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1

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

Khan Asif, Iliyas Mohammad, Khan Khalid, Mursaleen Mohammad

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

328--342

EN

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.

2

Approximating curve by a single segment of B-Spline or Bézier curve directly in CAD environment

Sobolak Mariusz, Połowniak Piotr, Marciniec Adam, Jagiełowicz Patrycja Ewa

Advances in Manufacturing Science and Technology

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2020

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Vol. 44, nr 3

84--92

EN

The paper presents the method of approximating curves with a single segment of the B-Spline and Bézier curves. The method for determining a single curve segment using the optimization methods in the CATIA environment is shown. The algorithms of simulated annealing and design of experiment are used for optimization. For the same purpose, a new original procedure for determining the distance between the given curves using explicit parameters in the CATIA environment was also used. This approximation of the cyclic curves results in the curve oscillation as shown in the examples. The results show that the approximation method with Bézier curve using control points as “free” points can be applied to obtain the best results of approximation.

3

Ocena dynamiczna wybranych sposobów łączenia elementów trasy o zróżnicowanej krzywiźnie

Koc W., Palikowska K.

TTS Technika Transportu Szynowego

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2012

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R. 19, nr 9

1785--1807, CD

PL

Artykuł przedstawia porównanie właściwości dynamicznych kubicznych krzywych C-Bezier i PH krzywych Bezier piątego stopnia na tle krzywej typu K0 uzyskanej przy zastosowaniu uniwersalnej metody modelowania krzywizny. Właściwości dynamiczne i możliwości zastosowania wymienionych krzywych w projektowaniu dróg kolejowych omówiono na przykładach łączenia krzywą przejścia dwóch łuków kołowych odwrotnych oraz dwóch łuków zgodnych (bez przypadku zawierania się jednego łuku w drugim).

EN

Comparison of the dynamic properties of the cubic C-Bezier curves and the PH quintic Bezier curves against the K0 curve obtained using universal modeling curvature method is presented in the article. The dynamic properties and application prospects of the mentioned curves in the railway route design are presented on two cases of joining two circular arcs: with S-shaped and C-shaped transition curves (without the case when one circle is inside the other).