Constrained Shape Control of Bicubic B-Spline Surfaces by Knots

Abstract

Constrained modification of B-spline surfaces is essential in geometric design. Modification tools by purely knot alteration are presented in this paper: moving an isoparametric line to a specified location and dragging a point of the surface to a predefined point. Both methods yield smoother change than the well-known control point repositioning, while in the first case symmetric bodies can be deformed in a constrained way by automatically preserving their symmetry. Since the modified surface remains in the original convex hull, these techniques can be useful tools in the fine tuning phase, when users do not want to change the overall shape of the body