Chapter

Advances in Geometric Modeling and Processing

Volume 4975 of the series Lecture Notes in Computer Science pp 384-397

A Revisit to Least Squares Orthogonal Distance Fitting of Parametric Curves and Surfaces

  • Yang LiuAffiliated withDept. of Computer Science, The University of Hong Kong
  • , Wenping WangAffiliated withDept. of Computer Science, The University of Hong Kong

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Abstract

Fitting of data points by parametric curves and surfaces is demanded in many scientific fields. In this paper we review and analyze existing least squares orthogonal distance fitting techniques in a general numerical optimization framework. Two new geometric variant methods ( https://static-content.springer.com/image/chp%3A10.1007%2F978-3-540-79246-8_29/MediaObjects/978-3-540-79246-8_29_IEq1_HTML.png and https://static-content.springer.com/image/chp%3A10.1007%2F978-3-540-79246-8_29/MediaObjects/978-3-540-79246-8_29_IEq2_HTML.png ) are proposed. The geometric meanings of existing and modified optimization methods are also revealed.

Keywords

orthogonal distance fitting parametric curve and surface fitting nonlinear least squares numerical optimization