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[project @ 2007-10-11 16:26:36 by jwe]
author jwe
date Thu, 11 Oct 2007 16:26:37 +0000
parents 8b0cfeb06365
children fd42779a8428
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7006:039ef140ac35 7007:6304d9ea0a30
39 The 3- and N-dimensional extension of the Delaunay triangulation are 39 The 3- and N-dimensional extension of the Delaunay triangulation are
40 given by @code{delaunay3} and @code{delaunayn} respectively. 40 given by @code{delaunay3} and @code{delaunayn} respectively.
41 @code{delaunay3} returns a set of tetrahedra that satisfy the 41 @code{delaunay3} returns a set of tetrahedra that satisfy the
42 Delaunay circum-circle criteria. Similarly, @code{delaunayn} returns the 42 Delaunay circum-circle criteria. Similarly, @code{delaunayn} returns the
43 N-dimensional simplex satisfying the Delaunay circum-circle criteria. 43 N-dimensional simplex satisfying the Delaunay circum-circle criteria.
44 The N-dimensional extension of a triangulation is called a tesselation. 44 The N-dimensional extension of a triangulation is called a tessellation.
45 45
46 @DOCSTRING(delaunay3) 46 @DOCSTRING(delaunay3)
47 47
48 @DOCSTRING(delaunayn) 48 @DOCSTRING(delaunayn)
49 49
117 117
118 @node Identifying points in Triangulation 118 @node Identifying points in Triangulation
119 @subsection Identifying points in Triangulation 119 @subsection Identifying points in Triangulation
120 120
121 It is often necessary to identify whether a particular point in the 121 It is often necessary to identify whether a particular point in the
122 N-dimensional space is within the Delaunay tesselation of a set of 122 N-dimensional space is within the Delaunay tessellation of a set of
123 points in this N-dimensional space, and if so which N-Simplex contains 123 points in this N-dimensional space, and if so which N-Simplex contains
124 the point and which point in the tesselation is closest to the desired 124 the point and which point in the tessellation is closest to the desired
125 point. The functions @code{tsearch} and @code{dsearch} perform this 125 point. The functions @code{tsearch} and @code{dsearch} perform this
126 function in a triangulation, and @code{tsearchn} and @code{dsearchn} in 126 function in a triangulation, and @code{tsearchn} and @code{dsearchn} in
127 an N-dimensional tesselation. 127 an N-dimensional tessellation.
128 128
129 To identify whether a particular point represented by a vector @var{p} 129 To identify whether a particular point represented by a vector @var{p}
130 falls within one of the simplices of an N-Simplex, we can write the 130 falls within one of the simplices of an N-Simplex, we can write the
131 Cartesian coordinates of the point in a parametric form with respect to 131 Cartesian coordinates of the point in a parametric form with respect to
132 the N-Simplex. This parametric form is called the Barycentric 132 the N-Simplex. This parametric form is called the Barycentric
356 @node Convex Hull 356 @node Convex Hull
357 @section Convex Hull 357 @section Convex Hull
358 358
359 The convex hull of a set of points is the minimum convex envelope 359 The convex hull of a set of points is the minimum convex envelope
360 containing all of the points. Octave has the functions @code{convhull} 360 containing all of the points. Octave has the functions @code{convhull}
361 and @code{convhulln} to calculate the convec hull of 2-dimensional and 361 and @code{convhulln} to calculate the convex hull of 2-dimensional and
362 N-dimensional sets of points. 362 N-dimensional sets of points.
363 363
364 @DOCSTRING(convhull) 364 @DOCSTRING(convhull)
365 365
366 @DOCSTRING(convhulln) 366 @DOCSTRING(convhulln)