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Fast evaluation of the minimum zone form errors of freeform NURBS surfaces
ZHANG Xiangchao * #,ZHANG Hao,HE Xiaoying,XU Min
Shanghai Engineering Research Center for Ultra-Precision Optical Manufacturing, Fudan Universtiy, Shanghai, 200438
*Correspondence author
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Funding: National Natural Science Foundation of China （No.No. 51205064）, Research Fund for the Doctoral Program of Higher Education （No.No. 20120071120018）, Shanghai Natural Science Foundation （No.No. 12ZR1441100）
Opened online:28 September 2014
Accepted by: none
Citation: ZHANG Xiangchao,ZHANG Hao,HE Xiaoying.Fast evaluation of the minimum zone form errors of freeform NURBS surfaces[OL]. [28 September 2014] http://en.paper.edu.cn/en_releasepaper/content/4610664
 
 
Nowadays freeform components are more and more commonly employed in precision engineering and it is crucial to evaluate their form qualities. The widely adopted PV parameters for form errors need to be evaluated in the sense of minimum zone, which is a non-differentiable optimization problem, and very difficult to be solved. Currently NURBS has become a ubiquitous data format in computer aided design and manufacturing. However, little can be found concerning the minimum zone fitting between the NURBS surfaces and measured data, due to the mathematical complexity of this problem. A fast evaluation strategy is proposed in this paper. It is implemented in three stages. The NURBS model is decomposed into Bezier patches first and the iterative closest point matching is implemented. And then the relative position is refined by the orthogonal distance least squares fitting. Finally the minimum zone fitting is carried out by the primal-dual interior point method. The solutions are recursively updated by line search until the Karush-Kuhn-Tucker conditions are satisfied. Numerical experiments proved that the proposed method is capable of minimum zone fitting for freeform NURBS surfaces with very high accuracy and efficiency.
Keywords:freeform surface; form error; NURBS; minimum zone; primal-dual interior point method
 
 
 

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