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Approximation of conic sections by weighted Lupaş post-quantum Bézier curves

Khan Asif, Iliyas Mohammad, Khan Khalid, Mursaleen Mohammad

Demonstratio Mathematica

2022

Vol. 55, nr 1

328--342

This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via (p,q) -integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigating from geometric point of view. Their degree elevation properties and de Casteljau algorithm have been studied. It has been shown that quadratic weighted Lupaş post-quantum Bézier curves can represent conic sections in two-dimensional plane. Graphical analysis has been presented to discuss geometric interpretation of weight and conic section representation by weighted Lupaş post-quantum Bézier curves. This new generalized weighted Lupaş post-quantum Bézier curve provides better approximation and flexibility to a particular control point as well as control polygon due to extra parameter p and q in comparison to classical rational Bézier curves, Lupaş q -Bézier curves and weighted Lupaş q -Bézier curves.

Rendering rational curves on raster devices

Kiciak P.

Machine Graphics and Vision

1998

Vol. 7, No. 1/2

427-436

We present a very fast and accurate procedure of redering rational Bezier curves on a raster device. The method uses a homographic reparameterization of the curve to obtain the numerator and denominator represented in the monomial basisi and uses the Horner scheme to compute them. The fixed point arithmetics used in the implementation is accompanied by a tounding arror analysis that guarantees the accuracy of the curve image.