Fairing spline curves and surfaces by minimizing energy

Caiming Zhang, Pifu Zhang, Fuhua Cheng

Research output: Contribution to journalArticlepeer-review

76 Scopus citations

Abstract

New algorithms for the classical problem of fairing cubic spline curves and bicubic spline surfaces are presented. To fair a cubic spline curve or a bicubic spline surface with abnormal portions, the algorithms (automatically or interactively) identify the 'bad' data points and replace them with new points produced by minimizing the strain energy of the new curve or surface. The proposed algorithms are more general than the existing algorithms in that the new algorithms can adjust more than one 'bad' data point in each modification step and they include the existing algorithms [Computer-Aided Design 15(5) (1983) 288-293; 28 (1996) 59-66] as special cases. Test results of the new algorithms are included.

Original languageEnglish
Pages (from-to)913-923
Number of pages11
JournalCAD Computer Aided Design
Volume33
Issue number13
DOIs
StatePublished - Nov 2001

Bibliographical note

Funding Information:
The consulting support of Drs Paul Stewart and Yifan Chen of the Ford Research Lab is deeply appreciated. We also thank the reviewers for several comments and suggestions which improved the quality of the paper. Caiming Zhang is a postdoctoral fellow in the Graphics and Geometric Modeling Lab at the University of Kentucky. He received a BS and an ME in computer science from the Shandong University in 1982 and 1984, respectively, and a doctorate degree in Engineering from the Tokyo Institute of Technology, Japan. His research interests included computer-aided geometric design and modeling, computer graphics and image processing. His permanent address is Department of Computer Science, Shandong University, Jinan, China. Pifu Zhang is a postdoctoral fellow in the Graphics and Geometric Modelling Lab at the University of Kentucky. He received his BEngng and ME in mechanical engineering from Hunan Agricultural University and Beijing Agricultural Engineering University in 1983 and 1987, respectively, and a doctorate degree in Engineering from Hunan University, China, in 1998. His research interests include computer-aided geometric design and modeling, computer graphics, visualization, and mesh generation. Fuhua (Frank) Cheng is Professor of Computer Science and Supervisor of the Graphics and Geometric Modeling Lab at the University of Kentucky where he joined the faculty in 1986. He is also an Adjunct Professor of Applied Mathematics at the Shandong University of Technology, Jinan, China. He received a BS and an MS in mathematics from the National Tsing Hua University in Taiwan in 1973 and 1975, respectively, an MS in mathematics, an MS in computer science, and a PhD in applied mathematics and computer science from the Ohio State University, in 1978, 1980 and 1982, respectively. Dr Cheng has held visiting positions at the University of Tokyo and the University of Aizu, Japan. His research interests include computer-aided geometric modeling, computer graphics, and parallel computing in geometric modeling and computer graphics.

Keywords

  • Curve/surface fairing
  • Interpolation
  • Smoothness
  • Splines curves/surfaces
  • Strain energy

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

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