Parameter optimization in approximating curves and surfaces to measurement data

doi:10.1016/0167-8396(91)90016-5

Computer Aided Geometric Design

Volume 8, Issue 4, October 1991, Pages 267-290

https://doi.org/10.1016/0167-8396(91)90016-5 Get rights and content

Abstract

Curves and surfaces are often required to be approximated to the measurement data points in modeling industrial parts. A total approximation procedure involves assigning parameter values, least-squares fitting, and parameter optimization. In this article, a parameter optimization method is suggested based on the non-linear least-squares optimization procedure due to Levenberg-Marquardt. An explicit expression, for the sum of the squares of the fitting errors at each of the data points, is minimized treating the parameters as the variables. This optimization process has been compared with a number of published methods [Hoschek '88, Hoschek et al. '89, and Rogers & Fog '89] using cubic B-spline basis functions. Examples are provided for the approximation of curves and surfaces and their offsets.

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Parameter optimization in approximating curves and surfaces to measurement data

Abstract

Computer-aided Design

Computer Aided Geometric Design

Computer-aided Design

Computer Aided Geometric Design

Computer Aided Geometric Design

Computer-aided Design

Computer-aided Design

Computer Aided Geometric Design

Computer-aided Design