Datensatz

Zusammenfassung

We present an efficient method to automatically compute a smooth
approximation of large functional scattered data sets given over
arbitrarily shaped planar domains. Our approach is based on the
construction of a $C^1$-continuous bivariate cubic spline and our method
offers optimal approximation order. Both local
variation and non-uniform distribution of the data are taken into account
by using local polynomial least squares approximations of varying degree.
Since we only need to solve small linear systems and no triangulation of
the scattered data points is required, the overall complexity of the
algorithm is linear in the total number of points. Numerical examples
dealing with several real world scattered data sets with up to millions of
points demonstrate the efficiency of our method. The resulting spline
surface is of high visual quality and can be efficiently evaluated for
rendering and modeling. In our implementation we achieve real-time frame
rates for typical fly-through sequences and interactive frame rates for
recomputing and rendering a locally modified spline surface.