High-order Extraction Method of Iso-curvature Lines on B-spline Surfaces

摘要

Curvature information is one of the important geometric intrinsic properties of B-spline surfaces. In order to achieve the high-accuracy extraction and rendering of iso-curvature lines on surfaces, we propose a high-order extraction method of iso-curvature lines on B-spline surface by functional composition theory. Firstly, the B-spline surface and its parametric domain are subdivided by knot insertion, then the corresponding part of iso-curvature lines in the parametric domain is obtained according to curvature value at the sampling points by Marching Square method. After converting each sub-patch on each knot interval into Bezier surface, the high-order represent at ion of the iso-curvature lines on B-spline surface can be obtained by functional composition method. The proposed method can be used for the extraction of iso-curvature lines of mean curvature, Gaussian curvature, maximum and minimum principal curvature on B-spline surfaces. Several examples are shown to illustrate the efficiency of the proposed method.