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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia
2018
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| Online Access: | http://journalarticle.ukm.my/12415/ http://journalarticle.ukm.my/12415/1/31%20Azhar%20Ahmad.pdf |
| _version_ | 1848812994822144000 |
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| author | Azhar Ahmad, R.U. Gobithaasan, |
| author_facet | Azhar Ahmad, R.U. Gobithaasan, |
| author_sort | Azhar Ahmad, |
| building | UKM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T00:11:08Z |
| format | Article |
| id | oai:generic.eprints.org:12415 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:11:08Z |
| publishDate | 2018 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org: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 |
| spellingShingle | Azhar Ahmad, R.U. Gobithaasan, Rational quadratic Bézier spirals |
| title | Rational quadratic Bézier spirals |
| title_full | Rational quadratic Bézier spirals |
| title_fullStr | Rational quadratic Bézier spirals |
| title_full_unstemmed | Rational quadratic Bézier spirals |
| title_short | Rational quadratic Bézier spirals |
| title_sort | rational quadratic bézier spirals |
| url | http://journalarticle.ukm.my/12415/ http://journalarticle.ukm.my/12415/ http://journalarticle.ukm.my/12415/1/31%20Azhar%20Ahmad.pdf |