Explicit Recursive Generation of Lupaş q-Bézier Curves

To obtain Lupaş q-Bézier curves by recursive evaluation algorithms with better properties, new de Casteljau algorithms and Lupaş q-Bézier curves with symmetry are constructed by means of Pascal-type formula and reparameterization. A new de Casteljau algorithm with explicit matrix representation is constructed by applying Pascal-type formula, and the algorithm shares three properties with de Casteljau algorithm of classical Bézier curves. Lupaş q-Bernstein basis functions and Lupaş q-Bézier curves with symmetry are gained from reparameterization, moreover, Lupaş q-Bézier curves reparameterized can be generated by multiply bidiagonal matrices successively on control polygon. In addition, numerical examples of using one Lupaş q-Bézier curve to approximate two blending Bézier curves are presented as a simple application of de Casteljau algorithm with explicit matrix representation and the effectiveness of the algorithm is verified.