Rational quadratic Bézier spirals

Azhar Ahmad, and R.U. Gobithaasan, (2018) Rational quadratic Bézier spirals. Sains Malaysiana, 47 (9). pp. 2205-2211. ISSN 0126-6039


Official URL: http://www.ukm.my/jsm/malay_journals/jilid47bil9_2...


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.

Item Type:Article
Keywords:Bézier curves; Curvature; Monotonicity; Rational quadratics; Spirals
Journal:Sains Malaysiana
ID Code:12415
Deposited By: ms aida -
Deposited On:06 Dec 2018 06:12
Last Modified:07 Dec 2018 23:46

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