update packages

[CreaPhase.git] / octave_packages / m / geometry / tsearchn.m

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+## Copyright (C) 2007-2012 David Bateman
+##
+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@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 = size (t, 1);
+  [m, n] = size (x);
+  mi = size (xi, 1);
+  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 a
+  ## (N+1)-by-(N) matrix, and arbitrary point P in cartesion coordinates,
+  ## represented by a N-by-1 row vector can be written as
+  ##
+  ## P = Beta * T
+  ##
+  ## Where Beta is a 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 below is generalize 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])