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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.hh
* \brief Header file for the voronoicell and related classes. */
#ifndef VOROPP_CELL_HH
#define VOROPP_CELL_HH
#include <vector>
#include "config.hh"
#include "common.hh"
namespace voro {
/** \brief A class representing a single Voronoi cell.
*
* This class represents a single Voronoi cell, as a collection of vertices
* that are connected by edges. The class contains routines for initializing
* the Voronoi cell to be simple shapes such as a box, tetrahedron, or octahedron.
* It the contains routines for recomputing the cell based on cutting it
* by a plane, which forms the key routine for the Voronoi cell computation.
* It contains numerous routine for computing statistics about the Voronoi cell,
* and it can output the cell in several formats.
*
* This class is not intended for direct use, but forms the base of the
* voronoicell and voronoicell_neighbor classes, which extend it based on
* whether neighboring particle ID information needs to be tracked. */
class voronoicell_base {
public:
/** This holds the current size of the arrays ed and nu, which
* hold the vertex information. If more vertices are created
* than can fit in this array, then it is dynamically extended
* using the add_memory_vertices routine. */
int current_vertices;
/** This holds the current maximum allowed order of a vertex,
* which sets the size of the mem, mep, and mec arrays. If a
* vertex is created with more vertices than this, the arrays
* are dynamically extended using the add_memory_vorder routine.
*/
int current_vertex_order;
/** This sets the size of the main delete stack. */
int current_delete_size;
/** This sets the size of the auxiliary delete stack. */
int current_delete2_size;
/** This sets the total number of vertices in the current cell.
*/
int p;
/** This is the index of particular point in the cell, which is
* used to start the tracing routines for plane intersection
* and cutting. These routines will work starting from any
* point, but it's often most efficient to start from the last
* point considered, since in many cases, the cell construction
* algorithm may consider many planes with similar vectors
* concurrently. */
int up;
/** This is a two dimensional array that holds information
* about the edge connections of the vertices that make up the
* cell. The two dimensional array is not allocated in the
* usual method. To account for the fact the different vertices
* have different orders, and thus require different amounts of
* storage, the elements of ed[i] point to one-dimensional
* arrays in the mep[] array of different sizes.
*
* More specifically, if vertex i has order m, then ed[i]
* points to a one-dimensional array in mep[m] that has 2*m+1
* entries. The first m elements hold the neighboring edges, so
* that the jth edge of vertex i is held in ed[i][j]. The next
* m elements hold a table of relations which is redundant but
* helps speed up the computation. It satisfies the relation
* ed[ed[i][j]][ed[i][m+j]]=i. The final entry holds a back
* pointer, so that ed[i+2*m]=i. The back pointers are used
* when rearranging the memory. */
int **ed;
/** This array holds the order of the vertices in the Voronoi
* cell. This array is dynamically allocated, with its current
* size held by current_vertices. */
int *nu;
/** This in an array with size 3*current_vertices for holding
* the positions of the vertices. */
double *pts;
voronoicell_base();
~voronoicell_base();
void init_base(double xmin,double xmax,double ymin,double ymax,double zmin,double zmax);
void init_octahedron_base(double l);
void 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);
void translate(double x,double y,double z);
void draw_pov(double x,double y,double z,FILE *fp=stdout);
/** Outputs the cell in POV-Ray format, using cylinders for edges
* and spheres for vertices, to a given file.
* \param[in] (x,y,z) a displacement to add to the cell's
* position.
* \param[in] filename the name of the file to write to. */
inline void draw_pov(double x,double y,double z,const char *filename) {
FILE *fp=safe_fopen(filename,"w");
draw_pov(x,y,z,fp);
fclose(fp);
};
void draw_pov_mesh(double x,double y,double z,FILE *fp=stdout);
/** Outputs the cell in POV-Ray format as a mesh2 object to a
* given file.
* \param[in] (x,y,z) a displacement to add to the cell's
* position.
* \param[in] filename the name of the file to write to. */
inline void draw_pov_mesh(double x,double y,double z,const char *filename) {
FILE *fp=safe_fopen(filename,"w");
draw_pov_mesh(x,y,z,fp);
fclose(fp);
}
void draw_gnuplot(double x,double y,double z,FILE *fp=stdout);
/** Outputs the cell in Gnuplot format a given file.
* \param[in] (x,y,z) a displacement to add to the cell's
* position.
* \param[in] filename the name of the file to write to. */
inline void draw_gnuplot(double x,double y,double z,const char *filename) {
FILE *fp=safe_fopen(filename,"w");
draw_gnuplot(x,y,z,fp);
fclose(fp);
}
double volume();
double max_radius_squared();
double total_edge_distance();
double surface_area();
void centroid(double &cx,double &cy,double &cz);
int number_of_faces();
int number_of_edges();
void vertex_orders(std::vector<int> &v);
void output_vertex_orders(FILE *fp=stdout);
void vertices(std::vector<double> &v);
void output_vertices(FILE *fp=stdout);
void vertices(double x,double y,double z,std::vector<double> &v);
void output_vertices(double x,double y,double z,FILE *fp=stdout);
void face_areas(std::vector<double> &v);
/** Outputs the areas of the faces.
* \param[in] fp the file handle to write to. */
inline void output_face_areas(FILE *fp=stdout) {
std::vector<double> v;face_areas(v);
voro_print_vector(v,fp);
}
void face_orders(std::vector<int> &v);
/** Outputs a list of the number of sides of each face.
* \param[in] fp the file handle to write to. */
inline void output_face_orders(FILE *fp=stdout) {
std::vector<int> v;face_orders(v);
voro_print_vector(v,fp);
}
void face_freq_table(std::vector<int> &v);
/** Outputs a */
inline void output_face_freq_table(FILE *fp=stdout) {
std::vector<int> v;face_freq_table(v);
voro_print_vector(v,fp);
}
void face_vertices(std::vector<int> &v);
/** Outputs the */
inline void output_face_vertices(FILE *fp=stdout) {
std::vector<int> v;face_vertices(v);
voro_print_face_vertices(v,fp);
}
void face_perimeters(std::vector<double> &v);
/** Outputs a list of the perimeters of each face.
* \param[in] fp the file handle to write to. */
inline void output_face_perimeters(FILE *fp=stdout) {
std::vector<double> v;face_perimeters(v);
voro_print_vector(v,fp);
}
void normals(std::vector<double> &v);
/** Outputs a list of the perimeters of each face.
* \param[in] fp the file handle to write to. */
inline void output_normals(FILE *fp=stdout) {
std::vector<double> v;normals(v);
voro_print_positions(v,fp);
}
/** Outputs a custom string of information about the Voronoi
* cell to a file. It assumes the cell is at (0,0,0) and has a
* the default_radius associated with it.
* \param[in] format the custom format string to use.
* \param[in] fp the file handle to write to. */
inline void output_custom(const char *format,FILE *fp=stdout) {output_custom(format,0,0,0,0,default_radius,fp);}
void output_custom(const char *format,int i,double x,double y,double z,double r,FILE *fp=stdout);
template<class vc_class>
bool nplane(vc_class &vc,double x,double y,double z,double rsq,int p_id);
bool plane_intersects(double x,double y,double z,double rsq);
bool plane_intersects_guess(double x,double y,double z,double rsq);
void construct_relations();
void check_relations();
void check_duplicates();
void print_edges();
/** Returns a list of IDs of neighboring particles
* corresponding to each face.
* \param[out] v a reference to a vector in which to return the
* results. If no neighbor information is
* available, a blank vector is returned. */
virtual void neighbors(std::vector<int> &v) {v.clear();}
/** This is a virtual function that is overridden by a routine
* to print a list of IDs of neighboring particles
* corresponding to each face. By default, when no neighbor
* information is available, the routine does nothing.
* \param[in] fp the file handle to write to. */
virtual void output_neighbors(FILE *fp=stdout) {}
/** This a virtual function that is overridden by a routine to
* print the neighboring particle IDs for a given vertex. By
* default, when no neighbor information is available, the
* routine does nothing.
* \param[in] i the vertex to consider. */
virtual void print_edges_neighbors(int i) {};
/** 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. */
inline int 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. */
inline int cycle_down(int a,int p) {return a==0?nu[p]-1:a-1;}
protected:
/** This a one dimensional array that holds the current sizes
* of the memory allocations for them mep array.*/
int *mem;
/** This is a one dimensional array that holds the current
* number of vertices of order p that are stored in the mep[p]
* array. */
int *mec;
/** This is a two dimensional array for holding the information
* about the edges of the Voronoi cell. mep[p] is a
* one-dimensional array for holding the edge information about
* all vertices of order p, with each vertex holding 2*p+1
* integers of information. The total number of vertices held
* on mep[p] is stored in mem[p]. If the space runs out, the
* code allocates more using the add_memory() routine. */
int **mep;
inline void reset_edges();
template<class vc_class>
void check_memory_for_copy(vc_class &vc,voronoicell_base* vb);
void copy(voronoicell_base* vb);
private:
/** This is the delete stack, used to store the vertices which
* are going to be deleted during the plane cutting procedure.
*/
int *ds,*stacke;
/** This is the auxiliary delete stack, which has size set by
* current_delete2_size. */
int *ds2,*stacke2;
/** This stores the current memory allocation for the marginal
* cases. */
int current_marginal;
/** This stores the total number of marginal points which are
* currently in the buffer. */
int n_marg;
/** This array contains a list of the marginal points, and also
* the outcomes of the marginal tests. */
int *marg;
/** The x coordinate of the normal vector to the test plane. */
double px;
/** The y coordinate of the normal vector to the test plane. */
double py;
/** The z coordinate of the normal vector to the test plane. */
double pz;
/** The magnitude of the normal vector to the test plane. */
double prsq;
template<class vc_class>
void add_memory(vc_class &vc,int i,int *stackp2);
template<class vc_class>
void add_memory_vertices(vc_class &vc);
template<class vc_class>
void add_memory_vorder(vc_class &vc);
void add_memory_ds(int *&stackp);
void add_memory_ds2(int *&stackp2);
template<class vc_class>
inline bool collapse_order1(vc_class &vc);
template<class vc_class>
inline bool collapse_order2(vc_class &vc);
template<class vc_class>
inline bool delete_connection(vc_class &vc,int j,int k,bool hand);
template<class vc_class>
inline bool search_for_outside_edge(vc_class &vc,int &up);
template<class vc_class>
inline void add_to_stack(vc_class &vc,int lp,int *&stackp2);
inline bool plane_intersects_track(double x,double y,double z,double rs,double g);
inline void normals_search(std::vector<double> &v,int i,int j,int k);
inline bool search_edge(int l,int &m,int &k);
inline int m_test(int n,double &ans);
int check_marginal(int n,double &ans);
friend class voronoicell;
friend class voronoicell_neighbor;
};
/** \brief Extension of the voronoicell_base class to represent a Voronoi
* cell without neighbor information.
*
* This class is an extension of the voronoicell_base class, in cases when
* is not necessary to track the IDs of neighboring particles associated
* with each face of the Voronoi cell. */
class voronoicell : public voronoicell_base {
public:
using voronoicell_base::nplane;
/** Copies the information from another voronoicell class into
* this class, extending memory allocation if necessary.
* \param[in] c the class to copy. */
inline void operator=(voronoicell &c) {
voronoicell_base* vb((voronoicell_base*) &c);
check_memory_for_copy(*this,vb);copy(vb);
}
/** Cuts a Voronoi cell using by the plane corresponding to the
* perpendicular bisector of a particle.
* \param[in] (x,y,z) the position of the particle.
* \param[in] rsq the modulus squared of the vector.
* \param[in] p_id the plane ID, ignored for this case where no
* neighbor tracking is enabled.
* \return False if the plane cut deleted the cell entirely,
* true otherwise. */
inline bool nplane(double x,double y,double z,double rsq,int p_id) {
return nplane(*this,x,y,z,rsq,0);
}
/** Cuts a Voronoi cell using by the plane corresponding to the
* perpendicular bisector of a particle.
* \param[in] (x,y,z) the position of the particle.
* \param[in] p_id the plane ID, ignored for this case where no
* neighbor tracking is enabled.
* \return False if the plane cut deleted the cell entirely,
* true otherwise. */
inline bool nplane(double x,double y,double z,int p_id) {
double rsq=x*x+y*y+z*z;
return nplane(*this,x,y,z,rsq,0);
}
/** Cuts a Voronoi cell using by the plane corresponding to the
* perpendicular bisector of a particle.
* \param[in] (x,y,z) the position of the particle.
* \param[in] rsq the modulus squared of the vector.
* \return False if the plane cut deleted the cell entirely,
* true otherwise. */
inline bool plane(double x,double y,double z,double rsq) {
return nplane(*this,x,y,z,rsq,0);
}
/** Cuts a Voronoi cell using by the plane corresponding to the
* perpendicular bisector of a particle.
* \param[in] (x,y,z) the position of the particle.
* \return False if the plane cut deleted the cell entirely,
* true otherwise. */
inline bool plane(double x,double y,double z) {
double rsq=x*x+y*y+z*z;
return nplane(*this,x,y,z,rsq,0);
}
/** Initializes the Voronoi cell to be 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. */
inline void init(double xmin,double xmax,double ymin,double ymax,double zmin,double zmax) {
init_base(xmin,xmax,ymin,ymax,zmin,zmax);
}
/** Initializes the cell to be an octahedron with vertices at
* (l,0,0), (-l,0,0), (0,l,0), (0,-l,0), (0,0,l), and (0,0,-l).
* \param[in] l a parameter setting the size of the octahedron.
*/
inline void init_octahedron(double l) {
init_octahedron_base(l);
}
/** Initializes the cell to be a tetrahedron.
* \param[in] (x0,y0,z0) the coordinates of the first vertex.
* \param[in] (x1,y1,z1) the coordinates of the second vertex.
* \param[in] (x2,y2,z2) the coordinates of the third vertex.
* \param[in] (x3,y3,z3) the coordinates of the fourth vertex.
*/
inline void 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);
}
private:
inline void n_allocate(int i,int m) {};
inline void n_add_memory_vertices(int i) {};
inline void n_add_memory_vorder(int i) {};
inline void n_set_pointer(int p,int n) {};
inline void n_copy(int a,int b,int c,int d) {};
inline void n_set(int a,int b,int c) {};
inline void n_set_aux1(int k) {};
inline void n_copy_aux1(int a,int b) {};
inline void n_copy_aux1_shift(int a,int b) {};
inline void n_set_aux2_copy(int a,int b) {};
inline void n_copy_pointer(int a,int b) {};
inline void n_set_to_aux1(int j) {};
inline void n_set_to_aux2(int j) {};
inline void n_allocate_aux1(int i) {};
inline void n_switch_to_aux1(int i) {};
inline void n_copy_to_aux1(int i,int m) {};
inline void n_set_to_aux1_offset(int k,int m) {};
inline void n_neighbors(std::vector<int> &v) {v.clear();};
friend class voronoicell_base;
};
/** \brief Extension of the voronoicell_base class to represent a Voronoi cell
* with neighbor information.
*
* This class is an extension of the voronoicell_base class, in cases when the
* IDs of neighboring particles associated with each face of the Voronoi cell.
* It contains additional data structures mne and ne for storing this
* information. */
class voronoicell_neighbor : public voronoicell_base {
public:
using voronoicell_base::nplane;
/** This two dimensional array holds the neighbor information
* associated with each vertex. mne[p] is a one dimensional
* array which holds all of the neighbor information for
* vertices of order p. */
int **mne;
/** This is a two dimensional array that holds the neighbor
* information associated with each vertex. ne[i] points to a
* one-dimensional array in mne[nu[i]]. ne[i][j] holds the
* neighbor information associated with the jth edge of vertex
* i. It is set to the ID number of the plane that made the
* face that is clockwise from the jth edge. */
int **ne;
voronoicell_neighbor();
~voronoicell_neighbor();
void operator=(voronoicell &c);
void operator=(voronoicell_neighbor &c);
/** 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. */
inline bool nplane(double x,double y,double z,double rsq,int p_id) {
return nplane(*this,x,y,z,rsq,p_id);
}
/** 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. */
inline bool nplane(double x,double y,double z,int p_id) {
double rsq=x*x+y*y+z*z;
return nplane(*this,x,y,z,rsq,p_id);
}
/** 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. */
inline bool plane(double x,double y,double z,double rsq) {
return nplane(*this,x,y,z,rsq,0);
}
/** 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. */
inline bool plane(double x,double y,double z) {
double rsq=x*x+y*y+z*z;
return nplane(*this,x,y,z,rsq,0);
}
void init(double xmin,double xmax,double ymin,double ymax,double zmin,double zmax);
void init_octahedron(double l);
void 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);
void check_facets();
virtual void neighbors(std::vector<int> &v);
virtual void print_edges_neighbors(int i);
virtual void output_neighbors(FILE *fp=stdout) {
std::vector<int> v;neighbors(v);
voro_print_vector(v,fp);
}
private:
int *paux1;
int *paux2;
inline void n_allocate(int i,int m) {mne[i]=new int[m*i];}
inline void n_add_memory_vertices(int i) {
int **pp=new int*[i];
for(int j=0;j<current_vertices;j++) pp[j]=ne[j];
delete [] ne;ne=pp;
}
inline void n_add_memory_vorder(int i) {
int **p2=new int*[i];
for(int j=0;j<current_vertex_order;j++) p2[j]=mne[j];
delete [] mne;mne=p2;
}
inline void n_set_pointer(int p,int n) {
ne[p]=mne[n]+n*mec[n];
}
inline void n_copy(int a,int b,int c,int d) {ne[a][b]=ne[c][d];}
inline void n_set(int a,int b,int c) {ne[a][b]=c;}
inline void n_set_aux1(int k) {paux1=mne[k]+k*mec[k];}
inline void n_copy_aux1(int a,int b) {paux1[b]=ne[a][b];}
inline void n_copy_aux1_shift(int a,int b) {paux1[b]=ne[a][b+1];}
inline void n_set_aux2_copy(int a,int b) {
paux2=mne[b]+b*mec[b];
for(int i=0;i<b;i++) ne[a][i]=paux2[i];
}
inline void n_copy_pointer(int a,int b) {ne[a]=ne[b];}
inline void n_set_to_aux1(int j) {ne[j]=paux1;}
inline void n_set_to_aux2(int j) {ne[j]=paux2;}
inline void n_allocate_aux1(int i) {paux1=new int[i*mem[i]];}
inline void n_switch_to_aux1(int i) {delete [] mne[i];mne[i]=paux1;}
inline void n_copy_to_aux1(int i,int m) {paux1[m]=mne[i][m];}
inline void n_set_to_aux1_offset(int k,int m) {ne[k]=paux1+m;}
friend class voronoicell_base;
};
}
#endif

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