Geometric continuity of ruled surfaces Original Research Article

This paper develops a theory for higher order continuity of ruled surfaces constructed from ruled surface patches. Continuity is defined by the equivalence of a minimal set of geometric properties for the ruled surfaces and their evolutes using the dual arc element as the parameter of the surface. The method used is a completely new approach to higher-order continuity of ruled surfaces. Also, contact continuity is compared to continuity of the Frenet trihedrons and the curvatures. These continuity conditions can be used in design procedures for ruled surface segments in CAGD.