On transfinite interpolations with respect to convex domains (Q631073)

A compact formula for generating transfinite interpolants on convex domains (polytopes) is presented. It is based on Coons map and on barycentric blending functions. The interpolants are proved to be affinely stable in a second theorem. Thereby, an improvement over the usual approaches (e.g. with tensor products) is obtained. Some practical examples are presented as well.