Interpolations for temperature distributions: a method for all non-concave polygons

Abstract An approximation to a distribution governed by temperature readings taken at the edge of a polygonal domain can be constructed using interpolation functions which––in linear combination––satisfy first order, constancy and linearity conditions. The values prescribed by the normed interpolation function should be bounded between zero and one. This restriction is especially necessary when representing temperature, since negative values for temperature in Kelvin are physically unacceptable. Compliant interpolation functions can be constructed on all convex polygonal domains including those bounded by vertex and side-nodes.