An improved solution for deformation simulation of nonorthotropic geometric models

Abstract

Physically based deformation simulation has been studied for many years in computer graphics. In order to simulate more complex geometric models and better meet the designer's requirements, many anisotropic approaches have been proposed in recent years. However, most of the approaches focus on simulating orthotropic models. In comparison with orthotropic models, nonorthotropic ones allow the objects to have anisotropic behaviors along nonorthogonal directions. In this paper, we introduce an improved approach to simulate nonorthotropic geometric models under large deformation. The improvements are mainly twofold. First, a frame field is specified on a given undeformed object, that is, each point of the object is equipped with a frame. In each local frame, we construct three independent vectors and form a nonorthogonal coordinate. Second, we design the deformation properties along each axis in the local nonorthogonal coordinate to get a local constitutive model. The final nonorthotropic model is generated by transforming the designed model from local nonorthogonal coordinates to the global standard Cartesian coordinate. To improve the stability, we introduce a time-varying method to simultaneously track the local coordinates reorientation by pushing forward the original frame field to the deformed frame field. Experiments show that the deformation simulation using the designed nonorthotropic models exhibits anisotropic behaviors along different directions and are more stable than previous methods.