Abstract
Aspheric lenses are widely used as important parts of commercial optical products. Owing to their specific functionality, the aspheric surfaces of the lenses are mostly defined by highly complex functions incompatible with commercial manufacturing systems. This reduces lens data interoperability in downstream lens manufacture processes. It is necessary to represent such surfaces in standard formats such as non-uniform rational B-splines (NURBS) by approximating them without sacrificing their accuracy. This paper presents a solution for improving product data interoperability in aspheric lens manufacture. According to the surface type, the solution employs appropriate methods for approximating NURBS surfaces to aspheric surfaces of each type within a specified accuracy and correspondingly provides a simple way of interfacing lens data with commercial manufacturing systems. Some experimental results demonstrate its usefulness and quality.
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References
Piegl L, Tiller W (1995) The NURBS book. Springer, New York
Hoschek J, Lasser D (1993) Fundamentals of computer-aided geometric design. AK Peters
Zeid I (1991) CAD/CAM theory and practice, McGraw-Hill, New York
Owen J (1993) STEP: an introduction. Information Geometers, UK
ISO (2002) International organization for standardization database,http://www.iso.ch
APOMA (2002) American precision optics manufacturers association,http://www.apoma.org
Fischer RE, Tadic-Galeb B (2000) Optical system design. McGraw-Hill, New York
Park H, Kim K, Lee SC (2000) A method for approximate NURBS curve compatibility based on multiple curve refitting. Comput Aid 32(4):237–252
Burden RL, Faires JD (1989) Numerical analysis. PWS-KENT, Boston
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C: the art of scientific computing. Cambridge University Press, New York
Rogers DF, Fog NG (1989) Constrained B-spline curve and surface fitting. Comput Aid 21(10):641–648
Saux E, Daniel M (1999) Data reduction of polynomial curves using B-splines. Comput Aid 31(8):507–515
Vassilev TI (1996) Fair interpolation and approximation of B-splines by energy minimization and point insertion. Comput Aid 28(9):753–760
Celniker G, Gossard D (1991) Deformable curve and surface finite elements for free-form shape design. Comput Graph 25(4):257–266
Sarkar B, Menq CH (1991) Parameter optimization in approximating curves and surfaces to measurement data. Comput Aid G 8:267–290
Laurent-Gengoux P, Mekhilef M (1993) Optimization of a NURBS representation. Comput Aid 25(11):699–710
Park H (2001) An approximate lofting approach for B-spline surface fitting to functional surfaces. Int J Adv Manuf Technol 18(7):474–482
Piegl L, Tiller W (1996) Algorithm for approximate NURBS skinning. Comp Aid 28(9):699–706
Acknowledgements
This work was supported by Korea Research Foundation Grant (KRF-2002-003-D00444).
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Park, H. A solution for NURBS modelling in aspheric lens manufacture. Int J Adv Manuf Technol 23, 1–10 (2004). https://doi.org/10.1007/s00170-002-1518-5
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DOI: https://doi.org/10.1007/s00170-002-1518-5