Font Size: a A A

Rigidity Constraints For Shape Deformation

Posted on:2010-11-09Degree:DoctorType:Dissertation
Country:ChinaCandidate:Y ZhaoFull Text:PDF
GTID:1118360302979606Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
In recent years, due to the fast development of 3D shape scanning devices and techniques, triangular meshes become the main representation for complex 3D objects, and are widely employed in a variety of application fields, such as movie production, online game, computer animation, industry design, computer-aided diagnosis, scientific computing, historical relics protection, and military simulation. To meet different application requirements., digital geometry processing become the central and active field in computer graphics, hot topics mainly include data acquisition, curvature estimation, parameterization, smoothing and denoising, geometry completion, surface fitting, simplification, watermarking, compression and transmission, deformation, morphing, character animation, texture synthesis, remeshing, segmentation, rendering etc. One of the most difficult geometry processing operations is high quality shape deformation.The challenging problems in shape deformation are preserving geometric details and preventing unnatural volume changes as much as possible while satisfying the user constraints. There has been a considerable amount of research work for shape deformation. However, most of them only consider surface detail preservation. So certain volumetric features, such as local rigidity and volume, are hard to preserve, and apparent volume changes occur during extreme editing.To address these problems, we propose various rigidity constraints to prevent surface detail and volumetric distortions even under large deformations: the 3D shape is constrained to undergo an as-rigid-as-possible deformation by asking for the rigidity of its local behavior.The main contributions of this thesis include the following three aspects:(1) A new rigidity constraint is proposed for gradient domain mesh deformation to avoid apparent volume changes around largely deformed areas. Intuitively the proposed constraint can be regarded as several small cubes inside the mesh model. The user interactively specifies the cubes in the regions which are prone to volumetric distortions. During deformation, the rigidity constraints could prevent the relative movement of the mesh vertices, and make the mesh model behave like a solid object, thus avoiding apparent volume shrinkage.(2) To deal with large meshes, an efficient mesh deformation algorithm is presented. First, by conducting clustering-based simplification on the original mesh, the initial deformation result can be efficiently obtained, which achieves locally rigid deformation. Then through iteratively minimizing a quadric energy function, an optimal rigid transformation is estimated for each vertex to guarantee the continuity of the final deformation result, and make the original mesh deform as rigidly as possible, hence greatly reducing surface detail and volumetric distortions under large deformations.(3) To improve the generality and controllability, by embedding the input models into coarse tetrahedral control meshes, a unified shape editing framework is developed. This framework is efficient, robust, easy to control, supports various shape representations, and well transfers deformations between non-homeomorphous models. During deformation, a new rigidity energy is proposed to deform the control mesh as rigidly as possible, which yields intuitive detail and volume preservation even under extreme deformations. And an error-driven refinement approach is presented to further improve the deformation result. Then, based on this deformation scheme, a novel deformation transfer algorithm is introduced: the transfer process is performed between the source and target control meshes instead of between the source and target models, which effectively lessens the burden of the user and improves the efficiency.Although the above three techniques are independent, they complement each other. These techniques provide a practical and robust platform for shape deformation, which can deal with complex 3D objects and obtain high quality results. As the importance and popularity of deformation techniques, we will give a conclusion and discuss future work at the last chapter.
Keywords/Search Tags:digital geometry processing, shape deformation, deformation transfer, rigidity constraint, rigid deformation, surface detail preservation, volume preservation, clustering-based simplification, tetrahedral control mesh, error-driven refinement
PDF Full Text Request
Related items