Angle-constrained manipulation for cubic B-spline with cusp and its applications

Abstract

An efficient algorithm for generating cusped B-spline curves and cusped-edge B-spline surfaces with a specific angle constraint at the cusp is presented. The proposed method is based on the multiplicity property of knots. A required point of the original B-spline curve (boundary) is transformed from C2 into G2 continuity. The angle constraints are satisfied by modifying the control points. The cusped edge is presented on the original surface without trimming. Thus, the method offers a direct way of designing surfaces which can be applied in computer-aided design tools. A specific angle is given to control the sharpness of the cusp in a B-spline curve (boundary). This approach is widely applicable to general B-spline surfaces.