Developable Bézier patches: properties and design

Geometric design of quadratic and cubic developable Bezier patches from two boundary curves is studied in this paper. The conditions for developability are derived geometrically from the de Casteljau algorithm and expressed as a set of equations that must be fulfilled by the Bezier control points. This set of equations allows us to infer important properties of developable Bezier patches that provide useful parameters and simplify the solution process for the patch design. With one boundary curve freely specified, five more degrees of freedom are available for a second boundary curve of the same degree. Various methods are introduced that fully utilize these five degrees of freedom for the design of general quadratic and cubic developable Bezier patches in 3D space. A more restricted generalized conical model or cylindrical model provides simple solutions for higher-order developable patches. copyright 2002 Elsevier Science Ltd. All rights reserved.