text: // 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.h
   * \brief Header file for the voronoicell and related classes. */
  
  #ifndef VOROPP_CELL_H
  #define VOROPP_CELL_H
  
  #include <vector>
  
  #include "config.h"
  #include "common.h"
  
  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
  