We outline a new procedure for measuring free-form curves and surfaces using implicit polynomial equations. Such equations have long been known to offer certain advantages over the more traditional parametric methods. However, the lack of general procedures for obtaining implicit polynomial models of higher degree, which precisely represent arbitrary 3-D shapes, have prevented their general use in many practical applications, including rapid and precise metrology. Recent mathematical advances obtained at Brown University, experimentally verified using a state-of-the-art Chameleon coordinate measuring machine, have demonstrated potential advantages of implicit methods for modeling and measuring a variety of manufactured objects.
The Precise Measurement of Free-Form Surfaces1
Contributed by the Manufacturing Engineering Division for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received April 2000; Revised April 2001. Associate Editor: T. Kartess.
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Wolovich, W., Albakri, H., and Yalcin, H. (April 29, 2002). "The Precise Measurement of Free-Form Surfaces." ASME. J. Manuf. Sci. Eng. May 2002; 124(2): 326–332. https://doi.org/10.1115/1.1430677
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