Quantum (q, h)-Bézier surfaces based on bivariate (q, h)-blossoming
Keyword(s):
AbstractWe introduce the (q, h)-blossom of bivariate polynomials, and we define the bivariate (q, h)-Bernstein polynomials and (q, h)-Bézier surfaces on rectangular domains using the tensor product. Using the (q, h)-blossom, we construct recursive evaluation algorithms for (q, h)-Bézier surfaces and we derive a dual functional property, a Marsden identity, and a number of other properties for bivariate (q, h)-Bernstein polynomials and (q, h)-Bézier surfaces. We develop a subdivision algorithm for (q, h)-Bézier surfaces with a geometric rate of convergence. Recursive evaluation algorithms for quantum (q, h)-partial derivatives of bivariate polynomials are also derived.
2005 ◽
Vol 6
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pp. 108-115
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1997 ◽
Vol 14
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pp. 377-381
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2010 ◽
Vol 235
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pp. 785-804
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Vol 31
(5)
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pp. 265-276
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2013 ◽
Vol 225
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pp. 475-479
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2007 ◽
Vol 39
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pp. 1113-1119
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