The Rational Quadratic Trigonometric B&amp;#x00E9;zier Curve with Two Shape Parameters

Bashir, Uzma; Abbas, Muhammad; Majid, Ahmad Abd.; Ali, Jamaludin Md

doi:10.1109/cgiv.2012.22

Cited by 4 publications

(2 citation statements)

References 9 publications

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“…Afterwards a new set of basis functions based on exponential functions is introduced [6]. Further different set of basis functions involving shape parameters and trigonometric functions for curve and surface design is introduced [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Enhancing curve and surface applications with trigonometric polynomial basis functions

Rasheed,

Bashir,

Ibraheem

et al. 2024

PLoS ONE

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This article primarily focuses on the utilization and importance of parametric curves in surface design. It delves into the construction and applications of parametric curves, exploring the implementation of trigonometric polynomial basis functions that possess two shape parameters. Initially, these basis functions are employed in constructing both rational and non-rational curves. Later, they are employed to define the surfaces generated by these curves. The discussion includes rational surfaces, tensor product surfaces, and various specialized surfaces. The aim is to provide a comprehensive understanding of the role and potential of parametric curves in surface design.

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Section: Introductionmentioning

confidence: 99%

Enhancing curve and surface applications with trigonometric polynomial basis functions

Rasheed,

Bashir,

Ibraheem

et al. 2024

PLoS ONE

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“…These curves are referred to as offset curves [1]. Applications of offset curves include numerical control machining [2], shoe, textile, automotive industry and font designing. Offset curves are also used in robot path planning [3], surface generation [11], animation used in movies, pocket machining ( [1], [4]), ship designing and tolerance analysis [5].…”

Section: Introductionmentioning

confidence: 99%

Offset Approximation of Rational Trigonometric Bezier ´ Curves

Bashir

Rasheed

2021

Punjab Univ. j. math.

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Offset curves are one of the crucial curves, but the presence of square root function in the representation is main hindrance towards their applications in CAD/CAM. The presented technique is based on offset approximation using rational trigonometric Bezier curves. The idea is ´ to construct a new control polygon parallel to original one. The two end points of the offset control polygon have been taken as exact offset end points, while the middle control points and weights have been computed using definition of parallel curves. As a result, offsets of rational and nonrational trigonometric Bezier curves have been approximated by rational ´ cubic trigonometric Bezier curve. An error between exact and approxi- ´ mated offset curves have also been computed to show the efficacy of the method.

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