Developable Bézier patches: properties and design
نویسندگان
چکیده
Geometric design of quadratic and cubic developable Be Âzier 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 ful®lled by the Be Âzier control points. This set of equations allows us to infer important properties of developable Be Âzier patches that provide useful parameters and simplify the solution process for the patch design. With one boundary curve freely speci®ed, ®ve more degrees of freedom are available for a second boundary curve of the same degree. Various methods are introduced that fully utilize these ®ve degrees of freedom for the design of general quadratic and cubic developable Be Âzier patches in 3D space. A more restricted generalized conical model or cylindrical model provides simple solutions for higher-order developable patches. q 2002 Elsevier Science Ltd. All rights reserved.
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عنوان ژورنال:
- Computer-Aided Design
دوره 34 شماره
صفحات -
تاریخ انتشار 2002