Mercurial > octave
view scripts/geometry/tsearchn.m @ 31706:597f3ee61a48 stable
update Octave Project Developers copyright for the new year
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 06 Jan 2023 13:11:27 -0500 |
parents | 796f54d4ddbf |
children | 5f11de0e7440 |
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######################################################################## ## ## Copyright (C) 2007-2023 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]);