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Rational cubic trigonometric Bézier curve with two shape parameters

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Abstract

The current study presents rational cubic trigonometric Bézier curve with two shape parameters, which is a novel technique for drawing free form curves. The proposed curve retains most of the geometric properties of conventional rational cubic Bézier but is flexible due to the presence of shape parameters. The shape of the curve can be adjusted locally by altering the values of shape parameters as well as the weights. Using the given end point curvatures, conditions on shape parameters and weights have been driven so that the curve always lies in the convex hull of its control point. Later, this curve is used to generate piecewise rational trigonometric curves stitched together using parametric and geometric Hermite continuity conditions which can facilitate a designer to generate a smooth composition of curves in a situation where single curve does not work. The piecewise curves thus constructed are used to draw the layout of certain English and Arabic alphabets as an application in font designing.

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Acknowledgments

The authors are highly obliged to the anonymous reviewers for their valuable comments and suggestions that have improved the manuscript to the final version.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia

    Uzma Bashir & Jamaludin Md. Ali

  2. Lahore College for Women University, Lahore, Pakistan

    Uzma Bashir

Authors
  1. Uzma Bashir
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  2. Jamaludin Md. Ali
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Correspondence to Uzma Bashir.

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Communicated by Pascal Frey.

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Bashir, U., Ali, J.M. Rational cubic trigonometric Bézier curve with two shape parameters. Comp. Appl. Math. 35, 285–300 (2016). https://doi.org/10.1007/s40314-014-0194-z

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  • DOI: https://doi.org/10.1007/s40314-014-0194-z

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