Deformable simulation using force propagation model with finite element optimization

Abstract

A key challenge of deformable simulation is to satisfy the conflicting requirements of real-time interactivity and physical realism. In this paper, we present the mass–spring-based force propagation model (FPM) in which the simulation speed is tunable to maintain a balance between the two criteria. Deformation is modeled as a result of force propagation among the mass points in localized regions. Experiments have been performed to study the effects of the FPM parameters on the eventual deformation. Furthermore, a heuristic optimization technique is proposed to identify the model parameters for materials as specified by mechanical constants. We employ simulated annealing to tune the parameters automatically until the simulated shape of the FPM approximates the reference deformation as defined by the mathematically more rigorous finite element model. The proposed technique provides a feasible solution to the issue of parameter identification in mass–spring-based models.

Introduction

Deformable simulation finds many applications in computer graphics and related fields, including facial-tissue modeling, cloth animation, and virtual surgery planning and training. A major goal to all these applications is to achieve physically realistic deformation effects. Hence, deformable models based on physical laws have been developed in an attempt to accurately depict subtle interactions between virtual objects and external forces. One successful example is the mass–spring model. It is an efficient physics-based technique that models deformable object as a system of mass points connected with springs. By using this model, synthetic muscles have been constructed to animate facial expression [1], multilevel meshes are incorporated to simulate cloth [2], and mass–spring-based human organs are used to realize endoscopic surgical training in virtual environments [3]. On the other hand, to model the mechanical properties of materials with better accuracy, finite element method along with continuum mechanics is applied to deformable modeling. Discretization into a set of elements is carried out in finite element modeling (FEM) such that global deformation is considered locally in each element. Deformation within an element is taken into account by the interpolation of nodal displacements as governed by the underlying constitutive laws. While being more accurate, the computationally intensive finite element model is undesirable for applications that demand real-time interactions. For instance, high refresh rates for visual and haptic rendering are required in virtual reality applications. In the pursuit of physical realism for deformable modeling, it is therefore important to keep computations efficient.

In this paper, we deal with the problem by presenting an efficient deformable model based on mass–spring system, the force propagation model (FPM) [4]. It features tunable computational speed against realism by controlling the extent of localized deformation. In this model, deformation process is modeled as a sequence of ordered force propagation among the nodes in localized regions. Our approach is distinct from conventional mass–spring models in that laborious stiffness matrix formulation and computation-intensive matrix operations are not involved. Furthermore, a heuristic technique is employed to tackle a common issue to all mass–spring systems — specification of appropriate system parameters that reproduce the mechanical properties of real objects — by benchmarking against the corresponding finite element model. Our model is implemented with Java and Java 3D API to take advantage of Java's portability and accessibility over the Internet. The paper is organized as follows. Section 2 gives an overview of the related work on physically based deformable models. Section 3 presents the underlying principle of the FPM along with experimental results. Section 4 discusses the acquisition of appropriate model parameters by performing heuristic optimization against elastically deformable model based on the finite element method. Finally, Section 5 gives conclusions and future work.