Abstract
This paper investigates the number of degrees of freedom for geometric design of developable Be´zier 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 Be´zier control points. This set of equations enables us to infer important properties of developable Be´zier 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 Be´zier patches results in a composite developable Be´zier surface that has fewer degrees of freedom. This work provides the foundation for a systematic implementation of a computer-aided design system for developable Be´zier surfaces.
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