q-Poisson Bases and q-Poisson Curves

Abstract

We construct a new class of bases (q-Poisson bases) with one shape parameter based on q-integers. The q-Poisson bases have lots of good properties, including non-negativity, partition of unity, linear independence, which are suitable for modeling. Based on q-Poisson bases, we define q-Poisson curves, which have some properties similar to classical Poisson curves. We also present a degree elevation and de Casteljau algorithm for q-Poisson curve. The effect of the parameter q on q-Poisson curves is also studied. The introduction of the parameter q makes Poisson curves convenient and flexible for shape modeling.