Monge mapping using hierarchical NURBS

Abstract

Texture mapping is an efficient and effective tool in computer graphics and animation. While computationally very cost-effective, texture mapping may produce non-realistic appearances of shapes in 3D environment, especially when viewing closely. To improve the realism of 3D modeling, bump mapping technique is developed to add details with the 3D models on top of texture mapping. Bump mapping, however, offers only simple and visual enhancement. Displacement mapping technique can further improve the localized detail of geometry. In this paper, Monge mapping technique is developed for detail and local shape modification of NURBS represented geometry in a 3D environment. Based on multiresolution and refinement schemes, Hierarchical NURBS (H-NURBS) is first investigated to design a mechanism for the purpose of carrying localized geometric information. Monge mapping on H-NURBS patch can be easily performed via simple cut-and-paste operation. Parametric control of the local shapes is developed to facilitate easier and better 3D local modeling.