Adding draft angle to BB-spline and NURBS surfaces

BB-spline and NURBS surfaces are the most prevailing parametric surfaces in current CAD/CAM systems. Used for mould and die representations, they need sufficient draft angle in manufacturing processes. This paper tries to add draft angle to BB-spline and NURBS surfaces with minimum changes in their control nets and weights in the least square sense. An enhanced sufficient condition for BB-spline surfaces is introduced based on the convex combination, so as to improve the existing algorithm for adding draft angle to such surfaces. The draft angle distribution is visualized by a terrain, whose area under a certain level means that the corresponding part of the surface is too steep. Adding draft angle to this part can be expressed as a constraint on optimization. This idea is successfully applied to NURBS surfaces. Five examples demonstrate the effectiveness of the proposed methods.

► Enhance the draft angle conditions for bilinear interpolation & BB-spline surfaces.
► Optimization under the latter condition can add draft angle to BB-spline surfaces.
► Visualize the draft angle distribution all over a surface by a terrain.
► By comparing this terrain with a level, the ineligible regions become obvious.
► Propose a method for adding draft angle to NURBS surfaces.