Abstract: A method, apparatus and article of manufacture for generating an extended fillet surface with a computer which smoothly connects two base surfaces together based on the boundary curve of intersection between an offset of the first surface and an envelope of the second surface. An offset surface for the first base surface is created at a distance equal to the fillet radius. An envelope surface for a boundary curve of the second base surface is created and its intersection with the offset surface is determined. A spine curve is fitted to the intersection and contact curves projected onto the first and second surfaces according to the spine curve. A set of arcs is then generated between the contact curves where an endpoint of each arc within the set is tangent to the first base surface. The extended fillet surface is then constructed from the set of arcs being first-order geometric continuous (G.sub.1) to only one of the base surfaces.