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Radius Measurement of Fillet Regions of Polygonal Models by using Optimum Orthogonal Planes  

Han Y,-H. ((주)아이너스기술)
Publication Information
Korean Journal of Computational Design and Engineering / v.10, no.2, 2005 , pp. 114-120 More about this Journal
Abstract
This paper presents a novel method for radius measurement of fillet regions of polygonal models by using optimum onhogonal planes. The objective function for finding an optimum onhogonal plane is designed based on the orthogonality between the normal vectors of the faces in a filet region and the plane that is to be found. Direct search methods are employed to solve the defined optimization problem since no explicit derivatives of the object function can be calculated. Once an optimum orthogonal plane is obtained, the intersection between the onhogonal plane and the faces of interest is calculated, and necessary point data in the fillet region for measuring radii are extracted by some manipulation. Then, the radius of the fillet region in question is measured by least squares fitting of a circle to the extracted point data. The proposed radius measuring method could eliminate the burden of defining a plane for radius measurement, and automatically find a necessary optimum orthogonal plane. It has an advantage in that it can measure fillet radii without prior complicated segmentation of fillet regions and explicit information of neighboring surfaces. The proposed method is demonstrated trough some mea-surement examples.
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1 Chivate, P. N. and Jablokow, A. G., 'Solid-model Generation from Measured Point Data', ComputerAided Design, Vol. 25, No.9, pp. 587-600, 1993   DOI   ScienceOn
2 Watson, G. A., 'Least Squares Fitting of Circles and Ellipses to Measured Data', BIT Numerical Mathematics, Vol. 39, No. 1, pp. 176-191, 1999   DOI
3 Rosenfeld, A. and Weszka, J. S., 'An Improved Method of Angle Detection on Digital Curves', IEEE Transaction on Computers, Vol. C-24, pp. 940-941, 1975   DOI   ScienceOn
4 Arora, J. S., Introduction to Optimum Design, McGraw-Hill, 1989
5 Varady, T., Martin, R. R. and Cox, J., 'Reverse Engineering of Geometric Models-An Introduction', Computer-Aided Design, Vol. 29, No.4, pp. 255-268, 1997   DOI   ScienceOn
6 Kos, G., Martin, R. and Varady, T., 'Methods to Recover Constant Radius Rolling Ball Blends in Reverse Engineering', Computer-Aided Geometric Design, Vol. 17, No.2, pp. 127-60, 2000   DOI   ScienceOn
7 Hooke, R. and Jeeves, T. A., 'Direct Search Solution of Numerical and Statistical Problems', Journal of the ACM, Vol. 8, pp. 212-229, 1961   DOI
8 Press, W. H. et al., Numerical Recipes in C, Cambridge University Press, 1992
9 Lewis, R. M., 'Direct Search Methods: Then and Now', ICASE Report No. 2000-26, May 2000
10 Piegl, L. and Tiller, W., The NURBS Book, Springer-Verlag, 1995
11 Coope, I. D., 'Circle Fitting by Linear and Nonlinear Least Squares', Journal of Optimization Theory and Applications, Vol. 76, No.2, 1993