A Bound on the Implicit Degree of Polygonal Bézier Surfaces

Joe Warren

Chapter 33 in Algebraic Geometry and its Applications, 1994, pp 513-525 from Springer

Abstract: Abstract Recent work has shown that the triangular rational Bézier surface representation can be used to create polygonal surface patches. The key to the construction is the judicious use of zero weights in creating the surface parameterization. These zero weights introduce base points into the resulting rational parameterizations. Base points also lower the degree of the implicit representation of these polygonal surface patches. This paper states and proves in a simple, constructive manner a bound on the implicit degree of these rational surfaces.

Keywords: Base Point; Toric Variety; Surface Patch; Rational Surface; Newton Polygon (search for similar items in EconPapers)
Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2628-4_33

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DOI: 10.1007/978-1-4612-2628-4_33

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