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; 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; determining a first value for the scalar field corresponding to the edge point based on at least information associated with whether the edge is a face-varying boundary.