Physically based deformable models have been a hot topic in the computer graphics and visualization community. However, most of the implemented models work only for isotropic materials, leaving the more general anisotropic materials less studied. We look into the challenging issues in dynamics simulation and real time visualization for anisotropic materials, and present our theoretic and practical work along the way to provide an ultimate solution to deformation with such materials. First, our models are based on continuum mechanics and approximated by the Finite Element Method, and different approaches such as co rotated, invertible, and total Lagrangian explicit dynamics. Secondly, for controls of the deformation, we have focused on materials that have their own internal structures (fibers) that determine the dynamics behaviors. We propose a fibers incorporated deformable model that can approximate the anisotropic elastic material properties. The orientation information is combined into the existing deformable models by element transformations along the given directions, which provide a control of the desired deformation. Thirdly, constraints for the strain density in linear elastic models are analyzed, and a positive-definite elasticity tensor is derived for an anisotropic material. Fourthly, an orthotropic deformation controlling frame-field is conceptualized and the frame construction tool is developed for the user to define the desired material properties. A quaternion Laplacian smoothing algorithm is designed for propagating the rotation minimization frames into the entire object. And finally, the co rotational linear FEM model is coupled with the orthotropic frame-field to realize a dynamics system, which can deal with large anisotropic deformations.

Prediction of the 3D structure of protein-protein complexes is crucial for understanding the biological system of life and thus for designing drugs. However it is a challenging problem due to the flexibility of the backbone and side-chains of the receptor and ligand. In this paper, we present a new framework for fast and flexible protein-protein docking based on geometric and physicochemical complementarity. In our approach, we segment the protein surfaces into several local surface patches and describe the effect of side-chain flexibility on each patch by sampling the space of conformation of its side-chains. Then the geometric complementarity can be determined by matching these surface patches. During the matching, we propose a new 3D shape descriptor, Spherical Harmonics Descriptor. The main property of the Spherical Harmonics Descriptor is rotation invariance which avoids taking an exhaustive set of rotations for each pair of patches. Thus, the geometric complementarity matching problem is simplified to a histogram matching problem. This can greatly reduce the computational cost. Finally, the docking candidates are evaluated by a scoring function which can accommodate geometric complementarity and physicochemical matching. The experimental results demonstrate the high efficiency and accuracy of the proposed method.

Several studies have been made in finding the faces of an object depicted in a line drawing, but the problem has not been completely solved. Although existing methods can find the correct faces in most cases, there is no mechanism to ascertain that they are indeed correct, leaving the human user to do so. This paper uses a two-stage approach--find potential faces, then validate their correctness--to ensure that only correct faces are delivered ultimately. The face finding itself uses a double breadth-first search algorithm, which yields the shortest path, to find the potential faces. The basic premise is that the smallest faces found are more likely the correct ones. They serve as the "seed" potential faces, from which the algorithm proceeds to search for more faces. If the potential faces found satisfy the validation rules, then they are accepted as correct. Otherwise, the wrong potential faces are identified and removed, and new ones found in their place. The validation process is then repeated. The algorithm is fast and reliable, can deal with planar-faced manifold and nonmanifold objects, and can deliver the different results when a drawing has multiple interpretations. Our extensive tests show that the method can deal with most cases efficiently, including those that previous methods cannot solve.

A straightforward way to illustrate a 3D model is to use a line drawing. Faces in a 2D line drawing provide important information for reconstructing its 3D geometry. Manifold objects belong to a class of common solids and most solid systems are based on manifold geometry. In this paper, a new method is proposed for finding faces from single 2D line drawings representing manifolds. The face identification is formulated based on a property of manifolds: each edge of a manifold is shared exactly by two faces. The two main steps in our method are (1) searching for cycles from a line drawing and (2) searching for faces from the cycles. In order to speed up the face identification procedure, a number of properties, most of which relate to planar manifold geometry in line drawings, are presented to identify most of the cycles that are or are not real faces in a drawing, thus reducing the number of unknown cycles in the second searching. Schemes to deal with manifolds with curved faces and manifolds each represented by two or more disjoint graphs are also proposed. The experimental results show that our method can handle manifolds previous methods can handle, as well as those they cannot.

The faces in a 2D fine drawing of an object provide important information for the reconstruction of its 3D geometry. In this paper, a graph-based optimization method is proposed for identifying the faces is a line drawing. The face identification is formulated as a maximum weight clique problem. This formulation is proven to be equivalent to the formulation proposed by Shpitalni and Upson (1996). The advantage of our formulation is that it enables one to develop a much faster algorithm to find the faces in a drawing. The significant improvement in speed is derived from two algorithms provided: the depth-first graph search for quickly generating possible faces from a drawing; and the maximum weight clique finding for obtaining the optimal face configurations of the drawing. The experimental results shown that our algorithm generates the same results of face identification as Shpitalni and Lipson's method, but is much faster when dealing with objects of more than 20 faces.