Transfinite interpolation techniques have been extended to cover rectangular
patches having interior constraints. Interior constraints are specified along
isoparametric lines defined partly are wholly over the parametric range. The
technique helps incorporate additional data for controlling both the shape and
parainetrisation of the interior of a surface.
An immediate application for the technique is found in the area of
computational fluid dynamics (CFD) where these techniques are used to discretise
the computational domain. In CFD the isopararnetric surfaces are made to coincide
with the boundary of domain and fluid dynamic data at grid points (Points of
intersection of isoparametric lines) is computed by solving partial differential
equations governing fluid flow. The technique suggested in this paper gives
powerful control over the grid generation process.
The use of this technique is demonstrated by interpolating doubly curved
analytical surfaces such as ellipsoids using contour plots for comparison.
G. R. Shevare,
S. P. Mudur,
"Constrained-interior interpolating surfaces", Proc. SPIE 1251, Curves and Surfaces in Computer Vision and Graphics, (1 August 1990); doi: 10.1117/12.19737; https://doi.org/10.1117/12.19737