New mathematic result, application to mesh or have controlled points on a surface

Mathematicians ( Doug Hurdin ...) have just found how to exactly put points
on a surface in a regular manner. It seems it was not trivial....

Perhaps SW and CW could offer this very advanced possibility to have the
definitively best meshing solution.

(Ref science et vie n° 1054 july 2005)

 

Define "surface" and "regular manner".
Is "Doug Hurdin" the correct spelling?

 

This would be my guess as to the correct spelling

http://www.math.vanderbilt.edu/~hardin/

 

"Douglas Hardin"

Perhaps:
http://www.sciencedirect.com/scienc...serid=10&md5=86deab992afa7cf4c360ae607caf3ba7

Seems to be about approximating surfaces with polygon
meshs perhaps ... not all that good for precise
CAD things, IMHO.

 

When defining points on non-analytic surfaces (i.e. lofts and other
B-surfaces), most of the surface representation is actually only an
approximation of the true mathematical shape of the surface. Also true
for edges defined by B-surfaces in the parasolid model.

 

... surface representation is actually

Q: What's the "true" NURBS shape?
A: An approximation calculated to greater accuracy.

Wonder how many tri's in an STL of a 1 meter sphere calc'd to 1E-8 m
resolution.

 

Ed Saff and Doug Hardin, Vanderbilt, Nashville (Tenessee)

http://pass.maths.org.uk/latestnews/sep-dec04/bagel/

 

http://www.ams.org/notices/200410/fea-saff.pdf

 

Actually, if the desired underlying surface actually is a polynomial
or rational polynomial surface, the "approximation" may be rather
exact, to computational limits.

Your problems would arise when the underlying desired
analytic surface contains things like terms for trig or exponential
or log functions.