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NAO


NAO Interface Class NAPointOnManifold

Overview


The NAPointOnManifold class is a Base class for vectors. As the name implies, these are points on a Manifold, so in addition to a number of coordinates, there is a chart associated with each POM (as they are known to their friends). If you only work with Regions, or Mapped Regions, there is only one chart, and POM's are Euclidean vectors.

A PointOnManifold has a dimension, which is the number of coordinates, or the Base space dimension of the Manifold it lives on, and a list of coordinates.

NAO does not associate a POM with one Manifold, the same POM could live on any Manifold with the same Base Space Dimension, and enough charts.

User's Guide


To use this class, include the header file 
NAO/NAPtMfld.h
and link against library 
libNAOBase.a
The following member functions are available when classes are derived from this interface class, in addition to those provided by the parent class NATopLevel.

Pure Virtual Member Functions, which must be provided by derived classes:

Virtual Member Functions, which may or may not be provided by derived classes:
non Virtual Member Functions, which are provided by this base class and may not be replaced by a derived class:
The following classes are children of this base class:

Programmer's Guide


The base class stores the chart number (an int), and provides an implementation of the get and setChartNumber Member Functions.

Example


To print the PointOnManifold, we might do this: 
#include <NAO/NAPtMfld.h>

int i,n;
NAPointOnManifold *x;

n=x->getNumberOfCoordinates();

for(i=0;i<n;i++)
 {
  cout << "Coordinate " << i << " is " << x->getDoubleCoordinate(i) << endl;
 }
cout << "The chart is " << x->getChartNumber() << endl;

Now, the coordinates could be complex, single or double precision, float or int. NAO allows for these coordinates of unknown type with the NANumber class. Very inefficient of course, but if you wanted to do the same piece of code and correctly print the coordinates, you would do this: 

#include <NAO/NAPtMfld.h>
#include <NAO/UTNumb.h>

int i,n;
NAPointOnManifold *x;

n=x->getNumberOfCoordinates();

for(i=0;i<n;i++)
 {
  cout << "Coordinate " << i << " is ";
  NAPrint(x->getCoordinate(i),cout);
  cout << endl;
 }
cout << "The chart is " << x->getChartNumber() << endl;

For efficiency, the implementations of NAPointOnManifold all have a member function which returns a list of the coordinates.

Related Classes and Subroutines


The parent of this Interface class:

Siblings of this Interface class:

Children of this Interface class:

In addition to creating NAPointOnManifold's, and passing them to various member functions, there are a couple of operations between NAPointOnManifolds that are provided. If x, y and z are POM's, n an integer, and s a double, these operations are:

Created: Fri Oct 9 13:11:52 EDT 1998

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