Constrained Shape Scaling of Trimmed NURBS Surfaces

Abstract

Abstract A method to scale and deform a trimmed NURBS surface while holding the shape and size of specific features (trimming curves) unchanged is presented. The new surface is formed by scaling the given surface according to the scaling requirement first; and then attaching the (original) features to the scaled NURBS surface at appropriate locations. The attaching process requires several geometric operations and constrained free-form surface deformation. The resulting surface has the same features as the original surface and same boundary curves as the scaled surface while reflecting the shape and curvature distribution of the scaled surface. This is achieved by minimizing a shape-preserving objective function which covers all the factors in the deformation process such as bending, stretching and spring effects. The resulting surface maintains a NURBS representation and, hence, is compatible with most of the current data-exchange standards. Test results on several car parts with trimming curves are included. The, quality of the resulting surfaces is examined using the highlight line model.