Explicit Form Based High Efficient Mesh Deformation Techniques

As an important research topic of computer graphics which has been intensively studied, mesh deformation is widely used in many applications such as entertainment and virtual reality. Recently, as the increasing of mesh complexity, current methods are difficult to meet both the performance and quality requirements of applications.According to the formulation of the deformation functions, current mesh deformation meth-ods can be divided into two categories:explicit form based methods and implicit form based meth-ods. Explicit form based methods, including Skeletal-Subspace Deformation (SSD) and Free Form Deformation (FFD), share the following advantages:simple, fast and independent of model repre-sentation. But the drawback of these methods is the lack of efficient way to control the deformation effects, and it is hard to achieve high quality results under large deformation for these methods. Implicit form based methods, represented by gradient domain methods, are able to achieve high quality detail-preserving deformation results and support various constraints. But they mostly de-pend on manifold mesh and require solving large linear or non-linear systems, which lead to high memory and computation costs for complex models.This thesis focuses on the development of the explicit form based deformation techniques. Base on new explicit form deformation functions with high expression ability and optimization of gradient domain properties, several efficient deformation techniques are presented, which are able to achieve high quality deformation results in high performance, even for complex models. The main contributions include:●Propose a smooth interpolation deformation method based on tetrahedron control mesh. The traditional barycentric coordinates generate apparent first-order discontinuity artifacts across the boundary. To avoid such artifacts, we add a local transformation at each control vertex for interpolation, so that we can minimize the first-order discontinuity by optimizing the local transformations. Based on the explicit and local support formulation, the interpolation can be efficiently evaluated using modern GPUs and achieves high performance. Our method can also be applied to 2D image objects and deforming the control mesh.●Propose a cage based deformation transfer method. Previous methods can only transfer the deformation between manifold mesh. To avoid such limitation, the target model is first em-bedded into a cage by explicit interpolation function. The deformation gradient sequences of some user-selected points on the source are then extracted and used as the gradient con-straints in the cage to guide the target deformation. By employing such method, we can transfer deformation from various sources to geometric models in variant representations. The key part of this method is a green coordinates based subspace method, whose opti-mization is independent of the target model. It ensures that the deformation transfer can be independent of model representation and the nonlinear optimization can be efficiently solved. Besides, position, orientation and length constraints can be applied for supporting more controls to the deformation transfer results.●Propose a shape interpolation method based on precomputed trajectory warping. We present a new explicit form of trajectory, which regulates the linear interpolation trajectory with additional angular velocity component for tracing the local rotations. This nonlinear trajec-tory can efficiently eliminate the shrinking artifacts introduced by linear trajectory. We find trajectory parameters for each vertex by optimization with the consideration of as-rigid-as-possible deformation in the pre-computing stage. During run-time, the vertices coordinates on the intermediate shape can be computed in parallel according to the explicit formulation. Comparing with the implicit methods which reconstruct the intermediate shape by optimiza-tion, our method does not need to solve large linear system and is able to achieve extremely high performance. This technique can also be extended easily to multi-pose interpolation and tetrahedron models.