Function Representation of Solids Reconstructed from Scattered Surface Points and Contours

TLDR

The algorithm has potential applications in tomography, image processing, animation, and CAD for complex surfaces. The study proposes a novel volume‑spline method for reconstructing geometric models and surfaces from scattered points. The method employs volume splines that use a Green’s function to interpolate scalar values of a chosen carrier solid, and it also handles reconstruction from cross‑sections. The algorithm yields a solid representation defined by f(x,y,z) ≥ 0 and can automatically generate highly concave and branching objects.

Abstract

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.