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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.

Conic sections in axonometric projection

Banaszak Karolina

Journal Biuletyn of Polish Society for Geometry and Engineering Graphics

2018

Vol. 31

11--13

This paper demonstrates the classification and examples of the conic sections done in axonometry without the help of collineation. Presently there are no collineation transformations in most descriptive geometry programs. Therefore these sections were made without collineation with the use of only common elements.

W niniejszym artykule przedstawiono klasyfikację oraz przykłady przekrojów stożka wykonane w aksonometrii bez użycia kolineacji. Obecnie w większości programów geometrii wykreślnej nie ma przekształceń kolineacyjnych. Dlatego przekroje te zostały zrealizowane bez kolineacji z wykorzystaniem tylko elementów wspólnych.