A Multi‐sided Bézier Patch with a Simple Control Structure. (27th May 2016)

• Record Type: Journal Article
• Authors: Várady, Tamás; Salvi, Péter; Karikó, György
• Is Part Of: Computer graphics forum. Volume 35:Number 2(2016)
• Page Start: 307
• Page End: 317
• Publication Date: 2016-05-27
• Subjects: Categories and Subject Descriptors (according to ACM CCS) -- I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.12833
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract: A new n‐sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross‐derivatives 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 G 1 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.