Abstract
Geometric design of quadratic and cubic developable Bézier 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 Bézier control points. This set of equations allows us to infer important properties of developable Bézier 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 Bézier patches in 3D space. A more restricted generalized conical model or cylindrical model provides simple solutions for higher-order developable patches.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
