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• EQSP 1.10 Released

  EQSP 1.10 is the first public release of the Recursive Zonal Equal Area (EQ) Sphere Partitioning Toolbox. The EQ Sphere Partitioning Toolbox is a Matlab toolbox which provides algorithms for partitioning and point distribution on spheres of arbitrary dimension.

  posted by leopardi 1597 days ago

• eqsp eqsp-1.10 file released: eqsp-1.10.zip

  Recursive Zonal Equal Area (EQ) Sphere Partitioning Toolbox. Release 1.10 2005-06-26 Copyright 2004-2005 Paul Leopardi for the University of New South Wales. CHANGELOG For licensing, see COPYING For references, see AUTHORS Changes between Revision 1.02 and Release 1.10 as at 2005-06-26 =============================================================== 1) Renamed directories New name Old name ---------------------------------- eq_illustrations illustrations eq_partitions partitions eq_point_set_props point_set_props eq_region_props region_props eq_test test eq_utilities utilities 2) Renamed functions New name Old name ---------------------------------- eq_utilities: euc2sph_dist e2s sph2euc_dist s2e polar2cart s2x cart2polar2 x2s2 Other files affected by this change are: ./Contents.m eq_illustrations: project_s2_partition.m project_s3_partition.m show_s2_partition.m eq_partitions: eq_point_set.m eq_point_set_polar.m eq_point_set_props: calc_packing_density.m eq_region_props/private: max_diam_bound_of_regions.m max_vertex_diam_of_regions.m eq_utilities: Contents.m 3) Moved functions eq_illustrations/private to to eq_utilities fatcurve.m haslight.m Related changes: eq_utilities/fatcurve.m: o Flesh out description and examples Other files affected by this change are: ./Contents.m eq_utilities: Contents.m 4) Renamed documentation files New name Old name ---------------------------------- ./ AUTHORS AUTHORS.txt CHANGELOG CHANGELOG.txt COPYING COPYING.txt INSTALL INSTALL.txt These files amd all M files have been updated to reflect this change. 5) Changed documentation file format ./README.txt ./INSTALL.txt These files now have lines terminated by CR-LF to suit DOS and Windows Notepad. 6) Distinguish between info and error messages during installation and uninstallation ./: install_eq_toolbox.m uninstall_eq_toolbox.m private install.m uninstall.m 7) Drop old x2s2 code by Jakob Bjerkemo. eq_utilities/cart2polar2.m: Use cart2sph ./AUTHORS: Drop reference to x2s2, 2001-03-27 by Jakob Bjerkemo for School of Mathematics, UNSW. since this code is no longer used. 8) Optimizations eq_partitions/eq_point_set_polar.m Optimize running time: o use slice assignments o trade space for time by using a cache 9) Fixes for installation bugs ./install_eq_toolbox.m: o Restructure tests for existing pathdef.m file and guesses for pathdef_dir o Simplify tests after mkdir o On Windows, do not use [getenv('USERPROFILE') '\matlab'] directory private/savepathonly.m o Initialize cell array removed{} as size 0 rather than size 1 o On Windows, do not remove [getenv('USERPROFILE') '\matlab'] directory ./INSTALL Updated to reflect these fixes. 10) Other bug fixes eq_partitions/eq_regions.m: Fix bug in assignment of dim_1_rot eq_point_set_props/point_set_energy_dist.m Fix nasty but obvious bug by using separate variables dist and min_dist 11) Packaging uses *.zip rather than *.tar.gz ./INSTALL updated to reflect this. 12) New references ./AUTHORS: Add reference to [Leo05]. 13) Files in private modified and relicenced with permission ./AUTHORS updated to reflect this. 14) New Release number 1.10 Update release number in all Contents.m files, as well as AUTHORS CHANGELOG COPYING INSTALL.txt README.txt Changes between Revision 1.01 and Revision 1.02 as at 2005-04-24 ================================================================ 1) Optimizations eq_partitions/eq_regions.m: Optimize running time: o move 'if nargout' blocks, refactor slice assignments o trade space for time by using a cache eq_utilities/area_of_cap.m: o Use incomplete Beta function BETAINC for dim == 3, (when s_cap < pi/6 or s_cap > pi*5/6) and for all dim > 3. o Use sin(s_cap).^2 in preference to (1-cos(s_cap))/2. eq_utilities/sradius_of_cap.m: o Use asin rather than acos to avoid subtraction. o Use symmetry to avoid loss of accuracy in the Southern hemisphere. o Remove check for when area is close to area of sphere. Changes between Release 1.00 and Revision 1.01 as at 2005-03-16 =============================================================== 1) Optimizations eq_utilities/area_of_cap.m: Use incomplete Beta function BETAINC for dim > 8. Changes between first release of 2004-11-20 and Release 1.00 as at 2005-02-13 ============================================================================= The main semantic change is listed at 10.5) below, and elaborated here. Circle offset is now the default for EQ_POINT_SET_POLAR and EQ_REGIONS, because the original default placement of regions was arbitrary and haphazard. The main effect of this change is that the default result of partitions for dim > 1 has changed. This includes the default result for EQ_POINT_SET and all functions which call it. As a consequence, the energy of the default RZ point set for dim > 1 is likely to be different from the energy obtained from earlier versions of the software, including the version of 2004-11-20. List of changes. --------------- 1) Extensive help comments and updated copyright notices throughout. This includes Contents.m in each user-visible directory. 2) Complete restructure from a single directory to the following structure: .: AUTHORS.txt CHANGELOG.txt Contents.m COPYING.txt illustrations/ info.ins install_eq_toolbox.m INSTALL.txt partitions/ point_set_props/ private/ README.txt region_props/ test/ uninstall_eq_toolbox.m utilities/ illustrations: Contents.m illustration_options.m private/ project_point_set.m project_s2_partition.m project_s3_partition.m show_s2_partition.m show_r3_point_set.m illustrations/private: fatcurve.m haslight.m show_s2_sphere.m surf_jet.m x2eqarea.m x2stereo.m partitions: Contents.m illustrate_eq_algorithm.m partition_options.m private/ eq_caps.m eq_point_set.m eq_point_set_polar.m eq_regions.m partitions/private: bot_cap_region.m cap_colats.m centres_of_regions.m circle_offset.m ideal_region_list.m num_collars.m polar_colat.m rot3.m round_to_naturals.m s2_offset.m sphere_region.m top_cap_region.m point_set_props: calc_dist_coeff.m calc_energy_coeff.m calc_packing_density.m Contents.m point_set_dist_coeff.m point_set_energy_coeff.m point_set_energy_dist.m point_set_min_dist.m point_set_packing_density.m eq_dist_coeff.m eq_energy_coeff.m eq_energy_dist.m eq_min_dist.m eq_packing_density.m eq_point_set_property.m private: install.m savepathonly.m uninstall.m region_props: Contents.m private/ eq_diam_bound.m eq_diam_coeff.m eq_regions_property.m eq_vertex_diam_coeff.m eq_vertex_diam.m region_props/private: expand_region_for_diam.m max_diam_bound_of_regions.m max_vertex_diam_of_regions.m pseudo_region_for_diam.m test: Contents.m eq_area_error.m utilities: area_of_cap.m area_of_collar.m area_of_ideal_region.m area_of_sphere.m Contents.m e2s.m euclidean_dist.m ideal_collar_angle.m s2e.m s2x.m spherical_dist.m sradius_of_cap.m volume_of_ball.m x2s2.m 3) Wholesale renaming of functions Functions were renamed to make the names more consistent, more inutitive, more distinctive, and sometimes shorter. The change log before 2004-11-20 refers to functions by their old names. New name Old name ---------------------------------- illustrations: project_s2_partition.m illustrate_s2_partition.m project_s3_partition.m illustrate_s3_partition.m show_s2_partition.m plot3_s2_partition.m partitions: eq_caps.m part_to_caps.m eq_point_set.m partsphere.m eq_point_set_polar.m part_to_points.m eq_regions.m part_to_regions.m partitions/private: rot3.m rot.m point_set_props: point_set_energy_dist.m sphere_energy_dist.m point_set_min_dist.m sphere_min_dist.m region_props: eq_diam_bound.m max_diam_bound.m eq_diam_coeff.m vertex_diam_bound_coeff.m eq_vertex_diam_coeff.m vertex_diam_coeff.m eq_vertex_diam.m max_vertex_diam.m test: eq_area_error.m area_error.m 4) New functions, replaced functions, deleted functions The following functions are new. Many of these are mentioned in the changes listed below. install_eq_toolbox.m o Install using Toolbox Installer, with sensible defaults uninstall_eq_toolbox.m o Uninstall using Toolbox Installer. illustrations/illustration_options.m o Options for illustrations of RZ partitions illustrations/project_point_set.m o Use projection to illustrate a point set of S^2 or S^3 illustrations/show_r3_point_set.m o 3D illustration of a point set illustrations/private/haslight.m o Check if axis handle has a light attached illustrations/private/show_s2_sphere.m o Illustrate the unit sphere S^2 illustrations/private/surf_jet.m o Set up extreme color values using COLORMAP JET partitions/partition_options.m o Options for RZ partition partitions/private/s2_offset.m o Experimental offset rotation of S^2 point_set_props/calc_dist_coeff.m o Coefficient of minimum distance point_set_props/calc_packing_density.m o Density of packing given by minimum distance point_set_props/point_set_dist_coeff.m o Coefficient of minimum distance of a point set point_set_props/point_set_energy_coeff.m o Coefficient in expansion of energy of a point set point_set_props/point_set_energy_dist.m o r^(-s) energy and minimum distance of a point set point_set_props/point_set_min_dist.m o Minimum distance between points of a point set point_set_props/point_set_packing_density.m o Density of packing given by min dist of a point set point_set_props/eq_dist_coeff.m o Coefficient of minimum distance of an RZ point set point_set_props/eq_energy_coeff.m o Coefficient in expansion of energy of an RZ point set point_set_props/eq_min_dist.m o Minimum distance between points of an RZ point set point_set_props/eq_packing_density.m o Density of packing given by minimum distance of RZ point set point_set_props/eq_point_set_property.m o Property of an RZ point set private/install.m o Install toolbox directories private/savepathonly.m o Save the current MATLAB path to the file pathdef.m private/uninstall.m o Uninstall toolbox directories region_props/eq_regions_property.m o Property of regions of an RZ partition region_props/eq_vertex_diam_coeff.m o Coefficient of maximum vertex diameter of RZ partition The following functions have been replaced: list_energy_dist.m and list_energy_dist_squares.m, o Replaced by point_set_props/eq_energy_dist.m list_min_dist_powers.m and list_min_dist_squares.m, o Replaced by point_set_props/eq_min_dist.m doc.m, help.m, readme.m o Replaced by AUTHORS.txt, CHANGELOG.txt, README.txt and Contents.m stereoplot3.m o Replaced by illustrations/project_point_set.m The following functions have been deleted: calc_dist_ratio.m o Out of scope. dist_matrix.m, sphere_dist_matrix.m o Out of scope. minus_dist.m, minus_dist_sq.m o No longer needed. Were used in constrained nonlinear optimization to estimate diameter. r2s.m, s2r.m o Duplicates of e2s.m and s2e.m. region_is_cap.m, region_is_sphere.m o No longer needed. Were used to estimate diameter. run_diam_bound_coeff_from.m, run_vertex_diam_bound_coeff_from.m run_vertex_diam_bound_coeff.m, run_vertex_diam_coeff.m o Out of scope. Were used for batch jobs run from Linux shell scripts. 5) Use of subfunctions. The following M files now contain the subfunctions as listed. As a consequence, the subfunctions no longer exist as separate M files. illustrations/illustration_options.m: DUPLICATE_ERROR, OPTION_ERROR, VALUE_ERROR illustrations/project_s2_partition.m: PROJECT_S2_REGION, PROJECT_S2_EQ_POINT_SET illustrations/project_s3_partition.m: PROJECT_S3_REGION, PROJECT_S3_EQ_POINT_SET illustrations/show_s2_partition.m: SHOW_S2_REGION partitions/illustrate_eq_algorithm.m: OPTION_ARGUMENTS, ILLUSTRATE_STEPS_1_2, ILLUSTRATE_STEPS_3_5, ILLUSTRATE_STEPS_6_7 partitions/partition_options.m: DUPLICATE_ERROR, OPTION_ERROR, VALUE_ERROR point_set_props/calc_energy_coeff.m: SPHERE_INT_ENERGY point_set_props/point_set_energy_dist.m: POTENTIAL region_props/private/expand_region_for_diam.m: APPEND region_props/private/max_diam_bound_of_regions.m: DIAM_BOUND_REGION region_props/private/max_vertex_diam_of_regions.m: VERTEX_DIAM_REGION test/eq_area_error.m: AREA_OF_REGION utilities/area_of_cap.m: AREA_INTEGRAND_OF_CAP 6) Installation functions install_eq_toolbox.m, uninstall_eq_toolbox.m, which use the modified Toolbox Installer functions private/install.m and private/uninstall.m. Changes to private/install.m: o Do not warn on IS_INSTALLED; do not save info.ins o Use savepath rather than path2rc with Matlab 7 or greater Changes to private/uninstall.m o Use rmpath only when directory name is in path. o Do not warn on IS_INSTALLED; do not save info.ins o Use savepath rather than path2rc with Matlab 7 or greater o Use pathsep rather than ':', use lower case if not case sensitive 7) Partition options and illustration options functions. These make the user interface more consistent and easier to use. Partition options are implemented by partitions/partition_options.m and used by illustrations/project_s2_partition.m illustrations/project_s3_partition.m illustrations/show_s2_partition.m partitions/illustrate_eq_algorithm.m partitions/eq_point_set.m partitions/eq_point_set_polar.m partitions/eq_regions.m point_set_props/eq_energy_dist.m point_set_props/eq_point_set_property.m Illustration options are implemented by illustrations/illustration_options.m and used by illustrations/project_point_set.m illustrations/project_s2_partition.m illustrations/project_s3_partition.m illustrations/show_s2_partition.m illustrations/show_r3_point_set.m partitions/illustrate_eq_algorithm.m 8) Consistent acceptance of argument N as an arbitrary array. This also makes the user interface more consistent and easier to use. The following functions contain loops where N is flattened into a row matrix and the result is reshaped to the original array size of N. point_set_props/calc_energy_coeff.m point_set_props/eq_energy_dist.m point_set_props/eq_point_set_property.m region_props/eq_diam_coeff.m region_props/eq_regions_property.m test/eq_area_error.m The following function uses the function EQ_POINT_SET_PROPERTY: point_set_props/eq_min_dist.m The following functions use the function EQ_REGIONS_PROPERTY: region_props/eq_diam_bound.m region_props/eq_vertex_diam.m As a consequence of these changes, the following functions have been replaced: list_energy_dist.m and list_energy_dist_squares.m, replaced by point_set_props/eq_energy_dist.m list_min_dist_powers.m and list_min_dist_squares.m, replaced by point_set_props/eq_min_dist.m Also, region_props/eq_vertex_diam_coeff.m has been simplified. The following functions also use flatten and reshape, but for an argument other than N: utilities/area_of_cap.m for argument S_CAP utilities/sradius_of_cap.m for argument AREA 9) Checks for number of arguments. The following functions now use NARGCHK: partitions/eq_caps.m partitions/eq_point_set.m partitions/eq_point_set_polar.m partitions/eq_regions.m point_set_props/calc_dist_coeff.m point_set_props/calc_packing_density.m point_set_props/point_set_dist_coeff.m point_set_props/point_set_energy_coeff.m point_set_props/point_set_packing_density.m point_set_props/eq_dist_coeff.m point_set_props/eq_energy_coeff.m point_set_props/eq_energy_dist.m point_set_props/eq_min_dist.m point_set_props/eq_packing_density.m point_set_props/eq_point_set_property.m region_props/eq_diam_coeff.m test/eq_area_error.m The following functions now use NARGOUTCHK: partitions/eq_caps.m partitions/eq_regions.m region_props/eq_diam_coeff.m test/eq_area_error.m 10) Changes which affect one or a few functions. 10.1) illustrations/project_s2_partition.m Now uses normalized font sizes. 10.2) illustrations/project_s2_partition.m, illustrations/project_s3_partition.m o Now use illustrations/illustrate_point_set.m o Removed unnecessary calls to PACK 10.3) illustrations/show_s2_partition.m, illustrations/show_r3_point_set.m, o Now use new function SURF_JET to set up extreme values for COLARMAP JET. Also, SURF_JET uses HASLIGHT to determine if a light already exists, and only calls CAMLIGHT if there is no existing light. o Now use new function SHOW_S2_SPHERE to draw the unit sphere S^2. Also, SHOW_S2_SPHERE sets specular reflection of the unit sphere to 0. o show_s2_partition now uses PAUSE(0) to build up the illustration collar-by-collar rather than region-by-region. This is faster. 10.4) partitions/eq_caps.m Check for integer dim and N removed. 10.5) partitions/eq_point_set_polar.m, partitions/eq_regions.m, o Check for integer dim and N moved to earlier in the function. o Circle offset is now the default. o Now use new function S2_OFFSET. 10.6) partitions/eq_regions.m DIM_1_ROT is now consistently created whenever NARGOUT > 1. 10.7) test/area_error.m Call to PART_TO_REGIONS_FOR_DIAM corrected to call EQ_REGIONS. 10.8) utilities/circle_offset.m Details of the extra twist in CIRCLE_OFFSET have changed. Was MIN(4,FLOOR(N_BOT/4))/N_BOT and always applied, since the offset was optional. Is now 6/N_BOT and applied only if EXTRA_OFFSET is true. 10.9) utilities/sradius_of_cap.m Handles upper end point of interval more robustly. If ABS(AREA-AREA_OF_SPHERE(DIM)) < EPS then S_CAP is set to pi, instead of calling FZERO. 10.10) utilities/x2s2.m Now uses ATAN2. This makes X2S2(EQ_POINT_SET(2,N)) more consistent with EQ_POINT_SET_POLAR(2,N). Revision history before first release of 2004-11-20 =================================================== Matlab revision history ----------------------- append.m: 2004-01-05 Started. area_error.m: 2004-08-18 Use a multidimensional array for regions 2004-03-23 Simplify by removing options. 2004-01-20 Ensure that routine works whether N is a number or range specified by a row matrix . 2004-01-19 Started. area_integrand_of_cap.m: 2004-03-26 Area integrand for quadrature in area_of_cap. 2004-03-26 Started. area_of_cap.m: 2004-06-11 Fix incorrect case 5. Use expressions from Maple up to dim=8 2004-03-23 Use Lobatto quadrature rather than symbolic toolbox for dim > 5. Use the term "spherical radius" rather than just "angle". Rename variables to match use of "spherical radius". 2004-01-05 Started. area_of_collar.m: 2004-01-19 Started. area_of_ideal_region.m: 2004-01-19 Rename area_of_region to area_of_ideal_region. 2004-01-05 Started. area_of_region.m: 2004-03-23 Use the term "colatitude" rather than just "angle". Rename variables to match use of "colatitude". 2004-01-19 Started. area_of_sphere.m: 2004-05-24 Allow dim to be an array 2004-01-05 Started. bot_cap_region.m: 2004-01-19 Represent regions using two points only. Represent circle as [0,2*pi] to get area right. 2004-01-05 Started. calc_dist_ratio.m: 2004-01-19 Rename area_of_region to area_of_ideal_region. 2004-01-05 Started. calc_energy_coeff.m: 2004-01-05 Started. calc_energy_dist.m: 2004-01-05 Started. Changes from early Maple version: 1. Make s an optional parameter with default dim-1. 2. Return minimum distance rather than distance ratio. 3. Return two values, energy and min_dist, with min_dist optional. cap_colats.m: 2004-03-23 Rename function to cap_colats. Use the term "colatitude" rather than just "angle". Rename variables to match use of "colatitude". 2004-02-04 Improve variable names. 2004-01-19 Rename area_of_region to area_of_ideal_region. 2004-01-05 Started. centre_of_region.m: 2004-10-29 Started. centres_of_regions.m: 2004-10-29 Started. circle_offset.m: 2004-08-15 Bring centre points into alignment to match changes to part_to_caps and part_to_points. 2004-01-05 Started. diam_bound_coeff.m: 2004-06-21 Started, based on diam_bound. diam_bound_region.m: 2004-07-20 Ensure diam_bound <= 2 2004-07-15 Remove level parameter. Remove calls to region_is_boxy and corner_diam_region Use pseudo_region_for_diam 2004-06-21 Started, based on diam_region. diam_coeff.m: 2004-11-19 Removed - needs solve_diam_region which is too complicated 2004-03-23 Simplify by removing options. Simplify definition of diam coeff. 2004-01-22 Ensure that routine works whether N is a number or range specified by a row matrix. 2004-01-19 Rename area_of_region to area_of_ideal_region. 2004-01-12 Allow N to be an array. 2004-01-05 Started. diam_region.m: 2004-11-19 Removed - needs solve_diam_region which is too complicated 2004-08-18 Use the term 'vertex' rather than 'corner point'. 2004-06-28 Use region_is_boxy and region_is_cap 2004-06-21 Use corner_diam_region 2004-06-16 Use a number of different starting points for solve_diam_region 2004-03-23 Use Euclidean distance. 2004-01-19 Represent regions using two points only. 2004-01-05 Started. euclidean_dist.m: 2004-01-05 Started. expand_region_for_diam.m: 2004-08-18 Remove unused fuzz variable. Fix help comment. 2004-06-27 Use pseudo_region_for_diam 2004-03-23 Use the term "colatitude" rather than just "angle". Rename variables to match use of "colatitude". 2004-01-19 Started. ideal_collar_angle.m: 2004-10-19 Allow N to be an array 2004-06-02 Revert to definition as per revision 1.02 2004-04-08 Use factor of r2s(1) to avoid kink in value when Euclidean == 1 2004-04-08 Convert Euclidean to spherical distance only when Euclidean <= 1 2004-03-25 Convert Euclidean to spherical distance 2004-01-19 Rename area_of_region to area_of_ideal_region. 2004-01-05 Started. ideal_region_list.m: 2004-03-23 Use the term "colatitude" rather than just "angle". Rename variables to match use of "colatitude". 2004-02-04 Apply some optimizations. 2004-01-05 Started. illustrate_s2_partition.m: 2004-10-29 Add default fontsize and fix other defaults 2004-09-22 Add fontsize parameter 2004-08-19 Started, based on illustrate_s3_partition. illustrate_s2_points.m: 2004-08-19 Started, based on illustrate_s3_points. illustrate_s2_region.m: 2004-08-19 Started, based on illustrate_s3_region. illustrate_s3_partition.m: 2004-10-29 Match output arguments of part_to_regions 2004-08-18 Match output arguments of part_to_regions 2004-08-17 Optionally create a movie 2004-08-13 Started. illustrate_s3_points.m: 2004-01-05 Started. illustrate_s3_region.m: 2004-08-13 Started. list_energy_dist.m: 2004-01-05 Started. Changes from early Maple version: 1. Make s an optional parameter with default dim-1. 2. Return minimum distance rather than distance ratio. 3. Return two values, energy and min_dist, with min_dist optional. list_energy_dist_squares.m: 2004-01-05 Started. Changes from early Maple version: 1. Make s an optional parameter with default dim-1. 2. Return minimum distance rather than distance ratio. 3. Return two values, energy and min_dist, with min_dist optional. max_diam_bound.m: 2004-06-21 based on max_diam Started. max_diam_bound_of_regions.m: 2004-08-18 diam_bound_region no longer has a level parameter Use a multidimensional array for regions 2004-06-21 Started, based on max_diam_of_regions. max_diam.m: 2004-11-19 Removed - needs solve_diam_region which is too complicated 2004-03-23 Simplify by removing options. 2004-01-05 Started. max_diam_of_regions.m: 2004-11-19 Removed - needs solve_diam_region which is too complicated 2004-08-18 Use a multidimensional array for regions 2004-03-23 Use the term "colatitude" rather than "latitude". Rename variables to match use of "colatitude". 2004-01-05 Started. max_vertex_diam.m: 2004-08-18 Use the term 'vertex' rather than 'corner point'. 2004-07-26 Started, based on max_diam. max_vertex_diam_of_regions.m: 2004-08-18 Use a multidimensional array for regions Use the term 'vertex' rather than 'vertex point'. 2004-07-26 Started, based on max_diam_of_regions. num_collars.m: 2004-10-19 Allow N, c_polar and a_ideal to be arrays 2004-03-23 Simplify by removing options. Use floor(x+0.3) rather than rounding. Use the term "colatitude" rather than just "angle". Rename variables to match use of "colatitude". 2004-01-05 Started. partsphere.m: 2004-10-15 Correct help comments 2004-06-19 Match changes to part_to_points 2004-01-05 Started. part_to_caps.m: 2004-08-14 Make dim==1 consistent with dim>1 by returning the longitude of a sector enclosing the cumulative sum of arc lengths given by summing n_regions. 2004-03-23 Simplify by removing options. Use the term "colatitude" rather than just "angle". Rename variables to match use of "colatitude". 2004-01-05 Started. part_to_points.m: 2004-08-18 Fix O(3) rotation. 2004-08-14 Match change in part_to_caps for dim==1 2004-06-19 Simplify by removing options 2004-01-08 (Experimental) Rotate 2-spheres to prevent alignment of north poles. 2004-01-05 Started. part_to_regions.m: 2004-10-18 Remove output parameter top_n_regions Make output parameter dim_1_rot consistent with offset_regions 2004-08-18 Restore output parameter top_n_regions Fix O(3) rotation 2004-08-17 Use a multidimensional array for regions (Experimental) Return dim_1_rot array of O(3) offset rotations for dim=3. 2004-08-14 Match change in part_to_caps for dim==1 2004-03-23 Simplify by removing options. Use the term "colatitude" rather than just "angle". Rename variables to match use of "colatitude". 2004-01-19 Represent regions using two points only. 2004-01-05 Started. plot3_s2_partition.m: 2004-09-22 Add fontsize parameter 2004-08-19 Started, based on illustrate_s3_partition. plot3_s2_region.m: 2004-08-19 Started, based on illustrate_s3_region. polar_colat.m: 2004-10-19 Allow N to be an array, allow N==1, N==2. 2004-03-23 Rename function to polar_colat. Use the term "colatitude" rather than just "angle". Rename variables to match use of "colatitude". 2004-01-19 Rename area_of_region to area_of_ideal_region. 2004-01-05 Started. potential.m: 2004-08-05 Change ln to log 2004-01-05 Started. pseudo_region_for_diam.m: 2004-06-27 Started, based on expand_region_for_diam. r2s.m: 2004-03-25 Started. region_is_cap.m: 2004-06-28 Started, based on region_is_boxy. region_is_sphere.m: 2004-06-29 Started, based on region_is_cap. round_to_naturals.m: 2004-01-05 Started. s2e.m: 2004-07-02 Change name to s2e 2004-01-05 Started. s2r.m: 2004-01-05 Started. s2x.m: 2004-06-19 Normalize over all dimensions, not just the last one 2004-06-03 Optimize for speed. 2004-01-05 Started. solve_diam_region.m: 2004-11-19 Removed - too complicated - needs constrained nonlinear optimization 2004-06-16 Parameters s1 and s2 give the starting point. Return the points r1 and r2 to the caller. Adjust limits. Turn off all warnings. 2004-06-14 Turn off divideByZero warning. Define tolerance. Limit iterations, function evaluations, SQP iterations. 2004-06-14 Started. sphere_energy_dist.m: 2004-01-05 Started. Changes from early Maple version: 1. Change default s from 1 to dim-1. 2. Return minimum distance rather than distance ratio. 3. Return two values, energy and min_dist, with min_dist optional. sphere_int_energy.m: 2004-01-05 Started. sphere_region.m: 2004-01-19 Represent regions using two points only. Represent circle as [0,2*pi] to get area right. 2004-01-05 Started. spherical_dist.m: 2004-01-05 Started. sradius_of_cap.m: 2004-10-19 Allow area to be an array 2004-03-23 Use the term "spherical radius" rather than just "angle". Rename variables to match use of "spherical radius". 2004-01-05 Started. stereoplot3.m: 2004-01-05 Started. top_cap_region.m: 2004-01-19 Represent regions using two points only. 2004-01-05 Started. vertex_diam_bound_coeff.m: 2004-08-18 Use the term 'vertex' rather than 'corner point'. 2004-07-26 Started, based on diam_coeff. vertex_diam_coeff.m: 2004-08-18 Use the term 'vertex' rather than 'corner point'. 2004-07-26 Started, based on diam_coeff. vertex_diam_region.m: 2004-08-18 Use the term 'vertex' rather than 'corner point'. Fix help comment. 2004-01-05 Started, based on diam_region. volume_of_ball.m: 2004-08-19 Started, based on area_of_sphere. x2eqarea.m: 2004-08-20 Work correctly for all dimensions such that dim>0. 2004-08-13 Started, based on x2stereo. x2s2.m: 2004-03-23 Import from EFV program. Clean up. EFV$ Revision:10.8 $ 2003-10-29 PL Fix bug which occurred when X(1:0) == 0 EFV$ Revision:10.0 $ 2002-07-19 PL Allow points to be anywhere, avoid division by zero EFV$ Revision: 8.0 $ 2001-10-10 Adapted by Paul Leopardi Started. 2001-10-10 Jakob Bjerkemo 2001-03-27 School of Mathematics, UNSW x2stereo.m: 2004-08-20 Match changes to x2eqarea, including new definition of dim 2004-01-05 Started. Maple revision history ---------------------- 2003-12-11: Begin port to Matlab 2003-10-08: Use a common maximum for all tests. 2003-09-29: Make S^3 plotting a little more tolerant of deviations from the axis. Refine s2x. 2003-09-27: Spherical distance spherical_dist, and Euclidean distance euclidean_dist functions. Clean up conversions s2x and s2r. 2003-09-26: Plot energy coefficients. Fix functions which list energy and energy coefficients: they had incorrect array assignments. Gram determinant for S^2 points. 2003-09-25: Use Euclidean diameters as well as spherical diameters. Fix comments for partition to regions. Add an option for partition to regions to include "degenerate regions" for the caps and for whole spheres. When obtaining maximum diameters, include diameters of degenerate regions. Fix today's changes to comparsion of diameter coefficients for square numbers of points. Fix handling of number of arguments in all functions with optional arguments. 2003-09-24: Change partition to regions to return a list of lists of points, rather than a list of trees. Fix calculation of diameters: try to compare as many points as needed and as few as possible. Reverse order of angles in polar coordinates to better match conventions. Further improve plotting of S^3 points. This revision history. 2003-09-23: Add options round_n_regions, round_n_collars, offset_regions to all partition functions. 2003-09-18: Fix calculation of diameters: diameter is not necessarily the distance between opposite points. 2003-09-17: Calculate diameters of regions: list_diam_coeff, max_diam, diam_region. Improve plotting, with optional colours. 2003-09-16: Re-organize energy tests: test_energy_dist, list_energy, calc_energy_coeff, etc. 2003-09-16: Partition to centre points in Cartesian coordinates; partsphere with min_energy option, spiral_points. 2003-09-15: Plot S^3 using stereographic projection, print_energy_heading, test_energy, min_energy option for part_to_points. 2003-09-13: Partition to "centre" points: part_to_points, uses angular centre points. More extensive comments. 2003-09-12: Partion to regions: part_to_regions, using a tree structure. Partition to "centre" points: part_to_points, using circle_offset, test_sn to test energy and distance, 2003-09-07: Partition to corner points: part_to_corners. area_of_cap based on Le Gia and Sloan. Extensive comments and references. 2003-09-05: Partition to nested spherical caps: part_to_caps. area_of_cap based on explicit area integrals for specific dimensions.

  posted 1598 days ago

• File released: /eqsp/eqsp-1.10/eqsp-1.10.zip

  posted 1598 days ago

• Code committed

  Anonymous committed patchset 1 of module CVSROOT to the EQ Sphere Partitions CVS repository, changing 11 files

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• Project Information Updated

  leopardi registered the EQ Sphere Partitions project

  posted by leopardi 1655 days ago