Freeform Surface Blends Freeform Surface Blends Freeform Surface Blends Freeform Surface Blends 5 Acknowledgment Freeform Surface Blends Freeform Surface Blends Freeform Surface Blends Freeform Surface Blends 2.3 Cross Boundary Tangent Normalization Freeform Surface Blends Freeform Surface Blends 2.

This paper presents a symbolic approach to the computation of blend surfaces across piecewise polynomial and rational surfaces. Curves in the parameter space of the primary surfaces can be speci ed as the rail curves, also known as trimlines, of the blend. Several techniques which require various levels of user interaction are presented for de ning the cross boundary tangent curves along the rail curves. The resulting blend is represented as a polynomial surface having tangent plane continuity with the primary surfaces to an accuracy bounded only by the machine precision. Also presented is a normalizationmethod that approximates a unit vector eld, an approach that might bene t other applications such as o set approximation and animation curve construction.