Multilevel Solvers for Unstructured Surface Meshes

Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner

Mesh simplification with hierarchical shape analysis and iterative edge contraction

2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Surface Simplification of 3D Animation Models Using Robust Homogeneous Coordinate Transformation

The goal of 3D surface simplification is to reduce the storage cost of 3D models. A 3D animation model typically consists of several 3D models. Therefore, to ensure that animation models are realistic, numerous triangles are often required. However, animation models that have a high storage cost have a substantial computational cost. Hence, surface simplification methods are adopted to reduce the number of triangles and computational cost of 3D models. Quadric error metrics (QEM) has recently been identified as one of the most effective methods for simplifying static models. To simplify animation models by using QEM, Mohr and Gleicher summed the QEM of all frames. However, homogeneous coordinate problems cannot be considered completely by using QEM. To resolve this problem, this paper proposes a robust homogeneous coordinate transformation that improves the animation simplification method proposed by Mohr and Gleicher. In this study, the root mean square errors of the proposed method were compared with those of the method proposed by Mohr and Gleicher, and the experimental results indicated that the proposed approach can preserve more contour features than Mohr’s method can at the same simplification ratio

3D Mesh Simplification. A survey of algorithms and CAD model simplification tests

Simplification of highly detailed CAD models is an important step when CAD models are visualized or by other means utilized in augmented reality applications. Without simplification, CAD models may cause severe processing and storage is- sues especially in mobile devices. In addition, simplified models may have other advantages like better visual clarity or improved reliability when used for visual pose tracking. The geometry of CAD models is invariably presented in form of a 3D mesh. In this paper, we survey mesh simplification algorithms in general and focus especially to algorithms that can be used to simplify CAD models. We test some commonly known algorithms with real world CAD data and characterize some new CAD related simplification algorithms that have not been surveyed in previous mesh simplification reviews.Siirretty Doriast

Automatic Mesh Repair and Optimization for Quality Mesh Generation

Ph.DDOCTOR OF PHILOSOPH