NAO Class NARealEuclideanNSpace

Overview

RealEuclideanNSpace is an n-dimensional Manifold with one chart, which is the identity mapping. It is differential, with a metric which is the identity matrix everywhere, and a zero connection. It is open (has no boundary), and is not discrete.

This simple Manifold is very basic to NAO. The base space of all manifolds is a RealEuclideanNSpace, and often the target space of is as well.

User's Guide

To use this class, you must include the header file

NAO/RealNSp.h

and link against library

libNAOBase.a

The following constructors are provided:

NARealEuclideanNSpace(n );

Creates a real Euclidean n space of the given dimension.

int n ; The dimension for the new n-space. (Specified by user).

The following member functions are available in addition to those provided by the abstract interface NARegion:

NONE

Programmer's Guide

The RealEuclideanNSpace stores the dimension that is passed to the constructor, and uses this to implement all of the member functions of an NAManifold. Most of these are trivial.

Since these manifolds appear so frequently, these is a way to avoid constructing a new one. The routine
NACreateRealEuclideanNSpace(int)
checks a list of already allocated small dimensional RealEuclideanNSpaces, and returns one or allocates one if necessary.

Example

To create a RealEuclideanNSpace:

#include <NAO/RealNSp.h>

NAManifold *R1=new NARealEuclideanNSpace(1);

It is better, however to use the "factory":

NAManifold *R2=NACreateRealEuclideanNSpace(2);

Related Classes and Subroutines

The parent of this class:

NARegion

Siblings of this class:

Created: Fri Oct 9 14:38:51 EDT 1998

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