Mercurial > octave-nkf
view scripts/geometry/delaunay.m @ 17338:1c89599167a6
maint: End m-files with 1 blank line.
Simplifies automated grammarchecking script.
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author | Rik <rik@octave.org> |
---|---|
date | Wed, 28 Aug 2013 08:33:02 -0700 |
parents | c3c1ebfaa7dc |
children | d63878346099 |
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## Copyright (C) 1999-2012 Kai Habel ## ## 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} {} delaunay (@var{x}, @var{y}) ## @deftypefnx {Function File} {} delaunay (@var{x}) ## @deftypefnx {Function File} {} delaunay (@dots{}, @var{options}) ## @deftypefnx {Function File} {@var{tri} =} delaunay (@dots{}) ## Compute the Delaunay triangulation for a 2-D set of points. ## The return value @var{tri} is a set of triangles which satisfies the ## Delaunay circum-circle criterion, i.e., only a single data point from ## [@var{x}, @var{y}] is within the circum-circle of the defining triangle. ## The input @var{x} may also be a matrix with two columns where the first ## column contains x-data and the second y-data. ## ## The set of triangles @var{tri} is a matrix of size [n, 3]. Each ## row defines a triangle and the three columns are the three vertices ## of the triangle. The value of @code{@var{tri}(i,j)} is an index into ## @var{x} and @var{y} for the location of the j-th vertex of the i-th ## triangle. ## ## The optional last 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 are @code{@{"Qt", "Qbb", "Qc", "Qz"@}}. ## ## 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. ## ## If no output argument is specified the resulting Delaunay triangulation ## is plotted along with the original set of points. ## ## @example ## @group ## x = rand (1, 10); ## y = rand (1, 10); ## T = delaunay (x, y); ## VX = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ]; ## VY = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ]; ## axis ([0,1,0,1]); ## plot (VX, VY, "b", x, y, "r*"); ## @end group ## @end example ## @seealso{delaunay3, delaunayn, convhull, voronoi, triplot, trimesh, trisurf} ## @end deftypefn ## Author: Kai Habel <kai.habel@gmx.de> function tri = delaunay (varargin) if (nargin < 1 || nargin > 3) print_usage (); endif options = []; switch (nargin) case 1 if (! ismatrix (varargin{1}) || columns (varargin{1}) != 2) error ("delaunay: X must be a matrix with 2 columns"); else x = varargin{1}(:,1); y = varargin{1}(:,2); endif case 2 if (isnumeric (varargin{2})) x = varargin{1}; y = varargin{2}; elseif (ischar (varargin{2}) || iscellstr (varargin{2})) options = varargin{2}; if (! ismatrix (varargin{1}) && columns (varargin{1}) != 2) error ("delaunay: X must be a matrix with 2 columns"); else x = varargin{1}(:,1); y = varargin{1}(:,2); endif else error ("delaunay: OPTIONS must be a string or cell array of strings"); endif case 3 x = varargin{1}; y = varargin{2}; options = varargin{3}; if (! (ischar (options) || iscellstr (options))) error ("delaunay: OPTIONS must be a string or cell array of strings"); endif endswitch if (! (isequal(size(x),size(y)))) error ("delaunay: X and Y must be the same size"); endif T = delaunayn ([x(:), y(:)], options); if (nargout == 0) x = x(:).'; y = y(:).'; VX = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ]; VY = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ]; plot (VX, VY, "b", x, y, "r*"); else tri = T; endif endfunction %!demo %! old_state = rand ("state"); %! restore_state = onCleanup (@() rand ("state", old_state)); %! rand ("state", 1); %! x = rand (1,10); %! y = rand (1,10); %! T = delaunay (x,y); %! VX = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ]; %! VY = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ]; %! clf; %! plot (VX,VY,"b", x,y,"r*"); %! axis ([0,1,0,1]); %!testif HAVE_QHULL %! x = [-1, 0, 1, 0]; %! y = [0, 1, 0, -1]; %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,4;2,3,4]); %!testif HAVE_QHULL %! x = [-1, 0, 1, 0]; %! y = [0, 1, 0, -1]; %! assert (sortrows (sort (delaunay ([x(:) y(:)]), 2)), [1,2,4;2,3,4]); %!testif HAVE_QHULL %! x = [-1, 0, 1, 0, 0]; %! y = [0, 1, 0, -1, 0]; %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]); %!testif HAVE_QHULL %! x = [-1, 0; 0, 1; 1, 0; 0, -1; 0, 0]; %! assert (sortrows (sort (delaunay (x), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]); %!testif HAVE_QHULL %! x = [1 5 2; 5 6 7]; %! y = [5 7 8; 1 2 3]; %! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,4;1,3,4;1,3,5;3,4,6]); %% FIXME: Need input validation tests