1. A method for determining a scalar field on a subdivision surface, the method comprising: providing a surface mesh including an edge, the edge connecting a plurality of vertices, the edge adjacent to a plurality of faces, the plurality of vertices corresponding to a plurality of values for a scalar field; processing information associated with the surface mesh using a processor; determining a geometric location for an edge point on a subdivision surface based on at least information associated with the surface mesh, the edge point corresponding to the edge; determining whether the edge is a face-varying boundary based on at least information associated with the surface mesh; processing information associated with whether the edge is a face-varying boundary; computing a first value from the surface mesh for the scalar field corresponding to the edge point based on at least information associated with whether the edge is a face-varying boundary; wherein the plurality of vertices includes a first vertex and a second vertex; the plurality of faces includes a first face and a second face; the plurality of values includes a second value, a third value, a fourth value, and a fifth value; the first vertex corresponds to the second value for the first face and the third value for the second face; the second vertex corresponds to the fourth value for the first face and the fifth value for the second face; the subdivision surface includes a first face point and a second face point; the first face point corresponds to the first face; the second face point corresponds to the second face; the first face point is associated with a sixth value for the scalar field; the second face point is associated with a seventh value for the scalar field; The determining a first value for the scalar field corresponding to the edge point comprises if the edge is a face-varying boundary, the first value is equal to an average of the second value and the fourth value or an average of the third value and the fifth value.