B-Spline Surface Approximation to Cross-Sections Using Distance Maps

Abstract

The shape reconstruction of a 3D object from its 2D crosssections is important for reproducing it by NC machining or rapid prototyping. In this paper, we present a 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 crosssections is represented by a set of bicubic B-spline surfaces. This method provides a smooth surface model, yet realises efficient data reduction.