Fast corotational simulation for example-driven deformation

Highlights

• An example space energy is constructed based on the corotational Cauchy strain.

• The total energy functional can be fast worked out by solving a linear system.

• An effective error correction algorithm is given for realism and stability.

• The proposed method can be easily implemented by expansion the existing FEM code.

Abstract

We present a fast corotational finite element framework for example-driven deformation of 3-dimensional solids. An example-driven deformation space and an example space energy is constructed by introducing the modified linear Cauchy strain with rotation compensation. During this simulation, our adopted total energy functional is quadratic, and its corresponding optimization can be quickly worked out by solving a linear system. For addressing the possible errors, we propose an effective error-correction algorithm. Some related factors including the parameters and example weights are also discussed. Various experiments are demonstrated to show that the proposed method can achieve high quality results. Moreover, our method can avoid complex non-linear optimization, and it outperforms previous methods in terms of the calculation cost and implementation efficiency. Finally, other acceleration algorithms, such as the embedding technique for handling highly detailed meshes, can be easily integrated into our framework.

Introduction

Simulation of deforming objects is one of the active topics in computer graphics, and it has been widely applied in the movie industry, digital entertainment and product design. Over the years, researchers have conducted a large amount of excellent work on model deformation simulation, namely, editing, material modeling, user interaction and other related issues. With the repaid development of deformable model acquisition, example-driven deformation techniques [1], [2], [3] have received much attention, and their applications have also become the extension of the key frame animation and physical simulation.

Most of the approaches in the example-driven deformation domain construct an energy functional of the object and solve the corresponding optimization problems for obtaining the node positions and reconstructing the shapes. In general, the energy functional is composed of two parts, which are the deformation energy and the constraint energy introduced by examples. Moreover, the later part influences the simulation results by constructing an example deformation space. Both parts can be constructed by geometric and physical methods. In comparison, physical methods can more easily reflect the physical properties of the model materials.

Example-driven deformation can produce more diverse effects than conventional key frame techniques in many applications. However, the induced optimization problem always leads to complex non-linear solutions. This limits the simulation response time as well as the solution scale.

In this paper, an efficient computing framework for example-driven deformation is presented. Inspired by existing approaches, we construct an energy functional of the deformable models in a physically based context. For modeling the deformation metric, we apply a revised Cauchy strain for efficient simulation. At the same, the corotational method is integrated to tackle the large deformation problem and also to form the example deformable space.

Compared with previous methods, the proposed method is based on linear strain, and the induced optimization can be worked out quickly by simply solving a linear system. To address the possible errors, an effective error-correction algorithm is proposed. Moreover, it is easy for our framework to integrate the existing speed-up algorithms such as the embedding technique for highly detailed meshes.