Visualization of spatial data via heuristic search and surface fitting

The paper discusses the surfaces of 3D objects given a collection of points taken from the boundary of the objects. By combining heuristic search with surface fitting, surfaces can be constructed from a collection of points even when spacing of the points is too large to be handled by the popular volume-based approaches. The goal of the heuristic is to produce a polyhedron which determines the rough shape of the smooth simple surface to be constructed. More specifically, the heuristic search identifies, among the simple polyhedra whose vertices are exactly the given data points, the most natural simple polyhedron. Surface fitting generates a smooth piecewise quadric surface in a constructed neighbourhood Σ of the polyhedron produced by the heuristic search. A simple smooth surface that can be constructed within Σ is described