ERROR ANALYSIS FOR
SUBDIVISION SURFACES
 

WU Jianhuang^1,2  LIU Weijun¹  WANG Tianran¹

(1. Laboratory of Advanced Manufacture Technology,Shenyang Institute of Automation,
Chinese Academy of Sciences,Shenyang 110016;
2. Graduate School,Chinese Academy of Sciences,Beijing 100049)

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-specified 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 approach which can improve the surface smoothness of the produced 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: Subdivision surfaces subdivision scheme Error estimating Geometric modeling

CLC No: TP391

国家863计划资助项目(2001AA421160) . Received 20060303, received in revised form 20060806