Mercurial > hg > octave-nkf
changeset 8480:8ae26422a6ce
[docs] N-Simplex => N-simplex
author | Brian Gough <bjg@gnu.org> |
---|---|
date | Tue, 13 Jan 2009 00:25:37 -0500 |
parents | 79191b31a872 |
children | 00df69d7e698 |
files | doc/interpreter/geometry.txi |
diffstat | 1 files changed, 6 insertions(+), 6 deletions(-) [+] |
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--- a/doc/interpreter/geometry.txi +++ b/doc/interpreter/geometry.txi @@ -133,17 +133,17 @@ It is often necessary to identify whether a particular point in the N-dimensional space is within the Delaunay tessellation of a set of -points in this N-dimensional space, and if so which N-Simplex contains +points in this N-dimensional space, and if so which N-simplex contains the point and which point in the tessellation is closest to the desired point. The functions @code{tsearch} and @code{dsearch} perform this function in a triangulation, and @code{tsearchn} and @code{dsearchn} in an N-dimensional tessellation. To identify whether a particular point represented by a vector @var{p} -falls within one of the simplices of an N-Simplex, we can write the +falls within one of the simplices of an N-simplex, we can write the Cartesian coordinates of the point in a parametric form with respect to -the N-Simplex. This parametric form is called the Barycentric -Coordinates of the point. If the points defining the N-Simplex are given +the N-simplex. This parametric form is called the Barycentric +Coordinates of the point. If the points defining the N-simplex are given by @code{@var{N} + 1} vectors @var{t}(@var{i},:), then the Barycentric coordinates defining the point @var{p} are given by @@ -182,7 +182,7 @@ which gives the formula for the conversion of the Cartesian coordinates of the point @var{p} to the Barycentric coordinates @var{beta}. An important property of the Barycentric coordinates is that for all points -in the N-Simplex +in the N-simplex @example 0 <= @var{beta}(@var{i}) <= 1 @@ -191,7 +191,7 @@ @noindent Therefore, the test in @code{tsearch} and @code{tsearchn} essentially only needs to express each point in terms of the Barycentric coordinates -of each of the simplices of the N-Simplex and test the values of +of each of the simplices of the N-simplex and test the values of @var{beta}. This is exactly the implementation used in @code{tsearchn}. @code{tsearch} is optimized for 2-dimensions and the Barycentric coordinates are not explicitly formed.