Abstract: A new algorithm is proposed for the design of a smooth surfaces which is required to have a regular mesh of curvature curves without any umbilical points. A composite surface as smoothly joint by Bézier surface patches is used in the design procedure. By the alternative steps of optimization of curvature line networks and surface subdivision, the free from surface is generated which has a regular network of curvature curves without an umbilical point. Based on the resultant surface, a cyclide spline surface with regular structures, conical strip models and multi-layer support structures for freeform architectural surface design are easily obtained.

Key words: curvature line network, cyclide surface, umbilical point, surface design