Abstract

Lofting is an established method used in Computer Aided Design to to fit surfaces to a network of curves. It is a challenging task, however, to ensure smoothness of the fitted surface using an interpolatory method if the curves of the network are not compatible (i.e. they would have to continue smoothly over vertices). To overcome this problem we take an existing patch definition, effectively “stretch” them over neighbouring patches and blend them together smoothly. The results are blended together a second time for each face. This results in a surface approximating the curve network which is theoretically an infinitely smooth surface, although in practice we limit this to C^1.