twgee@watmath.waterloo.edu (Tom Gee) (10/30/87)
In my recent search of our local library, I have found it to be
woefully deficient in the topic of surface interpolation algorithms.
I am looking for an interpolation technique to allow me to generate a
surface from a number of non-equidistant data points. The only paper
I have found on surface spline interpolation was not sufficiently detailed
to allow me to construct the required programs.
If you know of any papers, algorithms or programs that perform a surface
interpolation using non-equidistant data points, *please* let me know.
Thanks.
---
"Everything is impermanent." Thomas Gee
--- Fountains of Paradise. University of
Waterloo,
{utzoo}!watmath!twgee Canada.kerlick@fred (G David Kerlick) (11/12/87)
Gentlemen and Ladies: For the interpolation of randomly scattered data in 2D or 3D, there are two main approaches. In the first approach, an auxiliary rectangular grid is used and the data is interpolated twice, first to the auxiliary grid, and then to the desired value of the independent variables. One can do tricks with smoothing splines, etc, to make the interpolation satisfy certain rules, for example that the interpolant nowhere attains a greater value then the original data (no overshoots). Typical of this approach is the paper of Tom Foley, ACM Transactions on Graphics, Vol 6 No 1 (Jan 1987) pp 1-18. In the second approach, the space of independent variables (x,y in the case of plotting f(x,y) ) is broken down in to triangular elements by means of the so-called Delaunay Triangulation. What is essentially a Delaunay triangulation is done e.g. in the NCAR plotting library. (National Center for Atmospheric Research, Boulder Colo). I don't know of a production code that does this in 3D (i.e. contours f(x,y,z) ). Papers on this approach include P.J. Green and R. Sibson, Computer Journal (UK) vol 21 pp 168-173 (1978) and a recent paper by C.L. Lawson, Computer Aided Geometrical Design, Vol 3 (1986) pp 231-246, and references cited therein. Hope this information is helpful. G. David Kerlick Advanced Computer Graphics Group NASA Ames Research Center Moffett Field California