Open AccessOffset Approximation of Rational Trigonometric Bezier ´ Curves
Author(s) -
Uzma Bashir,
Aqsa Rasheed
Publication year - 2021
Publication title -
the punjab university journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 1016-2526
DOI - 10.52280/pujm.2021.530505
Subject(s) - bézier curve , mathematics , offset (computer science) , trigonometry , polygon (computer graphics) , trigonometric functions , trigonometric polynomial , mathematical analysis , geometry , algorithm , computer science , telecommunications , frame (networking) , programming language
Offset curves are one of the crucial curves, but the presenceof square root function in the representation is main hindrance towardstheir 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 endpoints of the offset control polygon have been taken as exact offset endpoints, while the middle control points and weights have been computedusing 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 themethod.