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 to only one of the base surfaces .