Cubic polynomial patches through geodesics
We consider patches that contain any given 3D polynomial curve as a pregeodesic (i.e.geodesic up to reparametrization). A curve is a pregeodesic if and only if its rectifying plane coincides with the tangent plane to the surface, we use this fact to construct ruled cubic patches through pregeodesics and bicubic patches through pairs of pregeodesics. We also discuss the G1 G 1 connection of (1,k) ( 1 , k ) patches with abutting pregeodesics.
geodesic pregeodesic rectifying plane ribbon ruled patch