Parametric Spiral and Its Application as Transition Curve

Abstract

The Bezier curve representation is frequently utilized in computer-aided design (CAD) and computer-aided geometric design (CAGD) applications. The curve is defined geometrically, which means that the parameters have geometric meaning; they are just points in three-dimensional space. Since they are also polynomial, resulting algorithms are convenient for implementation in an interactive computer graphics environment. However, their polynomial nature causes problems in obtaining desirable shapes. Low degree (cubic and quartic curve) segments may have cusps, loops, and inflection points. Since a fair curve should only have curvature extrema wherever explicitly desired by the designer. But, generally curves do not allow this kind of behavior. Therefore, it would be required to constrain the proposed cubics and quartics, so that the spirals are designed in a favorable way. This thesis investigated the use of cubic spirals and quartic Bezier spirals as the alternative parametric representations to other spiral functions in the literature. These new parametric spirals were obtained by algebraic manipulation methods on the monotone curvature variation of each curve. Results are reported showing that the additional degree of freedom offers the designer a precise control of total-length and the ability to fine-tune their curvature distributions. The methods and algorithms to construct the , , and transition spirals have also been presented. We explore some common and new cases that may arise in the use of such spiral segments for practical application of CAD/CAGD. 1 G 2 G 3 G

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Cite this paper

@inproceedings{Ahmad2009ParametricSA, title={Parametric Spiral and Its Application as Transition Curve}, author={Azhar Ahmad and SAINS MALAYSIA}, year={2009} }