Abstract
Modifying the factorization of Bernstein polynomials, we propose a system of functions with two free parameters, which can be used for control point based curve modeling. Essential properties of functions such as nonnegativity, partition of unity, Hermite-like end properties, asymptotic behavior, symmetry, linear independence are shown. Consequently, the control point based curve obtained by these functions is closed for the affine transformation of its control points and has the convex hull, endpoint interpolation and endpoint tangency properties. The influence of the free parameters on the shape of the curve is studied as well.
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