A Blending Function Interpolant for the Curved Triangles and the Curved Quadrilaterals

Abstract:

      Blending function methods permit the exact interpolation of data given along curves or surfaces. These methods are useful for finite element analysis and for computer aided geometric design.This paper describes some new blending function methods for interpolating to function values and higher derivatives on the boundery of the curved triangles and the curved quadrilaterals. These interpolation schemes are constructed from a combination or blend of simpler interpolation functions. Interpolation method of this type is introduced in the paper of J. A. Gregory, where interpolation scheme had been provided for the triangles with the sides of straight lines. In this paper. Gregory's method is extended to interpolation on the curved triangles and the curved quadrilaterals.