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A Bound on the Implicit Degree of Polygonal Bézier Surfaces

In: Algebraic Geometry and its Applications

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  • Joe Warren

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.

Suggested Citation

  • Joe Warren, 1994. "A Bound on the Implicit Degree of Polygonal Bézier Surfaces," Springer Books, in: Chandrajit L. Bajaj (ed.), Algebraic Geometry and its Applications, chapter 33, pages 513-525, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2628-4_33
    DOI: 10.1007/978-1-4612-2628-4_33
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