1. A computer-implemented method of specifying an abritrary smooth scalar field on a graphical object modeled as a subdivision surface defined by a polygonal mesh, said polygonal mesh comprising a set of vertices, said scalar field defined as a function of the positions of said set of verticies, comprising: subdividing said polygonal mesh with a subdivision rule a sufficient number of times to obtain a desired resolution for said graphical object, establishing positions of verticies in a subdivided polygonal mesh; and evaluating said scalar field at said positions of vertices in said subdivided polygonal mesh, wherein said scalar field is evaluated on a subdivision surface having resolution greater than said desired resolution subdivided with said subdivision rule.