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From: Phil on 29 Jul 2010 15:35
Hi there,

I have 2D piecewise linear data over a triangulation given. From this data, I'd like to obtain an interpolation with (piecewise) polynomials of higher order (doesn't necessarily need to be polynomials). So it should look smoother. (Looks is not the main goal, but a side effect).

To get my point over better, if I had data on a uniform rectangular grid, I'd want something like bilinear interpolation.
(Interpolating first from the unstructured grid to a structured grid and then using bilinear interpolation will not work; the points are very unevenly distributed.)

Is there something like the bilinear interpolation but over unstructured triangles? One could patch a few neighboring ones together and do a similar thing (interpolating on arbitrary polygons), but that seems quite complicated.
On the other hand, in computer graphics, I'd suppose some useful techniques should exist, but I couldn't really find anything.

I'd appreciate any ideas or hints.
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