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A refinement of the variation diminishing property of Bézier curves

Computer Aided Geometric Design, 2010
For a given polynomial F(t)[email protected]?"i"="0^np"iB"i^n(t), expressed in the Bernstein basis over an interval [a,b], we prove that the number of real roots of F(t) in [a,b], counting multiplicities, does not exceed the sum of the number of real roots in [a,b] of the polynomial G(t)[email protected]?"i"="k^lp"iB"i"-"k^l^-^k(t) (counting ...
Rachid Ait-Haddou, Taishin Nomura
exaly   +3 more sources

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