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% Recursive Zonal Equal Area Sphere Partitioning Toolbox.
% Release 1.12 2024-10-14
%
%Functions by category
%=====================
%
%Installation
%------------
%
% install_eq_toolbox Install toolbox
% uninstall_eq_toolbox Uninstall toolbox
%
%Recursive zonal equal area sphere partitions
%--------------------------------------------
%
% Partitions
% eq_caps Partition a sphere into to nested spherical caps
% eq_regions Recursive zonal equal area (EQ) partition of sphere
%
% Point sets
% eq_point_set Center points of regions of EQ partition,
% in Cartesian coordinates
% eq_point_set_polar Center points of regions of an EQ partition,
% in spherical polar coordinates
%
% Partition options
% partition_options Options for EQ partition
%
%Properties of recursive zonal equal area sphere partitions
%----------------------------------------------------------
%
% Area
% eq_area_error Total area error and max area error per region of an
% EQ partition
%
% Diameter
% eq_diam_bound Maximum per-region diameter bound of EQ partition
% eq_vertex_diam Maximum vertex diameter of EQ partition
%
% eq_diam_coeff Coefficients of diameter bound and vertex diameter of
% EQ partition
% eq_vertex_diam_coeff Coefficient of maximum vertex diameter of EQ partition
%
%Hook for user-defined properties
% eq_regions_property Property of regions of an EQ partition
%
%Properties of EQ point sets
%---------------------------
%
% Energy and minimum distance
% eq_energy_dist Energy and minimum distance of an EQ point set
% point_set_energy_dist Energy and minimum distance of a point set
%
% Energy
% eq_energy_coeff Coefficient in expansion of energy of an EQ point set
% point_set_energy_coeff Coefficient in expansion of energy of a point set
% calc_energy_coeff Coefficient of second term in expansion of energy
%
% Minimum distance
% eq_min_dist Minimum distance between center points of an
% EQ partition
% point_set_min_dist Minimum distance between points of a point set
%
% eq_dist_coeff Coefficient of minimum distance of an EQ point set
% point_set_dist_coeff Coefficient of minimum distance of a point set
% calc_dist_coeff Coefficient of minimum distance
%
% Spherical cap packing density
% eq_packing_density Density of packing given by minimum distance of
% EQ point set
% point_set_packing_density Density of packing given by minimum distance of
% a point set
% calc_packing_density Density of packing given by minimum distance
%
% Hook for user-defined properties
% eq_point_set_property Property of an EQ point set
%
%Histogram utilities for S^2
%---------------------------
%
% eq_count_points_by_s2_region Given a set of points, count points in each of N regions of S^2
% eq_find_s2_region Given a set of points, partition S^2 into N regions
% and find the index of the region of containing each point
% in_s2_region Test that each of a set of points on S^2 is within a given region
%
%Illustrations
%-------------
%
% Illustration of algorithms
% illustrate_eq_algorithm Illustrate the EQ partition algorithm
%
% Illustration of EQ Partitions of S^2 or S^3
% show_s2_partition 3D illustration of an EQ partition of S^2
% project_s2_partition Use projection to illustrate an EQ partition of S^2
% project_s3_partition Use projection to illustrate an EQ partition of S^3
%
% Illustration of point sets on S^2 or S^3
% show_r3_point_set 3D illustration of a point set
% project_point_set Use projection to illustrate a point set of
% S^2 or S^3
% Illustration of a recursive zonal equal area sphere partition algorithm
% illustrate_eq_algorithm Illustrate the EQ partition algorithm
%
% Illustration options
% illustration_options Options for illustrations of EQ partitions
%
% Illustration utilities
% haslight Check if axis handle has a light attached
%
%Utilities
%---------
%
% area_of_cap Area of spherical cap
% area_of_collar Area of spherical collar
% area_of_ideal_region Area of one region of an EQ partition
% area_of_sphere Area of sphere
% cart2polar2 Convert Cartesian to spherical polar coordinates on S^2
% euc2sph_dist Convert Euclidean to spherical distance
% euclidean_dist Euclidean distance between two points
% fatcurve Create a parameterized cylindrical surface
% ideal_collar_angle Ideal angle for spherical collars of an EQ partition
% polar2cart Convert spherical polar to Cartesian coordinates
% sph2euc_dist Convert spherical to Euclidean distance
% spherical_dist Spherical distance between two points on the sphere
% sradius_of_cap Spherical radius of spherical cap of given area
% volume_of_ball Volume of the unit ball
%
%Tests
%-----
%
% Tests of all functions.
%
% If the previous text scrolled off the screen, try
% more on; help eq_sphere_partitions; more off;
% Copyright 2024 Paul Leopardi
% $Revision 1.12 $ $Date 2024-10-14 $
% Copyright 2004-2005 Paul Leopardi for the University of New South Wales.
% $Revision 1.10 $ $Date 2005-06-26 $
% Function changed name from e2s to euc2sph_dist
% Function changed name from s2e to sph2euc_dist
% Function changed name from s2x to polar2cart
% Function changed name from x2s2 to cart2polar2
% Add new function fatcurve
% Add new function haslight
% Clean up descriptions
% Documentation files renamed
% $Revision 1.00 $ $Date 2005-02-13 $
%
% For licensing, see COPYING.
% For references, see AUTHORS.
% For revision history, see CHANGELOG.