Diploma Thesis Percolation Simulation
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sphere.h File Reference

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Compounds

class  sphere

Functions

int getdim (const sphere &u)
REAL distance (sphere &sph1, sphere &sph2)
bool overlap (sphere &sph1, sphere &sph2)
bool overlap (sphere &sph1, sphere &sph2, sphere &temp)
bool overlap2 (sphere &sph1, sphere &sph2, sphere &temp)
ostream & operator<< (ostream &os, sphere &z)
REAL find_biggestradius (sphere *array, NUMLIST &sphlist)
double unitsphere (int dimension)
REAL give_fillingfactor (REAL radius, NUMBER numberofspheres, COORDFLOAT length, int dimension)
REAL ff_critical (NUMBER N, int dim)
REAL ff_critical_infinite_limit (int dim)
REAL ff_critical_guessed (NUMBER N, int dim)
REAL ff_critical_guessed (NUMBER N, int dim, REAL dummy)
REAL give_radius (REAL fillingfactor, NUMBER numberofspheres, COORDFLOAT length, int dimension)
REAL R_critical (NUMBER no_of_spheres, COORDFLOAT length, int dimension)
REAL R_critical_guessed (NUMBER no_of_spheres, COORDFLOAT length, int dimension)
REAL percolating_fillingfactor_for_two_spheres_verbose (int dim, COORDFLOAT length)
REAL percolating_fillingfactor_for_two_spheres (int dim)

Variables

double myPI = 2*acos(0.0)

Function Documentation

REAL distance (  sphere &    sph1,
sphere &    sph2
) 
 

Definition at line 90 of file sphere.h.

References sphere::c, length(), and REAL.

Referenced by counters::neighbour_l(), and counters::neighbour_naive(). 

00090                                            {            // reference instead of copy --> faster
00091         return ( length((sph1.c - sph2.c)));
00092 }

REAL ff_critical (  NUMBER    N,
int    dim
) 
 

Definition at line 152 of file sphere.h.

References critical_fillingfactor(), NUMBER, and REAL.

Referenced by ff_critical_guessed(). 

00152                                      {
00153         return critical_fillingfactor(dim,N);
00154 }

REAL ff_critical_guessed (  NUMBER    N,
int    dim,
REAL    dummy
) 
 

Definition at line 164 of file sphere.h.

References NUMBER, and REAL.

Referenced by counters::choose_optimal_cuts(), ff::ffbig_guessed(), ff::ffmean1_guessed(), ff::ffnoc_guessed(), ff::find_ffc_scanning_N_and_dim(), and ff::find_mean_ffc(). 

00164                                                          {
00165         return ff_critical_guessed(N, dim) ;
00166 }

REAL ff_critical_guessed (  NUMBER    N,
int    dim
) 
 

Definition at line 158 of file sphere.h.

References ff_critical(), ff_critical_infinite_limit(), NUMBER, and REAL. 

00158                                              {
00159         REAL temp=ff_critical(N,dim);
00160         if (temp==-1) return ff_critical_infinite_limit(dim);
00161         return temp;
00162 }

REAL ff_critical_infinite_limit (  int    dim ) 
 

Definition at line 155 of file sphere.h.

References pow(), and REAL.

Referenced by ff_critical_guessed(), and R_critical_guessed(). 

00155                                           {
00156         return pow(0.5,dim);    // good guess for high dimensions
00157 }

REAL find_biggestradius (  sphere *    array,
NUMLIST &    sphlist
) 
 

Definition at line 118 of file sphere.h.

References sphere::r, and REAL.

Referenced by counters::combine(), and starters::test_list(). 

00118                                                            {
00119 
00120         NUMLIST::iterator iter1;
00121         REAL biggest=0;
00122 
00123         for (iter1 =  sphlist.begin(); iter1 != sphlist.end(); ++iter1){
00124                 if ( array[*iter1].r > biggest) 
00125                         biggest= array[*iter1].r;
00126         }
00127         return biggest;
00128 }

int getdim (  const sphere &    u ) 
 

Definition at line 62 of file sphere.h.

References sphere::c.

Referenced by counters::count_analyze_and_return_clusters(), counters::count_clusters_iteratively(), counters::count_clusters_iteratively2(), counters::count_clusters_iteratively_only_selected_spherenumbers(), counters::divide_count_and_analyze(), counters::divide_d_times_count_and_analyze(), grid::divide_spheres_into_overlapping_boxes_and_conquer(), analyze::edgespheres(), grid::find_neighbours_in_a_box_recursion(), ff::find_one_ff_with_criterion(), ff::find_one_ffc(), counters::neighbour_l(), counters::neighbour_naive(), counters::neighbour_recursion(), grid::put_vector_into_boxes(), and counters::throw_dnc_count_analyze_step(). 

00062 {return getdim(u.c);}

REAL give_fillingfactor (  REAL    radius,
NUMBER    numberofspheres,
COORDFLOAT    length,
int    dimension
) 
 

Definition at line 146 of file sphere.h.

References COORDFLOAT, length(), NUMBER, pow(), REAL, and unitsphere().

Referenced by starters::into_file(), starters::into_file2(), starters::into_file7_pt1(), and starters::into_file8_pt1(). 

00146                                                                                                 {
00147         double density=(REAL)numberofspheres/pow(length, dimension);
00148         return density*unitsphere(dimension)*pow(radius,dimension);
00149 }

REAL give_radius (  REAL    fillingfactor,
NUMBER    numberofspheres,
COORDFLOAT    length,
int    dimension
) 
 

Definition at line 169 of file sphere.h.

References COORDFLOAT, length(), NUMBER, pow(), REAL, and unitsphere().

Referenced by counters::choose_optimal_cuts(), starters::into_file7_pt1(), starters::into_file8_pt1(), ff::is_the_biggestcluster_bigger_than_a_ratio(), ff::is_the_incl_meancluster_bigger_than_a_ratio(), ff::is_the_numberofcl_smaller_than_a_ratio(), ff::is_there_a_spanning_cluster(), ff::is_there_only_one_cluster(), R_critical(), R_critical_guessed(), datafiles::set_and_show_filename(), optimize::test_average_time_for_specified_cuts(), and datafiles::write_one_result(). 

00169                                                                                                 {
00170         double density=(REAL)numberofspheres/pow(length, dimension);
00171         return pow(( fillingfactor / density / unitsphere(dimension) ),(1/((double)dimension)));
00172 }

ostream& operator<< (  ostream &    os,
sphere &    z
) 
 

Definition at line 110 of file sphere.h.

References sphere::c, sphere::clno, sphere::clsz, and sphere::r. 

00110                                             {
00111   return os<<"["<<z.c<<" radius="<<z.r<<" clno="<<z.clno<<" clsize=" << z.clsz<<"]";
00112 }

bool overlap (  sphere &    sph1,
sphere &    sph2,
sphere &    temp
) 
 

Definition at line 98 of file sphere.h.

References sphere::c, length(), and sphere::r.

Referenced by overlap(), and test_measureclass(). 

00098                                                         {               // reference instead of copy --> faster
00099         temp.c  = sph1.c;
00100         temp.c -= sph2.c;               // using -= instead of - is much faster
00101         return ( length (temp.c) < (sph1.r + sph2.r) );
00102 }

bool overlap (  sphere &    sph1,
sphere &    sph2
) 
 

Definition at line 94 of file sphere.h.

References sphere::c, length(), and sphere::r. 

00094                                           {             // reference instead of copy --> faster
00095         return ( length((sph1.c - sph2.c)) < (sph1.r + sph2.r) );
00096 }

bool overlap2 (  sphere &    sph1,
sphere &    sph2,
sphere &    temp
) 
 

Definition at line 104 of file sphere.h.

References sphere::c, sphere::r, and squarelength().

Referenced by counters::combine(), counters::count_clusters_iteratively(), counters::count_clusters_iteratively2(), counters::count_clusters_iteratively_only_selected_spherenumbers(), grid::find_neighbours_in_a_box_recursion(), and counters::neighbour_recursion(). 

00104                                                          {              // no SQRT but radii * radii
00105         temp.c  = sph1.c;
00106         temp.c -= sph2.c;               // using -= instead of - is much faster
00107         return ( squarelength (temp.c) < (sph1.r + sph2.r) * (sph1.r + sph2.r) );
00108 }

REAL percolating_fillingfactor_for_two_spheres (  int    dim ) 
 

Definition at line 213 of file sphere.h.

References pow(), REAL, sqrt(), and unitsphere().

Referenced by starters::max_ff(). 

00214 { 
00215         return ( (2 * unitsphere(dim)* pow(0.5*sqrt(dim),dim) ) ) ;
00216 }

REAL percolating_fillingfactor_for_two_spheres_verbose (  int    dim,
COORDFLOAT    length
) 
 

Definition at line 190 of file sphere.h.

References COORDFLOAT, length(), pow(), REAL, sqrt(), and unitsphere().

Referenced by starters::max_ff(). 

00192 { 
00193         REAL diagonal=sqrt(dim)*length;  // Pythargoras:
00194                                                                          // sqrt (L*L + L*L)    
00195                                                                      // = sqrt(2)*L for 2dim, 
00196                                                                          //
00197                                                                          // sqrt(  sqrt(2)*L * sqrt(2)*L + L * L ) 
00198                                                                          // = sqrt(3)*L for 3dim;
00199                                                                          //
00200                                                                          // sqrt(  sqrt(3)*L * sqrt(3)*L + L * L ) 
00201                                                                          // = sqrt (4) * L = 2*L  for 4dim
00202                                                                          
00203         REAL radius = 0.5 * diagonal;                   // two touching spheres in opposite corners
00204 
00205         REAL vol_one_sphere=unitsphere(dim)*pow(radius, dim);
00206 
00207         REAL vol_space= pow(length, dim);
00208 
00209         return ( (2 * vol_one_sphere) / vol_space) ;
00210 }

REAL R_critical (  NUMBER    no_of_spheres,
COORDFLOAT    length,
int    dimension
) 
 

Definition at line 175 of file sphere.h.

References COORDFLOAT, critical_fillingfactor(), give_radius(), length(), NUMBER, and REAL.

Referenced by optimize::choose_cuts_with_reference_algo(), optimize::choose_dividings(), optimize::double_N_and_run_all_faster_cuts(), optimize::double_N_and_run_specified_cuts(), frontend::introduction(), starters::listcount(), optimize::new_vs_old_algo(), counters::reference_test(), and optimize::run_different_cuts(). 

00175                                                                          {
00176         REAL ffc=critical_fillingfactor(dimension,no_of_spheres);
00177         if (ffc==-1) return -1;
00178         return give_radius(ffc, no_of_spheres, length, dimension);
00179 }

REAL R_critical_guessed (  NUMBER    no_of_spheres,
COORDFLOAT    length,
int    dimension
) 
 

Definition at line 181 of file sphere.h.

References COORDFLOAT, critical_fillingfactor(), ff_critical_infinite_limit(), give_radius(), length(), NUMBER, and REAL.

Referenced by optimize::choose_cuts_with_reference_algo(), optimize::choose_dividings(), optimize::compare_recursion_and_Stoddard_iteration(), optimize::double_N_and_run_all_faster_cuts(), optimize::double_N_and_run_specified_cuts(), frontend::introduction(), starters::listcount(), optimize::new_vs_old_algo(), counters::reference_test(), optimize::run_different_cuts(), frontend::svg_frontend(), optimize::test_average_time_for_specified_cuts(), and test_spanningclusters(). 

00181                                                                                  {
00182         REAL ffc=critical_fillingfactor(dimension,no_of_spheres);
00183         if (ffc!=-1) return give_radius(ffc, no_of_spheres, length, dimension);
00184         else return give_radius(ff_critical_infinite_limit(dimension), no_of_spheres, length, dimension);
00185 }

double unitsphere (  int    dimension ) 
 

Definition at line 133 of file sphere.h.

References myPI, and pow().

Referenced by give_fillingfactor(), give_radius(), percolating_fillingfactor_for_two_spheres(), percolating_fillingfactor_for_two_spheres_verbose(), starters::unitspheredimensions(), datafiles::write_averaged_cuts_intro(), datafiles::write_cuts_intro(), datafiles::write_intro(), datafiles::write_intro7(), datafiles::write_intro8(), and datafiles::write_intro_square(). 

00133                                  {                                      // Otto Forster, Analysis 3, p. 52
00134         double halfdim=.5*dimension;
00135         double nominator=pow(myPI, (int)halfdim );
00136         double denominator=1;
00137         do {
00138                 denominator*=halfdim;
00139                 halfdim-=1;
00140         }while (halfdim>0);
00141         return (nominator/denominator);
00142 }

Variable Documentation

double myPI = 2*acos(0.0)
 

Definition at line 131 of file sphere.h.

Referenced by unitsphere().




Diploma Thesis Sourcecode Documentation
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www.AndreasKrueger.de/thesis/code