Mercurial > octave
view scripts/geometry/delaunayn.m @ 31253:a40c0b7aa376
maint: changes to follow Octave coding conventions.
* NEWS.8.md: Wrap lines to 72 chars.
* LSODE-opts.in: Use two spaces after sentence ending period.
* LSODE.cc: Use minimum of two spaces between code and start of comment.
* MemoizedFunction.m: Change copyright date to 2022 since this is the year it
was accepted into core. Don't wrap error() lines to 80 chars. Use newlines
to improve readability of switch statements. Use minimum of two spaces between
code and start of comment.
* del2.m, integral.m, interp1.m, interp2.m, griddata.m, inpolygon.m, waitbar.m,
cubehelix.m, ind2x.m, importdata.m, textread.m, logm.m, lighting.m, shading.m,
xticklabels.m, yticklabels.m, zticklabels.m, colorbar.m, meshc.m, print.m,
__gnuplot_draw_axes__.m, struct2hdl.m, ppval.m, ismember.m, iqr.m: Use a space
between comment character '#' and start of comment. Use hyphen for adjectives
describing dimensions such as "1-D".
* vectorize.m, ode23s.m: Use is_function_handle() instead of "isa (x, "function_handle")"
for clarity and performance.
* clearAllMemoizedCaches.m: Change copyright date to 2022 since this is the
year it was accepted into core. Remove input validation which is done by
interpreter. Use two newlines between end of code and start of BIST tests.
* memoize.m: Change copyright date to 2022 since this is the year it was
accepted into core. Re-wrap documentation to 80 chars. Use
is_function_handle() instead of "isa (x, "function_handle")" for clarity and
performance. Use two newlines between end of code and start of BIST tests.
Use semicolon for assert statements within %!test block. Re-write BIST tests
for input validation.
* __memoize__.m: Change copyright date to 2022 since this is the year it was
accepted into core. Use spaces in for statements to improve readability.
* unique.m: Add FIXME note to commented BIST test
* dec2bin.m: Remove stray newline at end of file.
* triplequad.m: Reduce doubly-commented BIST syntax using "#%!#" to "#%!".
* delaunayn.m: Use input variable names in error() statements. Use minimum of
two spaces between code and start of comment. Use hyphen for describing
dimensions. Use two newlines between end of code and start of BIST tests.
Update BIST tests to pass.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 03 Oct 2022 18:06:55 -0700 |
parents | 8b75954a4670 |
children | c8ad083a5802 |
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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{T} =} delaunayn (@var{pts}) ## @deftypefnx {} {@var{T} =} delaunayn (@var{pts}, @var{options}) ## Compute the Delaunay triangulation for an N-dimensional set of points. ## ## The Delaunay triangulation is a tessellation of the convex hull of a set of ## points such that no N-sphere defined by the N-triangles contains any other ## points from the set. ## ## The input matrix @var{pts} of size [n, dim] contains n points in a space of ## dimension dim. The return matrix @var{T} has size [m, dim+1]. Each row of ## @var{T} contains a set of indices back into the original set of points ## @var{pts} which describes a simplex of dimension dim. For example, a 2-D ## simplex is a triangle and 3-D simplex is a tetrahedron. ## ## An optional second argument, which must be a string or cell array of ## strings, contains options passed to the underlying qhull command. See the ## documentation for the Qhull library for details ## @url{http://www.qhull.org/html/qh-quick.htm#options}. ## The default options depend on the dimension of the input: ## ## @itemize ## @item 2-D and 3-D: @var{options} = @code{@{"Qt", "Qbb", "Qc"@}} ## ## @item 4-D and higher: @var{options} = @code{@{"Qt", "Qbb", "Qc", "Qx"@}} ## @end itemize ## ## If Qhull fails for 2-D input the triangulation is attempted again with ## the options @code{@{"Qt", "Qbb", "Qc", "Qz"@}} which may result in ## reduced accuracy. ## ## If @var{options} is not present or @code{[]} then the default arguments are ## used. Otherwise, @var{options} replaces the default argument list. ## To append user options to the defaults it is necessary to repeat the ## default arguments in @var{options}. Use a null string to pass no arguments. ## ## @seealso{delaunay, convhulln, voronoin, trimesh, tetramesh} ## @end deftypefn function T = delaunayn (pts, varargin) if (nargin < 1) print_usage (); endif ## NOTE: varargin options input validation is performed in __delaunayn__ if ((! isnumeric (pts)) || (ndims (pts) > 2)) error ("delaunayn: input PTS must be a 2-dimensional numeric array"); endif ## Perform delaunay calculation using either default or specified options if (isempty (varargin) || isempty (varargin{1})) try T = __delaunayn__ (pts); catch err if (columns (pts) <= 2) T = __delaunayn__ (pts, "Qt Qbb Qc Qz"); else rethrow (err); endif end_try_catch else T = __delaunayn__ (pts, varargin{:}); endif ## Begin check for and removal of trivial simplices if (! isequal (T, 0)) # skip trivial simplex check if no simplexes if (isa (pts, "single")) tol = 1e3 * eps ("single"); else tol = 1e3 * eps; endif ## Try to remove the ~zero volume simplices. The volume of the i-th simplex ## is given by abs(det(pts(T(i,2:end),:)-pts(T(i,1),:)))/factorial(ndim+1) ## (reference http://en.wikipedia.org/wiki/Simplex). Any simplex with a ## relative volume less than some arbitrary criteria is rejected. The ## criteria we use is the volume of a simplex corresponding to an ## orthogonal simplex (rectangle, rectangular prism, etc.) with edge lengths ## equal to the common-origin edge lengths of the original simplex. If the ## relative volume is 1e3*eps then the simplex is rejected. Note division ## of the two volumes means that the factor factorial(ndim+1) is dropped ## from volume calculations. [nt, nd] = size (T); # nt = simplex count, nd = # of simplex points dim = nd - 1; ## Calculate common origin edge vectors for each simplex (p2-p1,p3-p1,...) ## Store in 3-D array such that: ## rows = nt simplexes, cols = coordinates, pages = simplex edges edge_vecs = permute (reshape (pts(T(:, 2:nd), :).', [dim, nt, dim]), ... [2, 1, 3]) - pts(T(:, 1), :, ones (1, 1, dim)); ## Calculate orthogonal simplex volumes for comparison orthog_simplex_vols = sqrt (prod (sumsq (edge_vecs, 2), 3)); ## Calculate simplex volumes according to problem dimension if (nd == 3) ## 2-D: area = cross product of triangle edge vectors vol = edge_vecs(:,1,1) .* edge_vecs(:,2,2) ... - edge_vecs(:,1,2) .* edge_vecs(:,2,1); elseif (nd == 4) ## 3-D: vol = scalar triple product [a.(b x c)] vol = edge_vecs(:,1,1) .* ... (edge_vecs(:,2,2) .* edge_vecs(:,3,3) - ... edge_vecs(:,3,2) .* edge_vecs(:,2,3)) ... - edge_vecs(:,2,1) .* ... (edge_vecs(:,1,2) .* edge_vecs(:,3,3) - ... edge_vecs(:,3,2) .* edge_vecs(:,1,3)) ... + edge_vecs(:,3,1) .* ... (edge_vecs(:,1,2) .* edge_vecs(:,2,3) - ... edge_vecs(:,2,2) .* edge_vecs(:,1,3)); else ## 1-D and >= 4-D: simplex 'volume' proportional to det|edge_vecs| ## FIXME: Vectorize this for n-D inputs without excessive memory impact ## over __delaunayn__ itself, or move simplex checking into __delaunayn__; ## perhaps with an optimized page-wise determinant. ## See bug #60818 for speed/memory improvement attempts and concerns. vol = zeros (nt, 1); ## Reshape so det can operate in dim 1&2 edge_vecs = permute (edge_vecs, [3, 2, 1]); ## Calculate determinant for arbitrary problem dimension for ii = 1:nt vol(ii) = det (edge_vecs(:, :, ii)); endfor endif ## Mark simplices with relative volume < tol for removal idx = (abs ((vol) ./ orthog_simplex_vols)) < tol; ## Remove trivially small simplexes from T T(idx, :) = []; ## Ensure CCW node order for consistent outward normal (bug #53397) ## simplest method of maintaining positive unit normal direction is to ## reverse order of two nodes; this preserves 'nice' monotonic descending ## node 1 ordering. Currently ignores 1-D cases for compatibility. if (dim > 1 && any (negvol = (vol(! idx) < 0))) T(negvol, [2, 3]) = T(negvol, [3, 2]); endif endif endfunction ## Test 1-D input %!testif HAVE_QHULL %! assert (sortrows (sort (delaunayn ([1;2]), 2)), [1, 2]); %! assert (sortrows (sort (delaunayn ([1;2;3]), 2)), [1, 2; 2, 3]); ## Test 2-D input %!testif HAVE_QHULL %! x = [-1, 0; 0, 1; 1, 0; 0, -1; 0, 0]; %! assert (sortrows (sort (delaunayn (x), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]); ## Test 3-D input %!testif HAVE_QHULL %! x = [-1, -1, 1, 0, -1]; y = [-1, 1, 1, 0, -1]; z = [0, 0, 0, 1, 1]; %! assert (sortrows (sort (delaunayn ([x(:) y(:) z(:)]), 2)), %! [1,2,3,4;1,2,4,5]); ## 3-D test with trivial simplex removal %!testif HAVE_QHULL %! x = [0 0 0; 0 0 1; 0 1 0; 1 0 0; 0 1 1; 1 0 1; 1 1 0; 1 1 1; 0.5 0.5 0.5]; %! T = sortrows (sort (delaunayn (x), 2)); %! assert (rows (T), 12); ## 4-D single simplex test %!testif HAVE_QHULL %! x = [0 0 0 0; 1 0 0 0; 1 1 0 0; 0 0 1 0; 0 0 0 1]; %! T = sort (delaunayn (x), 2); %! assert (T, [1 2 3 4 5]); ## 4-D two simplices test %!testif HAVE_QHULL %! x = [0 0 0 0; 1 0 0 0; 1 1 0 0; 0 0 1 0; 0 0 0 1; 0 0 0 2]; %! T = sortrows (sort (delaunayn (x), 2)); %! assert (rows (T), 2); %! assert (T, [1 2 3 4 5; 2 3 4 5 6]); ## Test negative simplex produce positive normals ## 2-D test %!testif HAVE_QHULL <*53397> %! x = [-1, 0; 0, 1; 1, 0; 0, -1; 0, 0]; %! y = delaunayn (x); %! edges = permute (reshape (x(y(:, 2:end), :).', [2, 4, 2]), [2, 1, 3]) - ... %! x(y(:, 1), :, ones (1, 1, 2)); %! vol = edges(:,1,1) .* edges(:,2,2) - edges(:,1,2) .* edges(:,2,1); %! assert (all (vol >= 0)); ## 3-D test %!testif HAVE_QHULL <*53397> %! x = [[-1, -1, 1, 0, -1]',[-1, 1, 1, 0, -1]',[0, 0, 0, 1, 1]']; %! y = delaunayn (x); %! edges = permute (reshape (x(y(:, 2:end), :).', [3, 2, 3]), [2, 1, 3]) - ... %! x(y(:, 1), :, ones (1, 1, 3)); %! vol = edges(:,1,1) .* ... %! (edges(:,2,2) .* edges(:,3,3) - edges(:,3,2) .* edges(:,2,3)) ... %! - edges(:,2,1) .* ... %! (edges(:,1,2) .* edges(:,3,3) - edges(:,3,2) .* edges(:,1,3)) ... %! + edges(:,3,1) .* ... %! (edges(:,1,2) .* edges(:,2,3) - edges(:,2,2) .* edges(:,1,3)); %! assert (all (vol >= 0)); ## Input validation tests %!error <Invalid call> delaunayn () %!error <input PTS must be> delaunayn ("abc") %!error <input PTS must be> delaunayn ({1}) %!error <input PTS must be> delaunayn (true) %!error <input PTS must be> delaunayn (ones (3,3,3))