Abstract
This paper investigates the number of degrees of freedom for geometric design of developable Bézier surfaces. 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 Bézier control points. This set of equations enables us to infer important properties of developable Bézier patches that characterize the patch design and simplify its solution process. With one boundary curve freely specified in 3D space, five more degrees of freedom are available for the second boundary curve of the same degree. Imposing parametric or geometric continuities across the boundary of two adjacent developable Bézier patches results in a composite developable Bézier surface that has fewer degrees of freedom. This work provides the foundation for a systematic implementation of a computer-aided design system for developable Bézier surfaces.