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- W2952036833 abstract "The main goal of the paper is to introduce methods which compute B'ezier curves faster than Casteljau's method does. These methods are based on the spectral factorization of a $ntimes n$ Bernstein matrix, $B^e_n(s)= P_nG_n(s)P_n^{-1}$, where $P_n$ is the $ntimes n$ lower triangular Pascal matrix. So we first calculate the exact optimum positive value $t$ in order to transform $P_n$ in a scaled Toeplitz matrix, which is a problem that was partially solved by X. Wang and J. Zhou (2006). Then fast Pascal matrix-vector multiplications and strategies of polynomial evaluation are put together to compute B'ezier curves. Nevertheless, when $n$ increases, more precise Pascal matrix-vector multiplications allied to affine transformations of the vectors of coordinates of the control points of the curve are then necessary to stabilize all the computation." @default.
- W2952036833 created "2019-06-27" @default.
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- W2952036833 date "2010-06-22" @default.
- W2952036833 modified "2023-09-27" @default.
- W2952036833 title "On computing B'ezier curves by Pascal matrix methods" @default.
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