Constrained Scaling of Catmull-Clark Subdivision Surfaces

Shuhua Lai, Shiping Zou, Fuhua (Frank) Cheng

Research output: Contribution to journalArticlepeer-review


A method to scale a Catmull-Clark subdivision surface while holding the shape and size of specific features (sub-structures) unchanged is presented. The concept of a previous approach for trimmed NURBS surfaces, fix-and-stretch [20], is followed here, i.e., the new surface is formed by fixing selected regions of the given subdivision surface that contain the features, and scaling and stretching the remaining part. But the fixing process and the stretching process are performed differently because of the topology complexity of subdivision surfaces. The resulting surface is again a Catmull-Clark subdivision surface and the method ensures that the resulting surface reflects the shape and curvature distribution of the original surface. The contributions of the paper also include efficient strain energy computation techniques and energy optimization techniques for regions around extra-ordinary points. The new method can handle shapes that can not be represented by trimmed NURBS surfaces and, consequently, can be used for more challenging applications.

Original languageEnglish
Pages (from-to)7-16
Number of pages10
JournalComputer-Aided Design and Applications
Issue number1-4
StatePublished - 2004


  • Constrained deformation
  • Constrained scaling
  • Features
  • Strain energies
  • Subdivision surfaces
  • Trimmed NURBS surfaces

ASJC Scopus subject areas

  • Computational Mechanics
  • Computer Graphics and Computer-Aided Design
  • Computational Mathematics


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