A hybrid approach to smooth surface reconstruction from 2-D cross sections

Abstract

This article presents a hybrid approach to smooth surface reconstruction from serial cross sections, where the number of contours varies from section to section. In a triangular surface-based approach taken in most reconstruction methods, a triangular surface is constructed by stitching triangular patches over a triangular net generated from the compiled contours. In the proposed approach, the resulting surface is a G¹ composite surface consisting of three kinds of surfaces: skinned, branched, and capped surfaces. Each skinned surface is first represented by a B-spline surface approximating the serial contours of the skinned region and then is transformed into a mesh of rectangular Bezier patches. On branched and capped regions, triangular G¹ surfaces are constructed such that the connections between the triangular surfaces and their neighbouring surfaces are G¹ continuous. Because each skinned region is represented by an approximated rectangular C² surface instead of an interpolated triangular G¹ surface, the proposed approach can provide more visually pleasing surfaces and realize more efficient data reduction than the triangular surface-based approach. Some experimental results demonstrate its usefulness and quality.