octave: scripts/geometry/delaunayn.m annotate

annotate scripts/geometry/delaunayn.m @ 27919:1891570abac8

update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2020.

author	John W. Eaton <jwe@octave.org>
date	Mon, 06 Jan 2020 22:29:51 -0500
parents	b442ec6dda5c
children	bd51beb6205e

rev	line source
27919 1891570abac8 update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 27918 diff changeset	1 ## Copyright (C) 2007-2020 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	2 ##
b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	3 ## See the file COPYRIGHT.md in the top-level directory of this distribution
b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	4 ## or <https://octave.org/COPYRIGHT.html/>.
b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	5 ##
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	6 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	7 ## This file is part of Octave.
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	8 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	9 ## Octave is free software: you can redistribute it and/or modify it
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	10 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	11 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	12 ## (at your option) any later version.
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	13 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	14 ## Octave is distributed in the hope that it will be useful, but
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	15 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	17 ## GNU General Public License for more details.
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	18 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	19 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6846 diff changeset	20 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	21 ## <https://www.gnu.org/licenses/>.
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	22
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	23 ## -- texinfo --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20158 diff changeset	24 ## @deftypefn {} {@var{T} =} delaunayn (@var{pts})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20158 diff changeset	25 ## @deftypefnx {} {@var{T} =} delaunayn (@var{pts}, @var{options})
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	26 ## Compute the Delaunay triangulation for an N-dimensional set of points.
20158 7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	27 ##
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	28 ## The Delaunay triangulation is a tessellation of the convex hull of a set of
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	29 ## points such that no N-sphere defined by the N-triangles contains any other
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	30 ## points from the set.
19593 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	31 ##
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	32 ## The input matrix @var{pts} of size [n, dim] contains n points in a space of
20158 7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	33 ## dimension dim. The return matrix @var{T} has size [m, dim+1]. Each row of
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	34 ## @var{T} contains a set of indices back into the original set of points
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	35 ## @var{pts} which describes a simplex of dimension dim. For example, a 2-D
7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	36 ## simplex is a triangle and 3-D simplex is a tetrahedron.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	37 ##
21546 f7f97d7e9294 doc: Wrap m-file docstrings to 79 characters + newline (80 total). Rik <rik@octave.org> parents: 20852 diff changeset	38 ## An optional second argument, which must be a string or cell array of
f7f97d7e9294 doc: Wrap m-file docstrings to 79 characters + newline (80 total). Rik <rik@octave.org> parents: 20852 diff changeset	39 ## strings, contains options passed to the underlying qhull command. See the
f7f97d7e9294 doc: Wrap m-file docstrings to 79 characters + newline (80 total). Rik <rik@octave.org> parents: 20852 diff changeset	40 ## documentation for the Qhull library for details
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	41 ## @url{http://www.qhull.org/html/qh-quick.htm#options}.
7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	42 ## The default options depend on the dimension of the input:
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	43 ##
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	44 ## @itemize
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	45 ## @item 2-D and 3-D: @var{options} = @code{@{"Qt", "Qbb", "Qc", "Qz"@}}
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	46 ##
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	47 ## @item 4-D and higher: @var{options} = @code{@{"Qt", "Qbb", "Qc", "Qx"@}}
6826 8618f29520c6 [project @ 2007-08-24 16:02:07 by jwe] jwe parents: 6823 diff changeset	48 ## @end itemize
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	49 ##
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	50 ## If @var{options} is not present or @code{[]} then the default arguments are
19593 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	51 ## used. Otherwise, @var{options} replaces the default argument list.
446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	52 ## To append user options to the defaults it is necessary to repeat the
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	53 ## default arguments in @var{options}. Use a null string to pass no arguments.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	54 ##
19164 ba167badef9f Deprecate delaunay3 and extend delaunay to 3-D inputs. Rik <rik@octave.org> parents: 17744 diff changeset	55 ## @seealso{delaunay, convhulln, voronoin, trimesh, tetramesh}
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	56 ## @end deftypefn
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	57
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	58 function T = delaunayn (pts, varargin)
7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	59
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	60 if (nargin < 1)
6826 8618f29520c6 [project @ 2007-08-24 16:02:07 by jwe] jwe parents: 6823 diff changeset	61 print_usage ();
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	62 endif
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	63
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	64 T = __delaunayn__ (pts, varargin{:});
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	65
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	66 if (isa (pts, "single"))
19172 4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	67 tol = 1e3 * eps ("single");
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7208 diff changeset	68 else
19172 4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	69 tol = 1e3 * eps;
7795 df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7208 diff changeset	70 endif
df9519e9990c Handle single precision eps values David Bateman <dbateman@free.fr> parents: 7208 diff changeset	71
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	72 ## Try to remove the zero volume simplices. The volume of the i-th simplex is
25328 3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	73 ## given by abs(det(pts(T(i,1:end-1),:)-pts(T(i,2:end),:)))/factorial(ndim+1)
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	74 ## (reference http://en.wikipedia.org/wiki/Simplex). Any simplex with a
7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	75 ## relative volume less than some arbitrary criteria is rejected. The
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	76 ## criteria we use is the volume of the simplex corresponding to an
c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	77 ## orthogonal simplex is equal edge length all equal to the edge length of
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	78 ## the original simplex. If the relative volume is 1e3*eps then the simplex
7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	79 ## is rejected. Note division of the two volumes means that the factor
25328 3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	80 ## factorial(ndim+1) is dropped.
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	81 [nt, nd] = size (T);
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	82 if (nd == 3)
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	83 ## 2-D case
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	84 np = rows (pts);
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	85 ptsz = [pts, zeros(np, 1)];
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	86 p1 = ptsz(T(:,1), :);
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	87 p2 = ptsz(T(:,2), :);
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	88 p3 = ptsz(T(:,3), :);
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	89 p12 = p1 - p2;
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	90 p23 = p2 - p3;
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	91 det = cross (p12, p23, 2);
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	92 idx = abs (det(:,3) ./ sqrt (sumsq (p12, 2))) < tol & ...
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	93 abs (det(:,3) ./ sqrt (sumsq (p23, 2))) < tol;
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	94 else
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	95 ## FIXME: Vectorize this for loop or convert delaunayn to .oct function
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	96 idx = [];
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	97 for i = 1:nt
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	98 X = pts(T(i,1:end-1),:) - pts(T(i,2:end),:);
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	99 if (abs (det (X)) / sqrt (sumsq (X, 2)) < tol)
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	100 idx(end+1) = i;
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	101 endif
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	102 endfor
3b96348d5ccd delaunayn.m: Vectorize test for 2-D zero volume simplexes (bug #53689) Rik <rik@octave.org> parents: 25054 diff changeset	103 endif
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	104 T(idx,:) = [];
7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	105
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	106 endfunction
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	107
7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	108
19172 4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	109 %!testif HAVE_QHULL
4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	110 %! x = [-1, 0; 0, 1; 1, 0; 0, -1; 0, 0];
4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	111 %! assert (sortrows (sort (delaunayn (x), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]);
4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	112
4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	113 ## Test 3-D input
4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	114 %!testif HAVE_QHULL
4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	115 %! x = [-1, -1, 1, 0, -1]; y = [-1, 1, 1, 0, -1]; z = [0, 0, 0, 1, 1];
21580 ecce63c99c3f maint: Add semicolons to terminate code in %! blocks. Rik <rik@octave.org> parents: 21546 diff changeset	116 %! assert (sortrows (sort (delaunayn ([x(:) y(:) z(:)]), 2)), [1,2,3,4;1,2,4,5]);
19172 4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	117
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	118 ## FIXME: Need tests for delaunayn
13746 7ff0bdc3dc4c Revamp geometry functions dependent on Qhull (Bug #34604, Bug #33346) Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	119
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	120 ## Input validation tests
19172 4318cb91deac delaunayn.m: Slight performance increase and addition of BIST tests. Rik <rik@octave.org> parents: 19164 diff changeset	121 %!error delaunayn ()

Mercurial > octave

annotate scripts/geometry/delaunayn.m @ 27919:1891570abac8