Abstract: Subdivision surfaces have become popular geometric modeling primitive for representing free form shapes. An Efficient and effective error estimating method for subdivision surfaces is presented. A computing formula for the error estimating is derived based on the topological structure of the control mesh and subdivision rules. With this formula, one can predict how many steps of subdivision are necessary to meet a user-speci- fied error tolerance without subdividing the control meshes actually. Two examples in practical engineering application are given to show the usefulness and importance of the computing formula for subdivision surfaces. One is three-axis NC tool path generation for subdivision surface; The other is an ap-proach which can improve the surface smoothness of the pro-duced objects in rapid prototyping directly without referring to original CAD models. Our proposed method can be extended to other subdivision schemes and other free form surfaces.

Key words: Error estimating, Geometric modeling, subdivision scheme, Subdivision surfaces