کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6423200 | 1632177 | 2015 | 12 صفحه PDF | دانلود رایگان |
The (q,h)-Bernstein-Bézier curves are generalizations of both the h-Bernstein-Bézier curves and the q-Bernstein-Bézier curves. We investigate two essential features of (q,h)-Bernstein bases and (q,h)-Bézier curves: the variation diminishing property and the degree elevation algorithm. We show that the (q,h)-Bernstein bases for a non-empty interval [a,b] satisfy Descartes' law of signs on [a,b] when q>â1, qâ 0, and hâ¤minâ¡{(1âq)a,(1âq)b}. We conclude that the corresponding (q,h)-Bézier curves are variation diminishing. We also derive a degree elevation formula for (q,h)-Bernstein bases and (q,h)-Bézier curves over arbitrary intervals [a,b]. We show that these degree elevation formulas depend only on the parameter q and are independent of both the parameter h and the interval [a,b]. We investigate the convergence of the control polygons generated by repeated degree elevation. We show that unlike classical Bézier curves, the control polygons generated by repeated degree elevation for (q,h)-Bézier curves with 01. Here the control polygons generated by repeated degree elevation converge to a piecewise linear curve that depends only on q and the monomial coefficients of the 1/q-Bézier curve with the control points of the original (q,h)-Bézier curve in reverse order.
Journal: Applied Numerical Mathematics - Volume 96, October 2015, Pages 82-93