octave: scripts/geometry/tsearchn.m annotate

annotate scripts/geometry/tsearchn.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: 7001 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{idx} =} tsearchn (@var{x}, @var{t}, @var{xi})
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{idx}, @var{p}] =} tsearchn (@var{x}, @var{t}, @var{xi})
20158 7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	26 ## Search for the enclosing Delaunay convex hull.
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	27 ##
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	28 ## For @code{@var{t} = delaunayn (@var{x})}, finds the index in @var{t}
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	29 ## containing the points @var{xi}. For points outside the convex hull,
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	30 ## @var{idx} is NaN.
7503499a252b doc: Update docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	31 ##
21546 f7f97d7e9294 doc: Wrap m-file docstrings to 79 characters + newline (80 total). Rik <rik@octave.org> parents: 20852 diff changeset	32 ## If requested @code{tsearchn} also returns the Barycentric coordinates
f7f97d7e9294 doc: Wrap m-file docstrings to 79 characters + newline (80 total). Rik <rik@octave.org> parents: 20852 diff changeset	33 ## @var{p} of the enclosing triangles.
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	34 ## @seealso{delaunay, delaunayn}
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	35 ## @end deftypefn
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	36
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	37 function [idx, p] = tsearchn (x, t, xi)
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21751 diff changeset	38
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	39 if (nargin != 3)
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	40 print_usage ();
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	41 endif
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	42
14872 c2dbdeaa25df maint: use rows() and columns() to clarify m-files. Rik <octave@nomad.inbox5.com> parents: 14868 diff changeset	43 nt = rows (t);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	44 [m, n] = size (x);
14872 c2dbdeaa25df maint: use rows() and columns() to clarify m-files. Rik <octave@nomad.inbox5.com> parents: 14868 diff changeset	45 mi = rows (xi);
10548 479536c5bb10 Replace lowercase nan with NaN for visual cue in scripts Rik <code@nomad.inbox5.com> parents: 9245 diff changeset	46 idx = NaN (mi, 1);
479536c5bb10 Replace lowercase nan with NaN for visual cue in scripts Rik <code@nomad.inbox5.com> parents: 9245 diff changeset	47 p = NaN (mi, n + 1);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	48
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	49 ni = [1:mi].';
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	50 for i = 1 : nt
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	51 ## Only calculate the Barycentric coordinates for points that have not
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	52 ## already been found in a triangle.
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	53 b = cart2bary (x (t (i, :), :), xi(ni,:));
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	54
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	55 ## Our points xi are in the current triangle if
21751 b571fc85953f maint: Use two spaces after period to indicate sentence break. Rik <rik@octave.org> parents: 21546 diff changeset	56 ## (all (b >= 0) && all (b <= 1)). However as we impose that
b571fc85953f maint: Use two spaces after period to indicate sentence break. Rik <rik@octave.org> parents: 21546 diff changeset	57 ## sum (b,2) == 1 we only need to test all(b>=0). Note need to add
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	58 ## a small margin for rounding errors
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	59 intri = all (b >= -1e-12, 2);
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	60 idx(ni(intri)) = i;
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	61 p(ni(intri),:) = b(intri, :);
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	62 ni(intri) = [];
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	63 endfor
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21751 diff changeset	64
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	65 endfunction
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	66
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	67 function Beta = cart2bary (T, P)
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	68 ## Conversion of Cartesian to Barycentric coordinates.
24560 1c1adf6ab75d doc: Fix issues in geometry, polynomial, and interpolation chapters (bug #52835). Rik <rik@octave.org> parents: 23219 diff changeset	69 ## Given a reference simplex in N dimensions represented by an
1c1adf6ab75d doc: Fix issues in geometry, polynomial, and interpolation chapters (bug #52835). Rik <rik@octave.org> parents: 23219 diff changeset	70 ## N+1-by-N matrix, an arbitrary point P in Cartesian coordinates,
1c1adf6ab75d doc: Fix issues in geometry, polynomial, and interpolation chapters (bug #52835). Rik <rik@octave.org> parents: 23219 diff changeset	71 ## represented by an N-by-1 column vector can be written as
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	72 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	73 ## P = Beta * T
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	74 ##
24560 1c1adf6ab75d doc: Fix issues in geometry, polynomial, and interpolation chapters (bug #52835). Rik <rik@octave.org> parents: 23219 diff changeset	75 ## Where Beta is an N+1 vector of the barycentric coordinates. A criteria
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	76 ## on Beta is that
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	77 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	78 ## sum (Beta) == 1
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	79 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	80 ## and therefore we can write the above as
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	81 ##
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	82 ## P - T(end, :) = Beta(1:end-1) * (T(1:end-1,:) - ones (N,1) * T(end,:))
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	83 ##
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	84 ## and then we can solve for Beta as
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	85 ##
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	86 ## Beta(1:end-1) = (P - T(end,:)) / (T(1:end-1,:) - ones (N,1) * T(end,:))
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	87 ## Beta(end) = sum (Beta)
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	88 ##
24560 1c1adf6ab75d doc: Fix issues in geometry, polynomial, and interpolation chapters (bug #52835). Rik <rik@octave.org> parents: 23219 diff changeset	89 ## Note code below is generalized for multiple values of P, one per row.
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	90 [M, N] = size (P);
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	91 Beta = (P - ones (M,1) * T(end,:)) / (T(1:end-1,:) - ones (N,1) * T(end,:));
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	92 Beta (:,end+1) = 1 - sum (Beta, 2);
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 21751 diff changeset	93
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	94 endfunction
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	95
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	96
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	97 %!shared x, tri
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	98 %! x = [-1,-1;-1,1;1,-1];
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	99 %! tri = [1, 2, 3];
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	100 %!test
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	101 %! [idx, p] = tsearchn (x,tri,[-1,-1]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	102 %! assert (idx, 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	103 %! assert (p, [1,0,0], 1e-12);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	104 %!test
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	105 %! [idx, p] = tsearchn (x,tri,[-1,1]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	106 %! assert (idx, 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	107 %! assert (p, [0,1,0], 1e-12);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	108 %!test
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	109 %! [idx, p] = tsearchn (x,tri,[1,-1]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	110 %! assert (idx, 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	111 %! assert (p, [0,0,1], 1e-12);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	112 %!test
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	113 %! [idx, p] = tsearchn (x,tri,[-1/3,-1/3]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	114 %! assert (idx, 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	115 %! assert (p, [1/3,1/3,1/3], 1e-12);
6823 9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	116 %!test
9fddcc586065 [project @ 2007-08-24 08:27:27 by dbateman] dbateman parents: diff changeset	117 %! [idx, p] = tsearchn (x,tri,[1,1]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	118 %! assert (idx, NaN);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	119 %! assert (p, [NaN, NaN, NaN]);

Mercurial > octave

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