Mercurial > octave
view scripts/geometry/tsearchn.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 363fb10055df |
children | 72ef3d097059 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2007-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{idx} =} tsearchn (@var{x}, @var{t}, @var{xi}) ## @deftypefnx {} {[@var{idx}, @var{p}] =} tsearchn (@var{x}, @var{t}, @var{xi}) ## Search for the enclosing Delaunay convex hull. ## ## For @code{@var{t} = delaunayn (@var{x})}, finds the index in @var{t} ## containing the points @var{xi}. For points outside the convex hull, ## @var{idx} is NaN. ## ## If requested @code{tsearchn} also returns the Barycentric coordinates ## @var{p} of the enclosing triangles. ## @seealso{delaunay, delaunayn} ## @end deftypefn function [idx, p] = tsearchn (x, t, xi) if (nargin != 3) print_usage (); endif nt = rows (t); [m, n] = size (x); mi = rows (xi); idx = NaN (mi, 1); p = NaN (mi, n + 1); ni = [1:mi].'; for i = 1 : nt ## Only calculate the Barycentric coordinates for points that have not ## already been found in a triangle. b = cart2bary (x (t (i, :), :), xi(ni,:)); ## Our points xi are in the current triangle if ## (all (b >= 0) && all (b <= 1)). However as we impose that ## sum (b,2) == 1 we only need to test all(b>=0). Note need to add ## a small margin for rounding errors intri = all (b >= -1e-12, 2); idx(ni(intri)) = i; p(ni(intri),:) = b(intri, :); ni(intri) = []; endfor endfunction function Beta = cart2bary (T, P) ## Conversion of Cartesian to Barycentric coordinates. ## Given a reference simplex in N dimensions represented by an ## N+1-by-N matrix, an arbitrary point P in Cartesian coordinates, ## represented by an N-by-1 column vector can be written as ## ## P = Beta * T ## ## Where Beta is an N+1 vector of the barycentric coordinates. A criteria ## on Beta is that ## ## sum (Beta) == 1 ## ## and therefore we can write the above as ## ## P - T(end, :) = Beta(1:end-1) * (T(1:end-1,:) - ones (N,1) * T(end,:)) ## ## and then we can solve for Beta as ## ## Beta(1:end-1) = (P - T(end,:)) / (T(1:end-1,:) - ones (N,1) * T(end,:)) ## Beta(end) = sum (Beta) ## ## Note code below is generalized for multiple values of P, one per row. [M, N] = size (P); Beta = (P - ones (M,1) * T(end,:)) / (T(1:end-1,:) - ones (N,1) * T(end,:)); Beta (:,end+1) = 1 - sum (Beta, 2); endfunction %!shared x, tri %! x = [-1,-1;-1,1;1,-1]; %! tri = [1, 2, 3]; %!test %! [idx, p] = tsearchn (x,tri,[-1,-1]); %! assert (idx, 1); %! assert (p, [1,0,0], 1e-12); %!test %! [idx, p] = tsearchn (x,tri,[-1,1]); %! assert (idx, 1); %! assert (p, [0,1,0], 1e-12); %!test %! [idx, p] = tsearchn (x,tri,[1,-1]); %! assert (idx, 1); %! assert (p, [0,0,1], 1e-12); %!test %! [idx, p] = tsearchn (x,tri,[-1/3,-1/3]); %! assert (idx, 1); %! assert (p, [1/3,1/3,1/3], 1e-12); %!test %! [idx, p] = tsearchn (x,tri,[1,1]); %! assert (idx, NaN); %! assert (p, [NaN, NaN, NaN]);