comparison doc/interpreter/geometry.txi @ 19627:446c46af4b42 stable

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author John W. Eaton <jwe@octave.org>
date Tue, 20 Jan 2015 08:26:57 -0500
parents d63878346099
children 0e1f5a750d00
comparison
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4 @c 4 @c
5 @c Octave is free software; you can redistribute it and/or modify it 5 @c Octave is free software; you can redistribute it and/or modify it
6 @c under the terms of the GNU General Public License as published by the 6 @c under the terms of the GNU General Public License as published by the
7 @c Free Software Foundation; either version 3 of the License, or (at 7 @c Free Software Foundation; either version 3 of the License, or (at
8 @c your option) any later version. 8 @c your option) any later version.
9 @c 9 @c
10 @c Octave is distributed in the hope that it will be useful, but WITHOUT 10 @c Octave is distributed in the hope that it will be useful, but WITHOUT
11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
13 @c for more details. 13 @c for more details.
14 @c 14 @c
15 @c You should have received a copy of the GNU General Public License 15 @c You should have received a copy of the GNU General Public License
16 @c along with Octave; see the file COPYING. If not, see 16 @c along with Octave; see the file COPYING. If not, see
17 @c <http://www.gnu.org/licenses/>. 17 @c <http://www.gnu.org/licenses/>.
18 18
19 @node Geometry 19 @node Geometry
20 @chapter Geometry 20 @chapter Geometry
21 21
22 Much of the geometry code in Octave is based on the Qhull 22 Much of the geometry code in Octave is based on the Qhull
23 library@footnote{Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., 23 library@footnote{Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T.,
24 @cite{The Quickhull Algorithm for Convex Hulls}, ACM Trans. on Mathematical 24 @cite{The Quickhull Algorithm for Convex Hulls}, ACM Trans. on Mathematical
25 Software, 22(4):469--483, Dec 1996, @url{http://www.qhull.org}}. 25 Software, 22(4):469--483, Dec 1996, @url{http://www.qhull.org}}.
26 Some of the documentation for Qhull, particularly for the options that 26 Some of the documentation for Qhull, particularly for the options that
27 can be passed to @code{delaunay}, @code{voronoi} and @code{convhull}, 27 can be passed to @code{delaunay}, @code{voronoi} and @code{convhull},
28 etc., is relevant to Octave users. 28 etc., is relevant to Octave users.
29 29
30 @menu 30 @menu
31 * Delaunay Triangulation:: 31 * Delaunay Triangulation::
32 * Voronoi Diagrams:: 32 * Voronoi Diagrams::
44 points falls within any of the circum-circles. 44 points falls within any of the circum-circles.
45 45
46 In general there are only three points on the circumference of any 46 In general there are only three points on the circumference of any
47 circum-circle. However, in some cases, and in particular for the 47 circum-circle. However, in some cases, and in particular for the
48 case of a regular grid, 4 or more points can be on a single 48 case of a regular grid, 4 or more points can be on a single
49 circum-circle. In this case the Delaunay triangulation is not unique. 49 circum-circle. In this case the Delaunay triangulation is not unique.
50 50
51 @DOCSTRING(delaunay) 51 @DOCSTRING(delaunay)
52 52
53 The 3- and N-dimensional extension of the Delaunay triangulation are 53 The 3- and N-dimensional extension of the Delaunay triangulation are
54 given by @code{delaunay3} and @code{delaunayn} respectively. 54 given by @code{delaunay3} and @code{delaunayn} respectively.
55 @code{delaunay3} returns a set of tetrahedra that satisfy the 55 @code{delaunay3} returns a set of tetrahedra that satisfy the
56 Delaunay circum-circle criteria. Similarly, @code{delaunayn} returns the 56 Delaunay circum-circle criteria. Similarly, @code{delaunayn} returns the
57 N-dimensional simplex satisfying the Delaunay circum-circle criteria. 57 N-dimensional simplex satisfying the Delaunay circum-circle criteria.
58 The N-dimensional extension of a triangulation is called a tessellation. 58 The N-dimensional extension of a triangulation is called a tessellation.
59 59
60 @DOCSTRING(delaunay3) 60 @DOCSTRING(delaunay3)
61 61
62 @DOCSTRING(delaunayn) 62 @DOCSTRING(delaunayn)
286 such that all points in @code{@var{v}(@var{p})}, a partitions of the 286 such that all points in @code{@var{v}(@var{p})}, a partitions of the
287 tessellation where @var{p} is a member of @var{s}, are closer to @var{p} 287 tessellation where @var{p} is a member of @var{s}, are closer to @var{p}
288 than any other point in @var{s}. The Voronoi diagram is related to the 288 than any other point in @var{s}. The Voronoi diagram is related to the
289 Delaunay triangulation of a set of points, in that the vertexes of the 289 Delaunay triangulation of a set of points, in that the vertexes of the
290 Voronoi tessellation are the centers of the circum-circles of the 290 Voronoi tessellation are the centers of the circum-circles of the
291 simplices of the Delaunay tessellation. 291 simplices of the Delaunay tessellation.
292 292
293 @DOCSTRING(voronoi) 293 @DOCSTRING(voronoi)
294 294
295 @DOCSTRING(voronoin) 295 @DOCSTRING(voronoin)
296 296
326 diagram, and which points of a set of points is in a polygon can be had 326 diagram, and which points of a set of points is in a polygon can be had
327 with the @code{polyarea} and @code{inpolygon} functions respectively. 327 with the @code{polyarea} and @code{inpolygon} functions respectively.
328 328
329 @DOCSTRING(polyarea) 329 @DOCSTRING(polyarea)
330 330
331 An example of the use of @code{polyarea} might be 331 An example of the use of @code{polyarea} might be
332 332
333 @example 333 @example
334 @group 334 @group
335 rand ("state", 2); 335 rand ("state", 2);
336 x = rand (10, 1); 336 x = rand (10, 1);
443 @end group 443 @end group
444 @end example 444 @end example
445 445
446 @noindent 446 @noindent
447 that interpolates from a random scattering of points, to a uniform 447 that interpolates from a random scattering of points, to a uniform
448 grid. 448 grid.
449 @ifnotinfo 449 @ifnotinfo
450 The output of the above can be seen in @ref{fig:griddata}. 450 The output of the above can be seen in @ref{fig:griddata}.
451 451
452 @float Figure,fig:griddata 452 @float Figure,fig:griddata
453 @center @image{griddata,4in} 453 @center @image{griddata,4in}