A Multi-sided Bézier Patch with a Simple Control Structure

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dc.contributor.authorVárady, Tamásen_US
dc.contributor.authorSalvi, Péteren_US
dc.contributor.authorKarikó, Györgyen_US
dc.contributor.editorJoaquim Jorge and Ming Linen_US
dc.date.accessioned2016-04-26T08:38:31Z
dc.date.available2016-04-26T08:38:31Z
dc.date.issued2016en_US
dc.description.abstractA new n-sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding crossderivatives are specified as conventional Bézier surfaces of arbitrary degrees. The surface is defined over a convex polygonal domain; local coordinates are computed from generalized barycentric coordinates; control points are multiplied by weighted, biparametric Bernstein functions. A method for interpolating a middle point is also presented. This Generalized Bézier (GB) patch is based on a new displacement scheme that builds up multi-sided patches as a combination of a base patch, n displacement patches and an interior patch; this is considered to be an alternative to the Boolean sum concept. The input ribbons may have different degrees, but the final patch representation has a uniform degree. Interior control points- other than those specified by the user-are placed automatically by a special degree elevation algorithm. GB patches connect to adjacent Bézier surfaces with G1 continuity. The control structure is simple and intuitive; the number of control points is proportional to those of quadrilateral control grids. The scheme is introduced through simple examples; suggestions for future work are also discussed.en_US
dc.description.number2en_US
dc.description.sectionheadersCurves & Surfacesen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume35en_US
dc.identifier.doi10.1111/cgf.12833en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages307-317en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12833en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.titleA Multi-sided Bézier Patch with a Simple Control Structureen_US
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