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- W3067162 abstract "By splitting the standard properties of Bézier curves into three categories, we show that the question “what is the natural generalization of a Bézier curve?” has a particularly satisfying answer: both the B-spline curves and the Pólya polynomials are natural generalizations of Bézier curves because Bézier curves inherit all their nice features from one or the other or both of these schemes. Moreover, the B-splines and the Pólya polynomials are related by the de Boor-Fix dual functionals. We also examine the split of Bézier features into B-spline and Pólya properties and the interconnections between these two curve forms and their properties. This analysis sheds some new light on the origins of, and connections between, many of the standard features of Bézier curves." @default.
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- W3067162 date "1989-01-01" @default.
- W3067162 modified "2023-09-23" @default.
- W3067162 title "What is the Natural Generalization of a Bézier Curve?" @default.
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- W3067162 doi "https://doi.org/10.1016/b978-0-12-460515-2.50010-x" @default.
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