Regions
A region is a piece of some Euclidean Space. Some examples of what we mean
by regions are
- The Line Segment [0,1], { x in R^1 | 0<=x<=1}.
.
- The Square [0,1]X[0,1], { (x,y) in R^2 | 0<=x<=1 and 0<=y<=1}.
.
- The Disk, { x in R^2 | ||x||<=1}.
.
- The Unit Ball, { x in R^3 | ||x||<=1}.
.
A region may consist of several disjoint pieces.
Notice that in all of these examples the region is described as the subset
of points in some space that satisfy a given condition. The member functions
that a Region provides return to the dimension of the space, and provide a
way to check the condition.
The member functions which regions provide are:
- getBaseSpaceDimension -- retrieve the dimension of the space
of which the region is a subset.
- isitInChart -- determines if a point is in the region.
If these names seem a little bizarre, it is because the notion of region
is going to be generalized to that of a mapped region, and then to a Manifold,
which is a collection of mapped regions (which will be called charts) which
have the same base space dimension and the same target space dimension
(please see the description of mapped regions).
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