Positivity-Preserving Scattered Data Interpolation

  • Abd. Rahni Mt. Piah
  • Tim N. T. Goodman
  • Keith Unsworth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)


The construction of a C 1 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bézier points in order to ensure that surfaces comprising cubic Bézier triangular patches are always positive. In the current work, simpler and more relaxed conditions are derived on the Bézier points. The gradients at the data sites are then calculated to ensure that these conditions are satisfied. Each triangular patch of the interpolating surface is formed as a convex combination of three cubic Bézier triangular patches. Its construction is local. A number of examples are presented.


Convex Combination Delaunay Triangulation Scattered Data Data Interpolation Positivity Constraint 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Abd. Rahni Mt. Piah
    • 1
  • Tim N. T. Goodman
    • 2
  • Keith Unsworth
    • 3
  1. 1.School of Mathematical SciencesUniversiti Sains MalaysiaPenangMalaysia
  2. 2.Department of MathematicsUniversity of DundeeDundeeScotland
  3. 3.Applied Computing GroupLincoln UniversityCanterburyNew Zealand

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