cell.cc
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cell.cc
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	// Voro++, a 3D cell-based Voronoi library
	//
	// Author : Chris H. Rycroft (LBL / UC Berkeley)
	// Email : chr@alum.mit.edu
	// Date : August 30th 2011

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

	#include <cmath>
	#include <cstring>

	#include "config.hh"
	#include "common.hh"
	#include "cell.hh"

	namespace voro {

	/** Constructs a Voronoi cell and sets up the initial memory. */
	voronoicell_base::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 double[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]), stacke(ds+current_delete_size),
	ds2(new int[current_delete2_size]), stacke2(ds2+current_delete_size),
	current_marginal(init_marginal), marg(new int[current_marginal]) {
	int i;
	for(i=0;i<3;i++) {
	mem[i]=init_n_vertices;mec[i]=0;
	mep[i]=new int[init_n_vertices*((i<<1)+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*((i<<1)+1)];
	}
	}

	/** The voronoicell destructor deallocates all the dynamic memory. */
	voronoicell_base::~voronoicell_base() {
	for(int i=current_vertex_order-1;i>=0;i--) if(mem[i]>0) delete [] mep[i];
	delete [] marg;
	delete [] ds2;delete [] ds;
	delete [] mep;delete [] mec;
	delete [] mem;delete [] pts;
	delete [] nu;delete [] ed;
	}

	/** Ensures that enough memory is allocated prior to carrying out a copy.
	* \param[in] vc a reference to the specialized version of the calling class.
	* \param[in] vb a pointered to the class to be copied. */
	template<class vc_class>
	void voronoicell_base::check_memory_for_copy(vc_class &vc,voronoicell_base* vb) {
	while(current_vertex_order<vb->current_vertex_order) add_memory_vorder(vc);
	for(int i=0;i<current_vertex_order;i++) while(mem[i]<vb->mec[i]) add_memory(vc,i,ds2);
	while(current_vertices<vb->p) add_memory_vertices(vc);
	}

	/** Copies the vertex and edge information from another class. The routine
	* assumes that enough memory is available for the copy.
	* \param[in] vb a pointer to the class to copy. */
	void voronoicell_base::copy(voronoicell_base* vb) {
	int i,j;
	p=vb->p;up=0;
	for(i=0;i<current_vertex_order;i++) {
	mec[i]=vb->mec[i];
	for(j=0;j<mec[i](2i+1);j++) mep[i][j]=vb->mep[i][j];
	for(j=0;j<mec[i](2i+1);j+=2i+1) ed[mep[i][j+2i]]=mep[i]+j;
	}
	for(i=0;i<p;i++) nu[i]=vb->nu[i];
	for(i=0;i<3*p;i++) pts[i]=vb->pts[i];
	}

	/** Copies the information from another voronoicell class into this
	* class, extending memory allocation if necessary.
	* \param[in] c the class to copy. */
	void voronoicell_neighbor::operator=(voronoicell &c) {
	voronoicell_base vb=((voronoicell_base) &c);
	check_memory_for_copy(*this,vb);copy(vb);
	int i,j;
	for(i=0;i<c.current_vertex_order;i++) {
	for(j=0;j<c.mec[i]*i;j++) mne[i][j]=0;
	for(j=0;j<c.mec[i];j++) ne[c.mep[i][(2i+1)j+2i]]=mne[i]+(ji);
	}
	}

	/** Copies the information from another voronoicell_neighbor class into this
	* class, extending memory allocation if necessary.
	* \param[in] c the class to copy. */
	void voronoicell_neighbor::operator=(voronoicell_neighbor &c) {
	voronoicell_base vb=((voronoicell_base) &c);
	check_memory_for_copy(*this,vb);copy(vb);
	int i,j;
	for(i=0;i<c.current_vertex_order;i++) {
	for(j=0;j<c.mec[i]*i;j++) mne[i][j]=c.mne[i][j];
	for(j=0;j<c.mec[i];j++) ne[c.mep[i][(2i+1)j+2i]]=mne[i]+(ji);
	}
	}

	/** Translates the vertices of the Voronoi cell by a given vector.
	* \param[in] (x,y,z) the coordinates of the vector. */
	void voronoicell_base::translate(double x,double y,double z) {
	x=2;y=2;z*=2;
	double *ptsp=pts;
	while(ptsp<pts+3*p) {
	(ptsp++)=x;(ptsp++)=y;*(ptsp++)=z;
	}
	}

	/** 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 vc_class>
	void voronoicell_base::add_memory(vc_class &vc,int i,int *stackp2) {
	int s=(i<<1)+1;
	if(mem[i]==0) {
	vc.n_allocate(i,init_n_vertices);
	mep[i]=new int[init_n_vertices*s];
	mem[i]=init_n_vertices;
	#if VOROPP_VERBOSE >=2
	fprintf(stderr,"Order %d vertex memory created\n",i);
	#endif
	} else {
	int j=0,k,*l;
	mem[i]<<=1;
	if(mem[i]>max_n_vertices) voro_fatal_error("Point memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
	#if VOROPP_VERBOSE >=2
	fprintf(stderr,"Order %d vertex memory scaled up to %d\n",i,mem[i]);
	#endif
	l=new int[s*mem[i]];
	int m=0;
	vc.n_allocate_aux1(i);
	while(j<s*mec[i]) {
	k=mep[i][j+(i<<1)];
	if(k>=0) {
	ed[k]=l+j;
	vc.n_set_to_aux1_offset(k,m);
	} else {
	int *dsp;
	for(dsp=ds2;dsp<stackp2;dsp++) {
	if(ed[*dsp]==mep[i]+j) {
	ed[*dsp]=l+j;
	vc.n_set_to_aux1_offset(*dsp,m);
	break;
	}
	}
	if(dsp==stackp2) voro_fatal_error("Couldn't relocate dangling pointer",VOROPP_INTERNAL_ERROR);
	#if VOROPP_VERBOSE >=3
	fputs("Relocated dangling pointer",stderr);
	#endif
	}
	for(k=0;k<s;k++,j++) l[j]=mep[i][j];
	for(k=0;k<i;k++,m++) vc.n_copy_to_aux1(i,m);
	}
	delete [] mep[i];
	mep[i]=l;
	vc.n_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 vc_class>
	void voronoicell_base::add_memory_vertices(vc_class &vc) {
	int i=(current_vertices<<1),j,*pp,pnu;
	if(i>max_vertices) voro_fatal_error("Vertex memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
	#if VOROPP_VERBOSE >=2
	fprintf(stderr,"Vertex memory scaled up to %d\n",i);
	#endif
	double *ppts;
	pp=new int*[i];
	for(j=0;j<current_vertices;j++) pp[j]=ed[j];
	delete [] ed;ed=pp;
	vc.n_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 double[3*i];
	for(j=0;j<3*current_vertices;j++) ppts[j]=pts[j];
	delete [] pts;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 vc_class>
	void voronoicell_base::add_memory_vorder(vc_class &vc) {
	int i=(current_vertex_order<<1),j,p1,*p2;
	if(i>max_vertex_order) voro_fatal_error("Vertex order memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
	#if VOROPP_VERBOSE >=2
	fprintf(stderr,"Vertex order memory scaled up to %d\n",i);
	#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;
	vc.n_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. */
	void voronoicell_base::add_memory_ds(int *&stackp) {
	current_delete_size<<=1;
	if(current_delete_size>max_delete_size) voro_fatal_error("Delete stack 1 memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
	#if VOROPP_VERBOSE >=2
	fprintf(stderr,"Delete stack 1 memory scaled up to %d\n",current_delete_size);
	#endif
	int dsn=new int[current_delete_size],dsnp=dsn,*dsp=ds;
	while(dsp<stackp) (dsnp++)=(dsp++);
	delete [] ds;ds=dsn;stackp=dsnp;
	stacke=ds+current_delete_size;
	}

	/** 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. */
	void voronoicell_base::add_memory_ds2(int *&stackp2) {
	current_delete2_size<<=1;
	if(current_delete2_size>max_delete2_size) voro_fatal_error("Delete stack 2 memory allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
	#if VOROPP_VERBOSE >=2
	fprintf(stderr,"Delete stack 2 memory scaled up to %d\n",current_delete2_size);
	#endif
	int dsn=new int[current_delete2_size],dsnp=dsn,*dsp=ds2;
	while(dsp<stackp2) (dsnp++)=(dsp++);
	delete [] ds2;ds2=dsn;stackp2=dsnp;
	stacke2=ds2+current_delete2_size;
	}

	/** 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. */
	void voronoicell_base::init_base(double xmin,double xmax,double ymin,double ymax,double zmin,double 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=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=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=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;
	*nu=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). */
	void voronoicell_base::init_octahedron_base(double l) {
	for(int i=0;i<current_vertex_order;i++) mec[i]=0;up=0;
	mec[4]=p=6;l*=2;
	*pts=-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=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=q;ed[1]=q+9;ed[2]=q+18;ed[3]=q+27;ed[4]=q+36;ed[5]=q+45;
	*nu=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. */
	void voronoicell_base::init_tetrahedron_base(double x0,double y0,double z0,double x1,double y1,double z1,double x2,double y2,double z2,double x3,double y3,double z3) {
	for(int i=0;i<current_vertex_order;i++) mec[i]=0;up=0;
	mec[3]=p=4;
	pts=x02;pts[1]=y02;pts[2]=z02;
	pts[3]=x12;pts[4]=y12;pts[5]=z1*2;
	pts[6]=x22;pts[7]=y22;pts[8]=z2*2;
	pts[9]=x32;pts[10]=y32;pts[11]=z3*2;
	int *q=mep[3];
	*q=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=q;ed[1]=q+7;ed[2]=q+14;ed[3]=q+21;
	*nu=nu[1]=nu[2]=nu[3]=3;
	}

	/** 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. */
	void voronoicell_base::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)
	printf("Relational error at point %d, edge %d.\n",i,j);
	}

	/** 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. */
	void voronoicell_base::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])
	printf("Duplicate edges: (%d,%d) and (%d,%d) [%d]\n",i,j,i,k,ed[i][j]);
	}

	/** Constructs the relational table if the edges have been specified. */
	void voronoicell_base::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]) voro_fatal_error("Relation table construction failed",VOROPP_INTERNAL_ERROR);
	}
	ed[i][nu[i]+j]=l;
	}
	}

	/** Starting from a point within the current cutting plane, this routine attempts
	* to find an edge to a point outside the cutting plane. This prevents the plane
	* routine from .
	* \param[in] vc a reference to the specialized version of the calling class.
	* \param[in,out] up */
	template<class vc_class>
	inline bool voronoicell_base::search_for_outside_edge(vc_class &vc,int &up) {
	int i,lp,lw,j(ds2),stackp2(ds2);
	double l;
	*(stackp2++)=up;
	while(j<stackp2) {
	up=*(j++);
	for(i=0;i<nu[up];i++) {
	lp=ed[up][i];
	lw=m_test(lp,l);
	if(lw==-1) return true;
	else if(lw==0) add_to_stack(vc,lp,stackp2);
	}
	}
	return false;
	}

	/** Adds a point to the auxiliary delete stack if it is not already there.
	* \param[in] vc a reference to the specialized version of the calling class.
	* \param[in] lp the index of the point to add.
	* \param[in,out] stackp2 a pointer to the end of the stack entries. */
	template<class vc_class>
	inline void voronoicell_base::add_to_stack(vc_class &vc,int lp,int *&stackp2) {
	for(int k(ds2);k<stackp2;k++) if(k==lp) return;
	if(stackp2==stacke2) add_memory_ds2(stackp2);
	*(stackp2++)=lp;
	}

	/** 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] vc a reference to the specialized version of the calling class.
	* \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 vc_class>
	bool voronoicell_base::nplane(vc_class &vc,double x,double y,double z,double rsq,int p_id) {
	int count=0,i,j,k,lp=up,cp,qp,rp,stackp(ds),stackp2(ds2),*dsp;
	int us=0,ls=0,qs,iqs,cs,uw,qw,lw;
	int edp,edd;
	double u,l,r,q;
	bool complicated_setup=false,new_double_edge=false,double_edge=false;
	bool exception=false;

	// Initialize the safe testing routine
	n_marg=0;px=x;py=y;pz=z;prsq=rsq;

	// Test approximately sqrt(n)/4 points for their proximity to the plane
	// and keep the one which is closest
	uw=m_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

	{
	if(uw==1) {
	// The test point is inside the cutting plane.
	us=0;
	do {
	lp=ed[up][us];
	lw=m_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) { exception=true; goto exit; }
	u=l;up=lp;
	for(us=0;us<ls;us++) {
	lp=ed[up][us];
	lw=m_test(lp,l);
	if(l<u) break;
	}
	if(us==ls) {
	us++;
	while(us<nu[up]) {
	lp=ed[up][us];
	lw=m_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=m_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) { exception=true; goto exit; }
	u=q;up=qp;
	for(us=0;us<qs;us++) {
	qp=ed[up][us];
	qw=m_test(qp,q);
	if(u<q) break;
	}
	if(us==qs) {
	us++;
	while(us<nu[up]) {
	qp=ed[up][us];
	qw=m_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;
	}
	}

	exit:
	if (exception) {
	// 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
	fputs("Bailed out of convex calculation\n",stderr);
	#endif
	qw=1;lw=0;
	for(qp=0;qp<p;qp++) {
	qw=m_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=m_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=m_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(vc);

	if(complicated_setup) {

	// We want to be strict about reaching the conclusion that the
	// cell is entirely within the cutting plane. It's not enough
	// to find a vertex that has edges which are all inside or on
	// the plane. If the vertex has neighbors that are also on the
	// plane, we should check those too.
	if(!search_for_outside_edge(vc,up)) return false;

	// 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[3p]=pts[3up];
	pts[3p+1]=pts[3up+1];
	pts[3p+2]=pts[3up+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];
	lw=m_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=m_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=m_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(vc);
	if(mec[nu[p]]==mem[nu[p]]) add_memory(vc,nu[p],stackp2);
	vc.n_set_pointer(p,nu[p]);
	ed[p]=mep[nu[p]]+((nu[p]<<1)+1)*mec[nu[p]]++;
	ed[p][nu[p]<<1]=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];
	vc.n_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=m_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=m_test(lp,l);
	}

	// Now search forwards from zero
	j=1;
	qp=ed[up][j];
	qw=m_test(qp,q);
	while(qw==-1) {
	j++;
	qp=ed[up][j];
	qw=m_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(vc);
	if(mec[nu[p]]==mem[nu[p]]) add_memory(vc,nu[p],stackp2);

	// Copy the edges of the original vertex into the new
	// one. Delete the edges of the original vertex, and
	// update the relational table.
	vc.n_set_pointer(p,nu[p]);
	ed[p]=mep[nu[p]]+((nu[p]<<1)+1)*mec[nu[p]]++;
	ed[p][nu[p]<<1]=p;
	us=i++;
	while(i<nu[up]) {
	qp=ed[up][i];
	qs=ed[up][nu[up]+i];
	vc.n_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];
	vc.n_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) {
	vc.n_copy(p,k,up,qs);
	vc.n_set(p,0,p_id);
	} else vc.n_copy(p,0,up,qs);

	// Add this point to the auxiliary delete stack
	if(stackp2==stacke2) add_memory_ds2(stackp2);
	*(stackp2++)=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][nu[qp]<<1]=-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(stackp==stacke) add_memory_ds(stackp);
	*(stackp++)=up;
	r=u/(u-l);l=1-r;
	pts[3p]=pts[3lp]r+pts[3up]*l;
	pts[3p+1]=pts[3lp+1]r+pts[3up+1]*l;
	pts[3p+2]=pts[3lp+2]r+pts[3up+2]*l;

	// This point will always have three edges. Connect one of them
	// to lp.
	nu[p]=3;
	if(mec[3]==mem[3]) add_memory(vc,3,stackp2);
	vc.n_set_pointer(p,3);
	vc.n_set(p,0,p_id);
	vc.n_copy(p,1,up,us);
	vc.n_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=m_test(lp,l);

	if(lw==1) {

	// The point is still in the cutting space. Just add it
	// to the delete stack and keep moving.
	qs=cycle_up(ed[qp][nu[qp]+qs],lp);
	qp=lp;
	q=l;
	if(stackp==stacke) add_memory_ds(stackp);
	*(stackp++)=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(vc);
	r=q/(q-l);l=1-r;
	pts[3p]=pts[3lp]r+pts[3qp]*l;
	pts[3p+1]=pts[3lp+1]r+pts[3qp+1]*l;
	pts[3p+2]=pts[3lp+2]r+pts[3qp+2]*l;
	nu[p]=3;
	if(mec[3]==mem[3]) add_memory(vc,3,stackp2);
	ls=ed[qp][qs+nu[qp]];
	vc.n_set_pointer(p,3);
	vc.n_set(p,0,p_id);
	vc.n_copy(p,1,qp,qs);
	vc.n_copy(p,2,lp,ls);
	ed[p]=mep[3]+7*mec[3]++;
	*ed[p]=cp;
	ed[p][1]=lp;
	ed[p][3]=cs;
	ed[p][4]=ls;
	ed[p][6]=p;
	ed[lp][ls]=p;
	ed[lp][nu[lp]+ls]=1;
	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(vc);

	// 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=m_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][nu[qp]<<1];
	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][nu[lp]<<1];
	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][nu[lp]<<1];
	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(vc);
	if(mec[k]==mem[k]) add_memory(vc,k,stackp2);

	// 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
	vc.n_set_aux1(k);
	edp=mep[k]+((k<<1)+1)*mec[k]++;
	i=0;
	while(i<nu[j]) {
	vc.n_copy_aux1(j,i);
	edp[i]=ed[j][i];
	edp[k+i]=ed[j][nu[j]+i];
	i++;
	}
	edp[k<<1]=j;

	// Remove the previous instance with
	// fewer vertices from the memory
	// structure
	edd=mep[nu[j]]+((nu[j]<<1)+1)*--mec[nu[j]];
	if(edd!=ed[j]) {
	for(lw=0;lw<=(nu[j]<<1);lw++) ed[j][lw]=edd[lw];
	vc.n_set_aux2_copy(j,nu[j]);
	vc.n_copy_pointer(edd[nu[j]<<1],j);
	ed[edd[nu[j]<<1]]=ed[j];
	}
	vc.n_set_to_aux1(j);
	ed[j]=edp;
	} else i=nu[j];
	} else {

	// Allocate a new vertex of order k
	vc.n_set_pointer(p,k);
	ed[p]=mep[k]+((k<<1)+1)*mec[k]++;
	ed[p][k<<1]=p;
	if(stackp2==stacke2) add_memory_ds2(stackp2);
	*(stackp2++)=qp;
	pts[3p]=pts[3qp];
	pts[3p+1]=pts[3qp+1];
	pts[3p+2]=pts[3qp+2];
	ed[qp][nu[qp]<<1]=-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;
	vc.n_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];
	vc.n_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;
	vc.n_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]=cp;
	ed[cp][nu[cp]+cs]=0;
	ed[rp][nu[rp]]=cs;

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

	// Add the points in the auxiliary delete stack,
	// and reset their back pointers
	for(dsp=ds2;dsp<stackp2;dsp++) {
	j=*dsp;
	ed[j][nu[j]<<1]=j;
	if(ed[j][nu[j]]!=-1) {
	ed[j][nu[j]]=-1;
	if(stackp==stacke) add_memory_ds(stackp);
	*(stackp++)=j;
	}
	}

	// Scan connections and add in extras
	for(dsp=ds;dsp<stackp;dsp++) {
	cp=*dsp;
	for(edp=ed[cp];edp<ed[cp]+nu[cp];edp++) {
	qp=*edp;
	if(qp!=-1&&ed[qp][nu[qp]]!=-1) {
	if(stackp==stacke) {
	int dis=stackp-dsp;
	add_memory_ds(stackp);
	dsp=ds+dis;
	}
	*(stackp++)=qp;
	ed[qp][nu[qp]]=-1;
	}
	}
	}
	up=0;

	// Delete them from the array structure
	while(stackp>ds) {
	--p;
	while(ed[p][nu[p]]==-1) {
	j=nu[p];
	edp=ed[p];edd=(mep[j]+((j<<1)+1)*--mec[j]);
	while(edp<ed[p]+(j<<1)+1) (edp++)=(edd++);
	vc.n_set_aux2_copy(p,j);
	vc.n_copy_pointer(ed[p][(j<<1)],p);
	ed[ed[p][(j<<1)]]=ed[p];
	--p;
	}
	up=*(--stackp);
	if(up<p) {

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

	// Memory management
	j=nu[up];
	edp=ed[up];edd=(mep[j]+((j<<1)+1)*--mec[j]);
	while(edp<ed[up]+(j<<1)+1) (edp++)=(edd++);
	vc.n_set_aux2_copy(up,j);
	vc.n_copy_pointer(ed[up][j<<1],up);
	vc.n_copy_pointer(up,p);
	ed[ed[up][j<<1]]=ed[up];

	// Edge management
	ed[up]=ed[p];
	nu[up]=nu[p];
	for(i=0;i<nu[up];i++) ed[ed[up][i]][ed[up][nu[up]+i]]=up;
	ed[up][nu[up]<<1]=up;
	} else up=p++;
	}

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

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

	/** 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 vc_class>
	inline bool voronoicell_base::collapse_order2(vc_class &vc) {
	if(!collapse_order1(vc)) 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][5i];k=mep[2][5i+1];
	if(j==k) {
	#if VOROPP_VERBOSE >=1
	fputs("Order two vertex joins itself",stderr);
	#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][5i+2];b=mep[2][5i+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(vc,j,a,false)) return false;
	if(!delete_connection(vc,k,b,true)) return false;
	}

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

	// Collapse any order 1 vertices if they were created
	if(!collapse_order1(vc)) 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 vc_class>
	inline bool voronoicell_base::collapse_order1(vc_class &vc) {
	int i,j,k;
	while(mec[1]>0) {
	up=0;
	#if VOROPP_VERBOSE >=1
	fputs("Order one collapse\n",stderr);
	#endif
	i=--mec[1];
	j=mep[1][3i];k=mep[1][3i+1];
	i=mep[1][3*i+2];
	if(!delete_connection(vc,j,k,false)) return false;
	--p;
	if(up==i) up=0;
	if(p!=i) {
	if(up==p) up=i;
	pts[3i]=pts[3p];
	pts[3i+1]=pts[3p+1];
	pts[3i+2]=pts[3p+2];
	for(k=0;k<nu[p];k++) ed[ed[p][k]][ed[p][nu[p]+k]]=i;
	vc.n_copy_pointer(i,p);
	ed[i]=ed[p];
	nu[i]=nu[p];
	ed[i][nu[i]<<1]=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 vc_class>
	inline bool voronoicell_base::delete_connection(vc_class &vc,int j,int k,bool hand) {
	int q=hand?k:cycle_up(k,j);
	int i=nu[j]-1,l,edp,edd,m;
	#if VOROPP_VERBOSE >=1
	if(i<1) {
	fputs("Zero order vertex formed\n",stderr);
	return false;
	}
	#endif
	if(mec[i]==mem[i]) add_memory(vc,i,ds2);
	vc.n_set_aux1(i);
	for(l=0;l<q;l++) vc.n_copy_aux1(j,l);
	while(l<i) {
	vc.n_copy_aux1_shift(j,l);
	l++;
	}
	edp=mep[i]+((i<<1)+1)*mec[i]++;
	edp[i<<1]=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]]+((nu[j]<<1)+1)*--mec[nu[j]];
	for(l=0;l<=(nu[j]<<1);l++) ed[j][l]=edd[l];
	vc.n_set_aux2_copy(j,nu[j]);
	vc.n_set_to_aux2(edd[nu[j]<<1]);
	vc.n_set_to_aux1(j);
	ed[edd[nu[j]<<1]]=edd;
	ed[j]=edp;
	nu[j]=i;
	return true;
	}

	/** 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. */
	double voronoicell_base::volume() {
	const double fe=1/48.0;
	double vol=0;
	int i,j,k,l,m,n;
	double ux,uy,uz,vx,vy,vz,wx,wy,wz;
	for(i=1;i<p;i++) {
	ux=pts-pts[3i];
	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[3k]-pts;
	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[3m]-pts;
	wy=pts[3*m+1]-pts[1];
	wz=pts[3*m+2]-pts[2];
	vol+=uxvywz+uyvzwx+uzvxwy-uzvywx-uyvxwz-uxvzwy;
	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[out] v the vector to store the results in. */
	void voronoicell_base::face_areas(std::vector<double> &v) {
	double area;
	v.clear();
	int i,j,k,l,m,n;
	double 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[3k]-pts[3i];
	uy=pts[3k+1]-pts[3i+1];
	uz=pts[3k+2]-pts[3i+2];
	vx=pts[3m]-pts[3i];
	vy=pts[3m+1]-pts[3i+1];
	vz=pts[3m+2]-pts[3i+2];
	wx=uyvz-uzvy;
	wy=uzvx-uxvz;
	wz=uxvy-uyvx;
	area+=sqrt(wxwx+wywy+wz*wz);
	k=m;l=n;
	m=ed[k][l];ed[k][l]=-1-m;
	}
	v.push_back(0.125*area);
	}
	}
	reset_edges();
	}


	/** Calculates the total surface area of the Voronoi cell.
	* \return The computed area. */
	double voronoicell_base::surface_area() {
	double area=0;
	int i,j,k,l,m,n;
	double 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[3k]-pts[3i];
	uy=pts[3k+1]-pts[3i+1];
	uz=pts[3k+2]-pts[3i+2];
	vx=pts[3m]-pts[3i];
	vy=pts[3m+1]-pts[3i+1];
	vz=pts[3m+2]-pts[3i+2];
	wx=uyvz-uzvy;
	wy=uzvx-uxvz;
	wz=uxvy-uyvx;
	area+=sqrt(wxwx+wywy+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. */
	void voronoicell_base::centroid(double &cx,double &cy,double &cz) {
	double tvol,vol=0;cx=cy=cz=0;
	int i,j,k,l,m,n;
	double ux,uy,uz,vx,vy,vz,wx,wy,wz;
	for(i=1;i<p;i++) {
	ux=pts-pts[3i];
	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[3k]-pts;
	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[3m]-pts;
	wy=pts[3*m+1]-pts[1];
	wz=pts[3*m+2]-pts[2];
	tvol=uxvywz+uyvzwx+uzvxwy-uzvywx-uyvxwz-uxvzwy;
	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=cxvol+0.5(*pts);
	cy=cyvol+0.5pts[1];
	cz=czvol+0.5pts[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.*/
	double voronoicell_base::max_radius_squared() {
	double r,s,ptsp=pts+3,ptse=pts+3*p;
	r=pts(pts)+pts[1]pts[1]+pts[2]*pts[2];
	while(ptsp<ptse) {
	s=ptsp(*ptsp);ptsp++;
	s+=ptsp(*ptsp);ptsp++;
	s+=ptsp(*ptsp);ptsp++;
	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. */
	double voronoicell_base::total_edge_distance() {
	int i,j,k;
	double 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[3k]-pts[3i];
	dy=pts[3k+1]-pts[3i+1];
	dz=pts[3k+2]-pts[3i+2];
	dis+=sqrt(dxdx+dydy+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] (x,y,z) a displacement vector to be added to the cell's position.
	* \param[in] fp a file handle to write to. */
	void voronoicell_base::draw_pov(double x,double y,double z,FILE* fp) {
	int i,j,k;double ptsp=pts,pt2;
	char posbuf1[128],posbuf2[128];
	for(i=0;i<p;i++,ptsp+=3) {
	sprintf(posbuf1,"%g,%g,%g",x+ptsp0.5,y+ptsp[1]0.5,z+ptsp[2]0.5);
	fprintf(fp,"sphere{<%s>,r}\n",posbuf1);
	for(j=0;j<nu[i];j++) {
	k=ed[i][j];
	if(k<i) {
	pt2=pts+3*k;
	sprintf(posbuf2,"%g,%g,%g",x+pt20.5,y+0.5pt2[1],z+0.5pt2[2]);
	if(strcmp(posbuf1,posbuf2)!=0) fprintf(fp,"cylinder{<%s>,<%s>,r}\n",posbuf1,posbuf2);
	}
	}
	}
	}

	/** Outputs the edges of the Voronoi cell in gnuplot format to an output stream.
	* \param[in] (x,y,z) a displacement vector to be added to the cell's position.
	* \param[in] fp a file handle to write to. */
	void voronoicell_base::draw_gnuplot(double x,double y,double z,FILE *fp) {
	int i,j,k,l,m;
	for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
	k=ed[i][j];
	if(k>=0) {
	fprintf(fp,"%g %g %g\n",x+0.5pts[3i],y+0.5pts[3i+1],z+0.5pts[3i+2]);
	l=i;m=j;
	do {
	ed[k][ed[l][nu[l]+m]]=-1-l;
	ed[l][m]=-1-k;
	l=k;
	fprintf(fp,"%g %g %g\n",x+0.5pts[3k],y+0.5pts[3k+1],z+0.5pts[3k+2]);
	} while (search_edge(l,m,k));
	fputs("\n\n",fp);
	}
	}
	reset_edges();
	}

	inline bool voronoicell_base::search_edge(int l,int &m,int &k) {
	for(m=0;m<nu[l];m++) {
	k=ed[l][m];
	if(k>=0) return true;
	}
	return false;
	}

	/** 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] (x,y,z) a displacement vector to be added to the cell's position.
	* \param[in] fp a file handle to write to. */
	void voronoicell_base::draw_pov_mesh(double x,double y,double z,FILE *fp) {
	int i,j,k,l,m,n;
	double *ptsp=pts;
	fprintf(fp,"mesh2 {\nvertex_vectors {\n%d\n",p);
	for(i=0;i<p;i++,ptsp+=3) fprintf(fp,",<%g,%g,%g>\n",x+ptsp0.5,y+ptsp[1]0.5,z+ptsp[2]0.5);
	fprintf(fp,"}\nface_indices {\n%d\n",(p-2)<<1);
	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);
	fprintf(fp,",<%d,%d,%d>\n",i,k,m);
	k=m;l=n;
	m=ed[k][l];ed[k][l]=-1-m;
	}
	}
	}
	fputs("}\ninside_vector <0,0,1>\n}\n",fp);
	reset_edges();
	}

	/** 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. */
	inline void voronoicell_base::reset_edges() {
	int i,j;
	for(i=0;i<p;i++) for(j=0;j<nu[i];j++) {
	if(ed[i][j]>=0) voro_fatal_error("Edge reset routine found a previously untested edge",VOROPP_INTERNAL_ERROR);
	ed[i][j]=-1-ed[i][j];
	}
	}

	/** 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 voronoicell_base::m_test(int n,double &ans) {
	double *pp=pts+n+(n<<1);
	ans=(pp++)px;
	ans+=(pp++)py;
	ans+=pppz-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 voronoicell_base::check_marginal(int n,double &ans) {
	int i;
	for(i=0;i<n_marg;i+=2) if(marg[i]==n) return marg[i+1];
	if(n_marg==current_marginal) {
	current_marginal<<=1;
	if(current_marginal>max_marginal)
	voro_fatal_error("Marginal case buffer allocation exceeded absolute maximum",VOROPP_MEMORY_ERROR);
	#if VOROPP_VERBOSE >=2
	fprintf(stderr,"Marginal cases buffer scaled up to %d\n",i);
	#endif
	int *pmarg=new int[current_marginal];
	for(int j=0;j<n_marg;j++) pmarg[j]=marg[j];
	delete [] marg;
	marg=pmarg;
	}
	marg[n_marg++]=n;
	marg[n_marg++]=ans>tolerance?1:(ans<-tolerance?-1:0);
	return marg[n_marg-1];
	}

	/** This routine calculates the unit normal vectors for every face.
	* \param[out] v the vector to store the results in. */
	void voronoicell_base::normals(std::vector<double> &v) {
	int i,j,k;
	v.clear();
	for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
	k=ed[i][j];
	if(k>=0) normals_search(v,i,j,k);
	}
	reset_edges();
	}

	/** This inline routine is called by 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 none of
	* the vector products are large enough, the routine may return (0,0,0) as the
	* normal vector.
	* \param[in] v the vector to store the results in.
	* \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]. */
	inline void voronoicell_base::normals_search(std::vector<double> &v,int i,int j,int k) {
	ed[i][j]=-1-k;
	int l=cycle_up(ed[i][nu[i]+j],k),m;
	double ux,uy,uz,vx,vy,vz,wx,wy,wz,wmag;
	do {
	m=ed[k][l];ed[k][l]=-1-m;
	ux=pts[3m]-pts[3k];
	uy=pts[3m+1]-pts[3k+1];
	uz=pts[3m+2]-pts[3k+2];

	// Test to see if the length of this edge is above the tolerance
	if(uxux+uyuy+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[3m]-pts[3k];
	vy=pts[3m+1]-pts[3k+1];
	vz=pts[3m+2]-pts[3k+2];

	// Construct the vector product of this edge with
	// the previous one
	wx=uzvy-uyvz;
	wy=uxvz-uzvx;
	wz=uyvx-uxvy;
	wmag=wxwx+wywy+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);
	v.push_back(wx*wmag);
	v.push_back(wy*wmag);
	v.push_back(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;
	}
	}
	v.push_back(0);
	v.push_back(0);
	v.push_back(0);
	return;
	}
	l=cycle_up(ed[k][nu[k]+l],m);
	k=m;
	} while (k!=i);
	v.push_back(0);
	v.push_back(0);
	v.push_back(0);
	}


	/** Returns the number of faces of a computed Voronoi cell.
	* \return The number of faces. */
	int voronoicell_base::number_of_faces() {
	int i,j,k,l,m,s=0;
	for(i=1;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;
	}

	/** Returns a vector of the vertex orders.
	* \param[out] v the vector to store the results in. */
	void voronoicell_base::vertex_orders(std::vector<int> &v) {
	v.resize(p);
	for(int i=0;i<p;i++) v[i]=nu[i];
	}

	/** Outputs the vertex orders.
	* \param[out] fp the file handle to write to. */
	void voronoicell_base::output_vertex_orders(FILE *fp) {
	if(p>0) {
	fprintf(fp,"%d",*nu);
	for(int nup=nu+1;nup<nu+p;nup++) fprintf(fp," %d",nup);
	}
	}

	/** Returns a vector of the vertex vectors using the local coordinate system.
	* \param[out] v the vector to store the results in. */
	void voronoicell_base::vertices(std::vector<double> &v) {
	v.resize(3*p);
	double *ptsp=pts;
	for(int i=0;i<3*p;i+=3) {
	v[i]=(ptsp++)0.5;
	v[i+1]=(ptsp++)0.5;
	v[i+2]=(ptsp++)0.5;
	}
	}

	/** Outputs the vertex vectors using the local coordinate system.
	* \param[out] fp the file handle to write to. */
	void voronoicell_base::output_vertices(FILE *fp) {
	if(p>0) {
	fprintf(fp,"(%g,%g,%g)",pts0.5,pts[1]0.5,pts[2]0.5);
	for(double ptsp=pts+3;ptsp<pts+3p;ptsp+=3) fprintf(fp," (%g,%g,%g)",ptsp0.5,ptsp[1]0.5,ptsp[2]0.5);
	}
	}


	/** Returns a vector of the vertex vectors in the global coordinate system.
	* \param[out] v the vector to store the results in.
	* \param[in] (x,y,z) the position vector of the particle in the global
	* coordinate system. */
	void voronoicell_base::vertices(double x,double y,double z,std::vector<double> &v) {
	v.resize(3*p);
	double *ptsp=pts;
	for(int i=0;i<3*p;i+=3) {
	v[i]=x+(ptsp++)0.5;
	v[i+1]=y+(ptsp++)0.5;
	v[i+2]=z+(ptsp++)0.5;
	}
	}

	/** Outputs the vertex vectors using the global coordinate system.
	* \param[out] fp the file handle to write to.
	* \param[in] (x,y,z) the position vector of the particle in the global
	* coordinate system. */
	void voronoicell_base::output_vertices(double x,double y,double z,FILE *fp) {
	if(p>0) {
	fprintf(fp,"(%g,%g,%g)",x+pts0.5,y+pts[1]0.5,z+pts[2]0.5);
	for(double ptsp=pts+3;ptsp<pts+3p;ptsp+=3) fprintf(fp," (%g,%g,%g)",x+ptsp0.5,y+ptsp[1]0.5,z+ptsp[2]0.5);
	}
	}

	/** This routine returns the perimeters of each face.
	* \param[out] v the vector to store the results in. */
	void voronoicell_base::face_perimeters(std::vector<double> &v) {
	v.clear();
	int i,j,k,l,m;
	double dx,dy,dz,perim;
	for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
	k=ed[i][j];
	if(k>=0) {
	dx=pts[3k]-pts[3i];
	dy=pts[3k+1]-pts[3i+1];
	dz=pts[3k+2]-pts[3i+2];
	perim=sqrt(dxdx+dydy+dz*dz);
	ed[i][j]=-1-k;
	l=cycle_up(ed[i][nu[i]+j],k);
	do {
	m=ed[k][l];
	dx=pts[3m]-pts[3k];
	dy=pts[3m+1]-pts[3k+1];
	dz=pts[3m+2]-pts[3k+2];
	perim+=sqrt(dxdx+dydy+dz*dz);
	ed[k][l]=-1-m;
	l=cycle_up(ed[k][nu[k]+l],m);
	k=m;
	} while (k!=i);
	v.push_back(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[out] v the vector to store the results in. */
	void voronoicell_base::face_vertices(std::vector<int> &v) {
	int i,j,k,l,m,vp(0),vn;
	v.clear();
	for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
	k=ed[i][j];
	if(k>=0) {
	v.push_back(0);
	v.push_back(i);
	ed[i][j]=-1-k;
	l=cycle_up(ed[i][nu[i]+j],k);
	do {
	v.push_back(k);
	m=ed[k][l];
	ed[k][l]=-1-m;
	l=cycle_up(ed[k][nu[k]+l],m);
	k=m;
	} while (k!=i);
	vn=v.size();
	v[vp]=vn-vp-1;
	vp=vn;
	}
	}
	reset_edges();
	}

	/** Outputs a list of the number of edges in each face.
	* \param[out] v the vector to store the results in. */
	void voronoicell_base::face_orders(std::vector<int> &v) {
	int i,j,k,l,m,q;
	v.clear();
	for(i=1;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);
	v.push_back(q);;
	}
	}
	reset_edges();
	}

	/** Computes the number of edges that each face has and outputs a frequency
	* table of the results.
	* \param[out] v the vector to store the results in. */
	void voronoicell_base::face_freq_table(std::vector<int> &v) {
	int i,j,k,l,m,q;
	v.clear();
	for(i=1;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((unsigned int) q>=v.size()) v.resize(q+1,0);
	v[q]++;
	}
	}
	reset_edges();
	}

	/** 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. */
	bool voronoicell_base::plane_intersects(double x,double y,double z,double rsq) {
	double g=xpts[3up]+ypts[3up+1]+zpts[3up+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. */
	bool voronoicell_base::plane_intersects_guess(double x,double y,double z,double rsq) {
	up=0;
	double g=xpts[3up]+ypts[3up+1]+zpts[3up+2];
	if(g<rsq) {
	int ca=1,cc=p>>3,mp=1;
	double m;
	while(ca<cc) {
	m=xpts[3mp]+ypts[3mp+1]+zpts[3mp+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. */
	inline bool voronoicell_base::plane_intersects_track(double x,double y,double z,double rsq,double g) {
	int count=0,ls,us,tp;
	double t;

	// The test point is outside of the cutting space
	for(us=0;us<nu[up];us++) {
	tp=ed[up][us];
	t=xpts[3tp]+ypts[3tp+1]+zpts[3tp+2];
	if(t>g) {
	ls=ed[up][nu[up]+us];
	up=tp;
	while (t<rsq) {
	if(++count>=p) {
	#if VOROPP_VERBOSE >=1
	fputs("Bailed out of convex calculation",stderr);
	#endif
	for(tp=0;tp<p;tp++) if(xpts[3tp]+ypts[3tp+1]+zpts[3tp+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=xpts[3tp]+ypts[3tp+1]+zpts[3tp+2];
	if(g>t) break;
	}
	if(us==ls) {
	us++;
	while(us<nu[up]) {
	tp=ed[up][us];
	g=xpts[3tp]+ypts[3tp+1]+zpts[3tp+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. */
	int voronoicell_base::number_of_edges() {
	int edges=0,*nup=nu;
	while(nup<nu+p) edges+=*(nup++);
	return edges>>1;
	}

	/** Outputs a custom string of information about the Voronoi cell. The string
	* of information follows a similar style as the C printf command, and detailed
	* information about its format is available at
	* http://math.lbl.gov/voro++/doc/custom.html.
	* \param[in] format the custom string to print.
	* \param[in] i the ID of the particle associated with this Voronoi cell.
	* \param[in] (x,y,z) the position of the particle associated with this Voronoi
	* cell.
	* \param[in] r a radius associated with the particle.
	* \param[in] fp the file handle to write to. */
	void voronoicell_base::output_custom(const char format,int i,double x,double y,double z,double r,FILE fp) {
	char fmp=(const_cast<char>(format));
	std::vector<int> vi;
	std::vector<double> vd;
	while(*fmp!=0) {
	if(*fmp=='%') {
	fmp++;
	switch(*fmp) {

	// Particle-related output
	case 'i': fprintf(fp,"%d",i);break;
	case 'x': fprintf(fp,"%g",x);break;
	case 'y': fprintf(fp,"%g",y);break;
	case 'z': fprintf(fp,"%g",z);break;
	case 'q': fprintf(fp,"%g %g %g",x,y,z);break;
	case 'r': fprintf(fp,"%g",r);break;

	// Vertex-related output
	case 'w': fprintf(fp,"%d",p);break;
	case 'p': output_vertices(fp);break;
	case 'P': output_vertices(x,y,z,fp);break;
	case 'o': output_vertex_orders(fp);break;
	case 'm': fprintf(fp,"%g",0.25*max_radius_squared());break;

	// Edge-related output
	case 'g': fprintf(fp,"%d",number_of_edges());break;
	case 'E': fprintf(fp,"%g",total_edge_distance());break;
	case 'e': face_perimeters(vd);voro_print_vector(vd,fp);break;

	// Face-related output
	case 's': fprintf(fp,"%d",number_of_faces());break;
	case 'F': fprintf(fp,"%g",surface_area());break;
	case 'A': {
	face_freq_table(vi);
	voro_print_vector(vi,fp);
	} break;
	case 'a': face_orders(vi);voro_print_vector(vi,fp);break;
	case 'f': face_areas(vd);voro_print_vector(vd,fp);break;
	case 't': {
	face_vertices(vi);
	voro_print_face_vertices(vi,fp);
	} break;
	case 'l': normals(vd);
	voro_print_positions(vd,fp);
	break;
	case 'n': neighbors(vi);
	voro_print_vector(vi,fp);
	break;

	// Volume-related output
	case 'v': fprintf(fp,"%g",volume());break;
	case 'c': {
	double cx,cy,cz;
	centroid(cx,cy,cz);
	fprintf(fp,"%g %g %g",cx,cy,cz);
	} break;
	case 'C': {
	double cx,cy,cz;
	centroid(cx,cy,cz);
	fprintf(fp,"%g %g %g",x+cx,y+cy,z+cz);
	} break;

	// End-of-string reached
	case 0: fmp--;break;

	// The percent sign is not part of a
	// control sequence
	default: putc('%',fp);putc(*fmp,fp);
	}
	} else putc(*fmp,fp);
	fmp++;
	}
	fputs("\n",fp);
	}

	/** This initializes the class to be a rectangular box. It calls the base class
	* initialization routine to set up the edge and vertex information, and then
	* sets up the neighbor information, with initial faces being assigned ID
	* numbers from -1 to -6.
	* \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. */
	void voronoicell_neighbor::init(double xmin,double xmax,double ymin,double ymax,double zmin,double zmax) {
	init_base(xmin,xmax,ymin,ymax,zmin,zmax);
	int *q=mne[3];
	*q=-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=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 class to be an octahedron. It calls the base class
	* initialization routine to set up the edge and vertex information, and then
	* sets up the neighbor information, with the initial faces being assigned ID
	* numbers from -1 to -8.
	* \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). */
	void voronoicell_neighbor::init_octahedron(double l) {
	init_octahedron_base(l);
	int *q=mne[4];
	*q=-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=q;ne[1]=q+4;ne[2]=q+8;ne[3]=q+12;ne[4]=q+16;ne[5]=q+20;
	}

	/** This initializes the class to be a tetrahedron. It calls the base class
	* initialization routine to set up the edge and vertex information, and then
	* sets up the neighbor information, with the initial faces being assigned ID
	* numbers from -1 to -4.
	* \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. */
	void voronoicell_neighbor::init_tetrahedron(double x0,double y0,double z0,double x1,double y1,double z1,double x2,double y2,double z2,double x3,double y3,double z3) {
	init_tetrahedron_base(x0,y0,z0,x1,y1,z1,x2,y2,z2,x3,y3,z3);
	int *q=mne[3];
	*q=-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=q;ne[1]=q+3;ne[2]=q+6;ne[3]=q+9;
	}

	/** This routine checks to make sure the neighbor information of each face is
	* consistent. */
	void voronoicell_neighbor::check_facets() {
	int i,j,k,l,m,q;
	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;
	q=ne[i][j];
	l=cycle_up(ed[i][nu[i]+j],k);
	do {
	m=ed[k][l];
	ed[k][l]=-1-m;
	if(ne[k][l]!=q) fprintf(stderr,"Facet error at (%d,%d)=%d, started from (%d,%d)=%d\n",k,l,ne[k][l],i,j,q);
	l=cycle_up(ed[k][nu[k]+l],m);
	k=m;
	} while (k!=i);
	}
	}
	reset_edges();
	}

	/** The class constructor allocates memory for storing neighbor information. */
	voronoicell_neighbor::voronoicell_neighbor() {
	int i;
	mne=new int*[current_vertex_order];
	ne=new int*[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<current_vertex_order;i++) mne[i]=new int[init_n_vertices*i];
	}

	/** The class destructor frees the dynamically allocated memory for storing
	* neighbor information. */
	voronoicell_neighbor::~voronoicell_neighbor() {
	for(int i=current_vertex_order-1;i>=0;i--) if(mem[i]>0) delete [] mne[i];
	delete [] mne;
	delete [] ne;
	}

	/** Computes a vector list of neighbors. */
	void voronoicell_neighbor::neighbors(std::vector<int> &v) {
	v.clear();
	int i,j,k,l,m;
	for(i=1;i<p;i++) for(j=0;j<nu[i];j++) {
	k=ed[i][j];
	if(k>=0) {
	v.push_back(ne[i][j]);
	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();
	}

	/** Prints the vertices, their edges, the relation table, and also notifies if
	* any memory errors are visible. */
	void voronoicell_base::print_edges() {
	int j;
	double *ptsp=pts;
	for(int i=0;i<p;i++,ptsp+=3) {
	printf("%d %d ",i,nu[i]);
	for(j=0;j<nu[i];j++) printf(" %d",ed[i][j]);
	printf(" ");
	while(j<(nu[i]<<1)) printf(" %d",ed[i][j]);
	printf(" %d",ed[i][j]);
	print_edges_neighbors(i);
	printf(" %g %g %g %p",ptsp,ptsp[1],ptsp[2],(void) ed[i]);
	if(ed[i]>=mep[nu[i]]+mec[nu[i]]*((nu[i]<<1)+1)) puts(" Memory error");
	else puts("");
	}
	}

	/** This prints out the neighbor information for vertex i. */
	void voronoicell_neighbor::print_edges_neighbors(int i) {
	if(nu[i]>0) {
	int j=0;
	printf(" (");
	while(j<nu[i]-1) printf("%d,",ne[i][j++]);
	printf("%d)",ne[i][j]);
	} else printf(" ()");
	}

	// Explicit instantiation
	template bool voronoicell_base::nplane(voronoicell&,double,double,double,double,int);
	template bool voronoicell_base::nplane(voronoicell_neighbor&,double,double,double,double,int);
	template void voronoicell_base::check_memory_for_copy(voronoicell&,voronoicell_base*);
	template void voronoicell_base::check_memory_for_copy(voronoicell_neighbor&,voronoicell_base*);

	}

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