.
 * \param[in] os an open output stream to write to. */
template<class n_option>
void voronoicell_base<n_option>::output_face_freq_table(ostream &os) {
        int *stat,*pstat,current_facet_size=init_facet_size,newc,maxf=0;
        stat=new int[current_facet_size];
        int i,j,k,l,m,q;
        for(i=0;i<current_facet_size;i++) stat[i]=0;
        for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
                k=ed[i][j];
                if(k>=0) {
                        q=1;
                        ed[i][j]=-1-k;
                        l=cycle_up(ed[i][nu[i]+j],k);
                        do {
                                q++;
                                m=ed[k][l];
                                ed[k][l]=-1-m;
                                l=cycle_up(ed[k][nu[k]+l],m);
                                k=m;
                        } while (k!=i);
                        if(q>=current_facet_size) {
                                newc=current_facet_size*2;
                                pstat=new int[newc];
                                for(k=0;k<current_facet_size;k++) pstat[k]=stat[k];
                                while(k<newc) pstat[k]=0;
                                delete [] stat;
                                current_facet_size=newc;
                                stat=pstat;
                        }
                        stat[q]++;
                        if(q>maxf) maxf=q;
                }
        }
        reset_edges();
        os << "(0," << stat[0] << ")";
        for(i=1;i<=maxf;i++) os << " (" << i << "," << stat[i] << ")";
        delete [] stat;
}

/** If the template is instantiated with the neighbor tracking turned on,
 * then this routine will label all the facets of the current cell. Otherwise
 * this routine does nothing. */
template<class n_option>
void voronoicell_base<n_option>::label_facets() {
        neighbor.label_facets();
}

/** If the template is instantiated with the neighbor tracking turned on, then
 * this routine will print out a list of all the neighbors of a given cell.
 * Otherwise, this routine does nothing.
 * \param[in] os an open output stream to write to.
 * \param[in] later a boolean value to determine whether or not to write a
 *                  space character before the first entry. */
template<class n_option>
void voronoicell_base<n_option>::output_neighbors(ostream &os,bool later) {
        neighbor.neighbors(os,later);
}

/** If the template is instantiated with the neighbor tracking turned on, then
 * this routine will check that the neighbor information is consistent, by
 * tracing around every facet, and ensuring that all the neighbor information
 * for that facet refers to the same neighbor. If the neighbor tracking isn't
 * turned on, this routine does nothing. */
template<class n_option>
void voronoicell_base<n_option>::check_facets() {
        neighbor.check_facets();
}

/** This routine tests to see whether the cell intersects a plane by starting
 * from the guess point up. If up intersects, then it immediately returns true.
 * Otherwise, it calls the plane_intersects_track() routine.
 * \param[in] (x,y,z) the normal vector to the plane.
 * \param[in] rsq the distance along this vector of the plane.
 * \return False if the plane does not intersect the plane, true if it does. */
template<class n_option>
bool voronoicell_base<n_option>::plane_intersects(fpoint x,fpoint y,fpoint z,fpoint rsq) {
        fpoint g=x*pts[3*up]+y*pts[3*up+1]+z*pts[3*up+2];
        if(g<rsq) return plane_intersects_track(x,y,z,rsq,g);
        return true;
}

/** This routine tests to see if a cell intersects a plane. It first tests a
 * random sample of approximately sqrt(p)/4 points. If any of those are
 * intersect, then it immediately returns true. Otherwise, it takes the closest
 * point and passes that to plane_intersect_track() routine.
 * \param[in] (x,y,z) the normal vector to the plane.
 * \param[in] rsq the distance along this vector of the plane.
 * \return False if the plane does not intersect the plane, true if it does. */
template<class n_option>
bool voronoicell_base<n_option>::plane_intersects_guess(fpoint x,fpoint y,fpoint z,fpoint rsq) {
        up=0;
        fpoint g=x*pts[3*up]+y*pts[3*up+1]+z*pts[3*up+2];
        if(g<rsq) {
                int ca=1,cc=p>>3,mp=1;
                fpoint m;
                while(ca<cc) {
                        m=x*pts[3*mp]+y*pts[3*mp+1]+z*pts[3*mp+2];
                        if(m>g) {
                                if(m>rsq) return true;
                                g=m;up=mp;
                        }
                        ca+=mp++;
                }
                return plane_intersects_track(x,y,z,rsq,g);
        }
        return true;
}

/* This routine tests to see if a cell intersects a plane, by tracing over the cell from
 * vertex to vertex, starting at up. It is meant to be called either by plane_intersects()
 * or plane_intersects_track(), when those routines cannot immediately resolve the case.
 * \param[in] (x,y,z) the normal vector to the plane.
 * \param[in] rsq the distance along this vector of the plane.
 * \param[in] g the distance of up from the plane.
 * \return False if the plane does not intersect the plane, true if it does. */
template<class n_option>
inline bool voronoicell_base<n_option>::plane_intersects_track(fpoint x,fpoint y,fpoint z,fpoint rsq,fpoint g) {
        int count=0,ls,us,tp;
        fpoint t;
        // The test point is outside of the cutting space
        for(us=0;us<nu[up];us++) {
                tp=ed[up][us];
                t=x*pts[3*tp]+y*pts[3*tp+1]+z*pts[3*tp+2];
                if(t>g) {
                        ls=ed[up][nu[up]+us];
                        up=tp;
                        while (t<rsq) {
                                if(++count>=p) {
#if VOROPP_VERBOSE >=1
                                        cerr << "Bailed out of convex calculation" << endl;
#endif
                                        for(tp=0;tp<p;tp++) if(x*pts[3*tp]+y*pts[3*tp+1]+z*pts[3*tp+2]>rsq) return true;
                                        return false;
                                }

                                // Test all the neighbors of the current point
                                // and find the one which is closest to the
                                // plane
                                for(us=0;us<ls;us++) {
                                        tp=ed[up][us];
                                        g=x*pts[3*tp]+y*pts[3*tp+1]+z*pts[3*tp+2];
                                        if(g>t) break;
                                }
                                if(us==ls) {
                                        us++;
                                        while(us<nu[up]) {
                                                tp=ed[up][us];
                                                g=x*pts[3*tp]+y*pts[3*tp+1]+z*pts[3*tp+2];
                                                if(g>t) break;
                                                us++;
                                        }
                                        if(us==nu[up]) return false;
                                }
                                ls=ed[up][nu[up]+us];up=tp;t=g;
                        }
                        return true;
                }
        }
        return false;
}

/** Counts the number of edges of the Voronoi cell.
 * \return the number of edges. */
template<class n_option>
int voronoicell_base<n_option>::number_of_edges() {
        int i,edges=0;
        for(i=0;i<p;i++) edges+=nu[i];
        return edges>>1;
}

/** This constructs the neighbor_track class, within a current
 * voronoicell_neighbor class. It allocates memory for neighbor storage in a
 * similar way to the voronoicell constructor.
 * \param[in] ivc a pointer to the parent voronoicell_neighbor class. */
neighbor_track::neighbor_track(voronoicell_base<neighbor_track> *ivc) : vc(ivc) {
        int i;
        mne=new int*[vc->current_vertex_order];
        ne=new int*[vc->current_vertices];
        for(i=0;i<3;i++) mne[i]=new int[init_n_vertices*i];
        mne[3]=new int[init_3_vertices*3];
        for(i=4;i<vc->current_vertex_order;i++) mne[i]=new int[init_n_vertices*i];
}

/** The destructor for the neighbor_track class deallocates the arrays
 * for neighbor tracking. */
neighbor_track::~neighbor_track() {
        for(int i=0;i<vc->current_vertex_order;i++) if(vc->mem[i]>0) delete [] mne[i];
        delete [] mne;
        delete [] ne;
}

/** This allocates a single array for neighbor tracking.
 * \param[in] i the vertex order of the array to be extended.
 * \param[in] m the size of the array to be extended. */
inline void neighbor_track::allocate(int i,int m) {
        mne[i]=new int[m*i];
}

/** This increases the size of the ne[] array.
 * \param[in] i the new size of the array. */
inline void neighbor_track::add_memory_vertices(int i) {
        int **pp;
        pp=new int*[i];
        for(int j=0;j<vc->current_vertices;j++) pp[j]=ne[j];
        delete [] ne;ne=pp;
}

/** This increases the size of the maximum allowable vertex order in the
 * neighbor tracking.
 * \param[in] i the new size of the neighbor vertex order array. */
inline void neighbor_track::add_memory_vorder(int i) {
        int **p2;
        p2=new int*[i];
        for(int j=0;j<vc->current_vertex_order;j++) p2[j]=mne[j];
        delete [] mne;mne=p2;
}

/** This initializes the neighbor information for a rectangular box and is
 * called during the initialization routine for the voronoicell class. */
inline void neighbor_track::init() {
        int *q;
        q=mne[3];
        q[0]=-5;q[1]=-3;q[2]=-1;
        q[3]=-5;q[4]=-2;q[5]=-3;
        q[6]=-5;q[7]=-1;q[8]=-4;
        q[9]=-5;q[10]=-4;q[11]=-2;
        q[12]=-6;q[13]=-1;q[14]=-3;
        q[15]=-6;q[16]=-3;q[17]=-2;
        q[18]=-6;q[19]=-4;q[20]=-1;
        q[21]=-6;q[22]=-2;q[23]=-4;
        ne[0]=q;ne[1]=q+3;ne[2]=q+6;ne[3]=q+9;
        ne[4]=q+12;ne[5]=q+15;ne[6]=q+18;ne[7]=q+21;
}

/** This initializes the neighbor information for an octahedron. The eight
 * initial faces are assigned ID numbers from -1 to -8. */
inline void neighbor_track::init_octahedron() {
        int *q;
        q=mne[4];
        q[0]=-5;q[1]=-6;q[2]=-7;q[3]=-8;
        q[4]=-1;q[5]=-2;q[6]=-3;q[7]=-4;
        q[8]=-6;q[9]=-5;q[10]=-2;q[11]=-1;
        q[12]=-8;q[13]=-7;q[14]=-4;q[15]=-3;
        q[16]=-5;q[17]=-8;q[18]=-3;q[19]=-2;
        q[20]=-7;q[21]=-6;q[22]=-1;q[23]=-4;
        ne[0]=q;ne[1]=q+4;ne[2]=q+8;ne[3]=q+12;ne[4]=q+16;ne[5]=q+20;
}

/** This initializes the neighbor information for an tetrahedron. The four
 * initial faces are assigned ID numbers from -1 to -4.*/
inline void neighbor_track::init_tetrahedron() {
        int *q;
        q=mne[3];
        q[0]=-4;q[1]=-3;q[2]=-2;
        q[3]=-3;q[4]=-4;q[5]=-1;
        q[6]=-4;q[7]=-2;q[8]=-1;
        q[9]=-2;q[10]=-3;q[11]=-1;
        ne[0]=q;ne[1]=q+3;ne[2]=q+6;ne[3]=q+9;
}

/** This is a basic operation to set a new pointer in the ne[] array.
 * \param[in] p the index in the ne[] array to set.
 * \param[in] n the order of the vertex. */
inline void neighbor_track::set_pointer(int p,int n) {
        ne[p]=mne[n]+n*vc->mec[n];
}

/** This is a basic operation to copy ne[c][d] to ne[a][b]. */
inline void neighbor_track::copy(int a,int b,int c,int d) {
        ne[a][b]=ne[c][d];
}

/** This is a basic operation to carry out ne[a][b]=c. */
inline void neighbor_track::set(int a,int b,int c) {
        ne[a][b]=c;
}

/** This is a basic operation to set the auxiliary pointer paux1.
 * \param[in] k the order of the vertex to point to. */
inline void neighbor_track::set_aux1(int k) {
        paux1=mne[k]+k*vc->mec[k];
}

/** This is a basic operation to copy a neighbor into paux1.*/
inline void neighbor_track::copy_aux1(int a,int b) {
        paux1[b]=ne[a][b];
}

/** This is a basic operation to copy a neighbor into paux1 with a shift. It is
 * used in the delete_connection() routine of the voronoicell class. */
inline void neighbor_track::copy_aux1_shift(int a,int b) {
        paux1[b]=ne[a][b+1];
}

/** This routine sets the second auxiliary pointer to a new section of memory,
 * and then copies existing neighbor information into it. */
inline void neighbor_track::set_aux2_copy(int a,int b) {
        paux2=mne[b]+b*vc->mec[b];
        for(int i=0;i<b;i++) ne[a][i]=paux2[i];
}

/** This is a basic routine to copy ne[b] into ne[a]. */
inline void neighbor_track::copy_pointer(int a,int b) {
        ne[a]=ne[b];
}

/** This sets ne[j] to the first auxiliary pointer. */
inline void neighbor_track::set_to_aux1(int j) {
        ne[j]=paux1;
}

/** This sets ne[j] to the second auxiliary pointer. */
inline void neighbor_track::set_to_aux2(int j) {
        ne[j]=paux2;
}

/** This prints out the neighbor information for vertex i. */
inline void neighbor_track::print_edges(int i) {
        cout << "    (";
        for(int j=0;j<vc->nu[i];j++) {
                cout << ne[i][j] << (j==vc->nu[i]-1?")":",");
        }
}

/** This allocates a new array and sets the auxiliary pointer to it. */
inline void neighbor_track::allocate_aux1(int i) {
        paux1=new int[i*vc->mem[i]];
}

/** This deletes a particular neighbor array and switches the pointer to the
 * auxiliary pointer. */
inline void neighbor_track::switch_to_aux1(int i) {
        delete [] mne[i];
        mne[i]=paux1;
}

/** This routine copies neighbor information into the auxiliary pointer. */
inline void neighbor_track::copy_to_aux1(int i,int m) {
        paux1[m]=mne[i][m];
}

/** This sets ne[k] to the auxiliary pointer with an offset. */
inline void neighbor_track::set_to_aux1_offset(int k,int m) {
        ne[k]=paux1+m;
}

/** This routine checks to make sure the neighbor information of each face is
 * consistent.*/
void neighbor_track::check_facets() {
        int **edp,*nup;edp=vc->ed;nup=vc->nu;
        int i,j,k,l,m,q;
        for(i=0;i<vc->p;i++) for(j=0;j<nup[i];j++) {
                k=edp[i][j];
                if(k>=0) {
                        edp[i][j]=-1-k;
                        q=ne[i][j];
                        l=vc->cycle_up(edp[i][nup[i]+j],k);
                        do {
                                m=edp[k][l];
                                edp[k][l]=-1-m;
                                if(ne[k][l]!=q) cerr << "Facet error at (" << k << "," << l << ")=" << ne[k][l] << ", started from (" << i << "," << j << ")=" << q << endl;
                                l=vc->cycle_up(edp[k][nup[k]+l],m);
                                k=m;
                        } while (k!=i);
                }
        }
        vc->reset_edges();
}

/** This routine provides a list of plane IDs.
 * \param[in] os an output stream to write to.
 * \param[in] later a boolean value to determine whether or not to write a
 *                  space character before the first entry. */
void neighbor_track::neighbors(ostream &os,bool later) {
        int **edp=vc->ed,*nup=vc->nu;
        int i,j,k,l,m;
        for(i=0;i<vc->p;i++) for(j=0;j<nup[i];j++) {
                k=edp[i][j];
                if(k>=0) {
                        if(later) os << " ";else later=true;
                        os << ne[i][j];
                        edp[i][j]=-1-k;
                        l=vc->cycle_up(edp[i][nup[i]+j],k);
                        do {
                                m=edp[k][l];
                                edp[k][l]=-1-m;
                                l=vc->cycle_up(edp[k][nup[k]+l],m);
                                k=m;
                        } while (k!=i);
                }
        }
        vc->reset_edges();
}

/** This routine labels the facets in an arbitrary order, starting from one. */
void neighbor_track::label_facets() {
        int **edp,*nup;edp=vc->ed;nup=vc->nu;
        int i,j,k,l,m,q=1;
        for(i=0;i<vc->p;i++) for(j=0;j<nup[i];j++) {
                k=edp[i][j];
                if(k>=0) {
                        edp[i][j]=-1-k;
                        ne[i][j]=q;
                        l=vc->cycle_up(edp[i][nup[i]+j],k);
                        do {
                                m=edp[k][l];
                                edp[k][l]=-1-m;
                                ne[k][l]=q;
                                l=vc->cycle_up(edp[k][nup[k]+l],m);
                                k=m;
                        } while (k!=i);
                        q++;
                }
        }
        vc->reset_edges();
}

---