Constrained Scaling of Catmull-Clark Subdivision Surfaces

Abstract

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.

Keywords:

• constrained scaling
• subdivision surfaces
• constrained deformation
• trimmed NURBS surfaces
• strain energies
• features