Constrained scaling of trimmed NURBS surfaces based on fix-and-stretch approach

C. Zhang, P. Zhang, F. Cheng

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


A new method to scale a trimmed NURBS surface while holding the shape and size of specific features (trimming curves) unchanged is presented. The new method is fix-and-stretch based: the new surface is formed by fixing selected regions of the given trimmed NURBS surface that contain the trimming curves and stretching the remaining part of the surface to reach certain boundary conditions. The stretching process is performed using an optimization process to ensure that the resulting surface reflects the shape and curvature distribution of the scaled version of the given surface. The resulting surface maintains a NURBS representation and, hence, is compatible with most of the current data-exchange standards. The new approach is more robust than a previous, attach-and-deform based approach in that it can tolerate scaling factors of bigger values (up to 2 in some cases). The new approach also guarantees that the features remain exactly the same after scaling. Test results on several car parts with trimming curves and comparison with the previous approach are included. The quality of the resulting surfaces is examined using the highlight line model. The presented technique is important for integrating standard parts into a sculptured product.

Original languageEnglish
Pages (from-to)103-112
Number of pages10
JournalCAD Computer Aided Design
Issue number1
StatePublished - Jan 2001

Bibliographical note

Funding Information:
The financial support of Ford Motor Company through a URP grant and Honda Motor Company through two HIG grants, and the consulting support of Drs Paul Stewart and Yifan Chen of the Ford Research Lab and Dr Shane Chang of the Honda R and D North America are deeply appreciated. We also thank the reviewers for several comments and suggestions which helped improve the quality of the paper.

ASJC Scopus subject areas

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


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