Abstract: We present a smooth surface construction based on the manifold approach of Grimm and Hughes. We demonstrate how this approach can relatively easily produce a number of desirable properties which are hard to achieve simultaneously with polynomial patches, subdivision or variational surfaces. Our surfaces are C^∞-continuous with explicit nonsingular C^∞ parameterizations, high-order flexible at control vertices, depend linearly on control points, have fixed-size local support for basis functions, and have good visual quality.