Function Representation of Solids Reconstructed from Scattered Surface Points and Contours

Abstract

This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x,y,z) ? 0. The volume spline is based on use of the Green s function for interpolation of scalar function values of a chosen"carrier" solid. Our algorithm is capable of generating highly concave and branching objects automatically. The particular case where the surface is reconstructed from cross-sections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD for bodies with complex surfaces.