Abstract: Using geometric method,a rational interpolation within convex polygons is constructed and extended to include side nodes.The computational expressions of rational shape functions are shown.Different from Wachspress' rational interpolation,the interpolations presented in this paper include no undetermined constant.A convex domain is approached by a convex polygon,and the approximated temperature distribution within the domain can be interpolated with the temperature data at the boundaries of the domain.The interpolated distribution of temperature within disc and square domains is calculated.

Key words: temperature distribution, rational interpolation, convex domain, polygonal element, shape function, side node