A control point based curve with two exponential shape parameters


A generalization of a recently developed trigonometric Bézier curve is presented in this paper. The set of original basis functions are generalized also for non-trigonometric functions, and essential properties, such as linear independence, nonnegativity and partition of unity are proved. The new curve—contrary to the original one—can be defined by arbitrary number of control points meanwhile it preserves the properties of the original curve.

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Correspondence to Miklós Hoffmann.

Additional information

This research was carried out as a part of the TAMOP-4.2.1.B-10/2/KONV-2010-0001 project with support by the European Union, co-financed by the European Social Fund. The third author was supported by the Australian Research Council and by Hungarian Scientific Research Grant OTKA NN102029.

Communicated by Tom Lyche.

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Hoffmann, M., Juhász, I. & Károlyi, G. A control point based curve with two exponential shape parameters. Bit Numer Math 54, 691–710 (2014). https://doi.org/10.1007/s10543-014-0468-2

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  • Blending functions
  • Generalized Bézier curve
  • Shape parameters

Mathematics Subject Classification (2000)

  • 68U05
  • 65D18
  • 65D07