Geometric Design of Uniform Developable B-Spline Surfaces

This paper studies geometric design of uniform developable B-spline surfaces from two boundary curves. The developability constraints are geometrically derived from the de Boor algorithm and expressed as a set of equations that must be fulfilled by the B-spline control points. These equations help characterize the number of degrees of freedom (DOF’s) for the surface design. For a cubic B-spline surface with a first boundary curve freely chosen, five more DOF’s are available for a second boundary curve when both curves contain four control points. There remain (7-2m) DOF’s for a cubic surface consisting of m consecutive patches with C2 continuity. The results are in accordance with previous findings for equivalent composite Bezier surfaces. Test examples are illustrated to demonstrate design methods that fully utilize the DOF’s without leading to over-constrained systems in the solution process. Providing a foundation for systematic implementation of a CAGD system for developable B-spline surfaces, this work has substantial improvements over past studies.Copyright © 2004 by ASME