B-spline surface approximation to cross-sections using distance maps

Abstract

The shape reconstruction of a 3D object from its 2D cross-sections is important for reproducing it by NC machining or rapid prototyping. In this paper, we present method of surface approximation to cross-sections with multiple branching problems. In this method, we first decompose each multiple branching problem into a set of single branching problems by providing a set of intermediate contours using distance maps. For each single branching region, a procedure then performs the skinning of contour curves represented by cubic B-spline curves on a common knot vector, each of which is fitted to its contour points within a given accuracy. In order to acquire a more compact representation for the surface, the method includes an algorithm for reducing the number of knots in the common knot vector. The approximation surface to the cross-sections is represented by a set of by cubic B-spline surfaces. This method provides a smooth surface model, yet realizes efficient data reduction.