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

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 C
²
into G
²
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.