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John,
> Why is there a field "ManifoldDimension" in a SimpleSet?
> . . .
> definition of manifold as "a subset of Rn, along with an invertable
> and differentiable function phi:Rm -> Rn", then are you adding the
> function phi to the class SimpleSet?
There is a ManifoldDimension partly because there is no explicit phi.
The manifold is not explicitly documented. But the ManifoldDimension
provides information about the topology of the Set. That is, the set
is generally defined by a finite set of points, either explict or
implicit (e.g., FloatSet, LinearSet), and a connection topology between
those points. A Set with DomainDimension = 3 and ManifoldDimension = 2
will have a topology consisting of squares or triangles, whereas a Set
with DomainDimension = 3 and ManifoldDimension = 3 will have a topology
consisting of cubes or tetrahedra.
There are other consequences of ManifoldDimension. If ManifoldDimension
!= DomainDimension then (at least our current) Set classes refuse to
interpolate since they cannot really be sure that the point being
interpolated to lies on the manifold.
To be sure, this whole business with ManifoldDimension is an area for
future development, since nothing in the existing system prohibits
Sets that do document phi. However, I believe that it is not the most
pressing need right now. Actually, the most pressing need is probably
UIs and other VisAD extension packages that hide the complexity of the
Data model (which leads into my answer to Glenn's email).
Regards,
Bill
- ----------------------------------------------------------
Bill Hibbard, SSEC, 1225 W. Dayton St., Madison, WI 53706
whibbard@xxxxxxxxxxxxx 608-263-4427 fax: 608-263-6738
http://www.ssec.wisc.edu/~billh/vis.html
- ----------------------------------------------------------
Bill Hibbard, SSEC, 1225 W. Dayton St., Madison, WI 53706
whibbard@xxxxxxxxxxxxx 608-263-4427 fax: 608-263-6738
http://www.ssec.wisc.edu/~billh/vis.html
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