BIT Numerical Mathematics

, Volume 54, Issue 3, pp 691–710 | Cite as

A control point based curve with two exponential shape parameters

  • Miklós Hoffmann
  • Imre Juhász
  • Gyula Károlyi


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.


Blending functions Generalized Bézier curve Shape parameters 

Mathematics Subject Classification (2000)

68U05 65D18 65D07 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Miklós Hoffmann
    • 1
  • Imre Juhász
    • 2
  • Gyula Károlyi
    • 3
  1. 1.Eszterházy Károly University CollegeEgerHungary
  2. 2.University of MiskolcMiskolc-EgyetemvárosHungary
  3. 3.School of Mathematics and PhysicsThe University of Queensland and Institute of Mathematics, Eötvös UniversityBudapestHungary

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