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About this paper
Khalid Khan, D.K. Lobiyal, Adem Kilicman
The authors construct a family of Bézier curves and tensor-product surfaces using Bernstein basis functions defined by (p,q)-integers. Each (p,q)-integer is (p^n−q^n)/(p−q), with p>q>0. They evaluate curves recursively by combining neighboring control points and establish nonnegativity, partition of unity, endpoint interpolation, and convex-hull containment. The construction extends q-Bézier methods and illustrates parameter-dependent shape changes, without demonstrating performance gains.
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