Rational quadratic Bézier spirals

Rational quadratic Bézier spirals

A quadratic Bézier representation withholds a curve segment with free from loops, cusps and inflection points. Furthermore, this rational form provides extra freedom to generate visually pleasing curves due to the existence of weights. In this paper, we propose sufficient conditions for rational qua...

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Main Authors: Azhar Ahmad, R.U. Gobithaasan
Format: Article
Language:English
Published: Penerbit Universiti Kebangsaan Malaysia 2018
Online Access:http://journalarticle.ukm.my/12415/
http://journalarticle.ukm.my/12415/
http://journalarticle.ukm.my/12415/1/31%20Azhar%20Ahmad.pdf
id ukm-12415
recordtype eprints
spelling ukm-124152018-12-07T23:46:22Z http://journalarticle.ukm.my/12415/ Rational quadratic Bézier spirals Azhar Ahmad, R.U. Gobithaasan, A quadratic Bézier representation withholds a curve segment with free from loops, cusps and inflection points. Furthermore, this rational form provides extra freedom to generate visually pleasing curves due to the existence of weights. In this paper, we propose sufficient conditions for rational quadratic Bézier curves to possess monotonic increasing/decreasing curvatures by means of monotone curvature tests which are based on the derivative of curvature functions. We have derived a simple interval of the middle weight that assures the construction of a family of rational quadratic Bézier curves to be planar spirals, which is characterized by the turning angle, end curvatures and the chords of control polygon. The proposed formulation can be used by CAD systems for aesthetic product design, highway/railway design and robot trajectory design avoiding unwanted curvature oscillations. Penerbit Universiti Kebangsaan Malaysia 2018-09 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/12415/1/31%20Azhar%20Ahmad.pdf Azhar Ahmad, and R.U. Gobithaasan, (2018) Rational quadratic Bézier spirals. Sains Malaysiana, 47 (9). pp. 2205-2211. ISSN 0126-6039 http://www.ukm.my/jsm/malay_journals/jilid47bil9_2018/KandunganJilid47Bil9_2018.htm
repository_type Digital Repository
institution_category Local University
institution Universiti Kebangasaan Malaysia
building UKM Institutional Repository
collection Online Access
language English
description A quadratic Bézier representation withholds a curve segment with free from loops, cusps and inflection points. Furthermore, this rational form provides extra freedom to generate visually pleasing curves due to the existence of weights. In this paper, we propose sufficient conditions for rational quadratic Bézier curves to possess monotonic increasing/decreasing curvatures by means of monotone curvature tests which are based on the derivative of curvature functions. We have derived a simple interval of the middle weight that assures the construction of a family of rational quadratic Bézier curves to be planar spirals, which is characterized by the turning angle, end curvatures and the chords of control polygon. The proposed formulation can be used by CAD systems for aesthetic product design, highway/railway design and robot trajectory design avoiding unwanted curvature oscillations.
format Article
author Azhar Ahmad,
R.U. Gobithaasan,
spellingShingle Azhar Ahmad,
R.U. Gobithaasan,
Rational quadratic Bézier spirals
author_facet Azhar Ahmad,
R.U. Gobithaasan,
author_sort Azhar Ahmad,
title Rational quadratic Bézier spirals
title_short Rational quadratic Bézier spirals
title_full Rational quadratic Bézier spirals
title_fullStr Rational quadratic Bézier spirals
title_full_unstemmed Rational quadratic Bézier spirals
title_sort rational quadratic bézier spirals
publisher Penerbit Universiti Kebangsaan Malaysia
publishDate 2018
url http://journalarticle.ukm.my/12415/
http://journalarticle.ukm.my/12415/
http://journalarticle.ukm.my/12415/1/31%20Azhar%20Ahmad.pdf
first_indexed 2023-09-18T20:02:33Z
last_indexed 2023-09-18T20:02:33Z
_version_ 1777406945383153664

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