Computational and Applied Mathematics

, Volume 33, Issue 2, pp 411–431 | Cite as

Shape-preserving trigonometric functions

  • Malik Zawwar Hussain
  • Maria Hussain
  • Amna Waseem


A control point form of quadratic trigonometric function is developed which obeys all the properties of Bézier curve. To preserve the shape of data, the quadratic trigonometric functions are transformed into \(GC^1\)-interpolating functions. The \(GC^1\)-interpolating functions have two free parameters in each subinterval to control the magnitude and direction of the tangent at the end points interval. Constraints are derived on these free parameters to interpolate positive, monotone and convex data. The order of approximation of developed interpolant is investigated as \(O( {h_{i}^{3}})\).


Shape preservation Trigonometric function Bézier curve Error estimation 

Mathematics Subject Classification (2000)

68U05 65D05 65D07 65D18 


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2013

Authors and Affiliations

  • Malik Zawwar Hussain
    • 1
  • Maria Hussain
    • 2
  • Amna Waseem
    • 1
  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan
  2. 2.Department of MathematicsLahore College for Women UniversityLahorePakistan

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