Abstract
Radial Basis Functions are widely used in scattered data interpolation. The surface-reconstruction method using radial basis functions consists of two steps: (i) computing an interpolating implicit function the zero set of which contains the points in the data set, followed by (ii) extraction of isocurves or isosurfaces. In this paper we focus on the second step, generalizing the work on certified meshing of implicit surfaces based on interval arithmetic (Plantinga and Vegter in Visual Comput. 23:45–58, 2007). It turns out that interval arithmetic, and even the usually faster affine arithmetic, are far too slow in the context of RBF-based implicit surface meshing. We present optimized strategies giving acceptable running times and better space complexity, exploiting special properties of RBF-interpolants. We present pictures and timing results confirming the improved quality of these optimized strategies.
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