Catmull-Rom cubic spline...

[Paul Heckbert]

aupetit wrote:
> 
> I would like a (hyper-)surface to pass through some given points.
> I am looking for a simple way to compute the gradient (tangente
> hyperplane)
> at a point knowing the "height" of its neighbors.
> The Catmull-Rom approach works for curves (intrinsic 1D) but does
> it exist some similar methods for surface (intrinsic 2D) ...

If you want a function z(x,y) that interpolates a set of (x,y,z)
points, this is called "scattered data interpolation".  Try radial
basis functions for this.  See the paper
http://www.gvu.gatech.edu/people/faculty/greg.turk/morph/morph.html
and specifically see the paper by Jean Duchon that they cite.

Paul Heckbert, Associate Professor
Computer Science Dept., Carnegie Mellon University
5000 Forbes Ave, Pittsburgh PA 15213-3891, USA

ph at cs.cmu.edu           http://www.cs.cmu.edu/~ph

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