12 research outputs found
Dynamic remeshing and applications
Triangle meshes are a flexible and generally accepted boundary representation for complex geometric shapes. In addition to their geometric qualities such as for instance smoothness, feature sensitivity ,or topological simplicity, intrinsic qualities such as the shape of the triangles, their distribution on the surface and the connectivity is essential for many algorithms working on them. In this thesis we present a flexible and efficient remeshing framework that improves these "intrinsic\u27; properties while keeping the mesh geometrically close to the original surface. We use a particle system approach and combine it with an iterative remeshing process in order to trim the mesh towards the requirements imposed by different applications. The particle system approach distributes the vertices on the mesh with respect to a user-defined scalar-field, whereas the iterative remeshing is done by means of "Dynamic Meshes\u27;, a combination of local topological operators that lead to a good natured connectivity. A dynamic skeleton ensures that our approach is able to preserve surface features, which are particularly important for the visual quality of the mesh. None of the algorithms requires a global parameterization or patch layouting in a preprocessing step, but works with simple local parameterizations instead. In the second part of this work we will show how to apply this remeshing framework in several applications scenarios. In particular we will elaborate on interactive remeshing, dynamic, interactive multiresolution modeling, semiregular remeshing and mesh simplification and we will show how the users can adapt the involved algorithms in a way that the resulting mesh meets their personal requirements
Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
The typical goal of surface remeshing consists in finding a mesh that is (1)
geometrically faithful to the original geometry, (2) as coarse as possible to
obtain a low-complexity representation and (3) free of bad elements that would
hamper the desired application. In this paper, we design an algorithm to
address all three optimization goals simultaneously. The user specifies desired
bounds on approximation error {\delta}, minimal interior angle {\theta} and
maximum mesh complexity N (number of vertices). Since such a desired mesh might
not even exist, our optimization framework treats only the approximation error
bound {\delta} as a hard constraint and the other two criteria as optimization
goals. More specifically, we iteratively perform carefully prioritized local
operators, whenever they do not violate the approximation error bound and
improve the mesh otherwise. In this way our optimization framework greedily
searches for the coarsest mesh with minimal interior angle above {\theta} and
approximation error bounded by {\delta}. Fast runtime is enabled by a local
approximation error estimation, while implicit feature preservation is obtained
by specifically designed vertex relocation operators. Experiments show that our
approach delivers high-quality meshes with implicitly preserved features and
better balances between geometric fidelity, mesh complexity and element quality
than the state-of-the-art.Comment: 14 pages, 20 figures. Submitted to IEEE Transactions on Visualization
and Computer Graphic
New Techniques for the Modeling, Processing and Visualization of Surfaces and Volumes
With the advent of powerful 3D acquisition technology, there is a growing demand
for the modeling, processing, and visualization of surfaces and volumes. The
proposed methods must be efficient and robust, and they must be able to extract the essential structure of the data and to easily and quickly convey the most significant information to a human observer. Independent of the specific nature of the data, the following fundamental problems can be identified: shape reconstruction from discrete samples, data analysis, and data compression.
This thesis presents several novel solutions to these problems for surfaces
(Part I) and volumes (Part II). For surfaces, we adopt the well-known triangle
mesh representation and develop new algorithms for discrete curvature estimation,detection of feature lines, and line-art rendering (Chapter 3), for connectivity encoding (Chapter 4), and for topology preserving compression of 2D vector fields (Chapter 5). For volumes, that are often given as discrete samples, we base our approach for reconstruction and visualization on the use of new trivariate spline spaces on a certain tetrahedral partition. We study the properties of the new spline spaces (Chapter 7) and present efficient algorithms for reconstruction and visualization by iso-surface rendering for both, regularly (Chapter 8) and irregularly (Chapter 9) distributed data samples
Dynamic Remeshing and Applications
Triangle meshes are a flexible and generally accepted boundary
representation for complex geometric shapes. In addition to their
geometric qualities and topological simplicity, \emph{intrinsic}
qualities such as the shape of the triangles, their distribution on
the surface and the connectivity are essential for many algorithms
working on them. In this paper we present a flexible and efficient
remeshing framework that improves these intrinsic properties while
keeping the mesh geometrically close to the original surface. We
use a particle system approach and combine it with an incremental
connectivity optimization process to trim the mesh towards the
requirements imposed by the user. The particle system uniformly
distributes the vertices on the mesh, whereas the connectivity
optimization is done by means of \emph{Dynamic Connectivity Meshes},
a combination of local topological operators that lead to a fairly
regular connectivity. A dynamic skeleton ensures that our approach
is able to preserve surface features, which are particularly
important for the visual quality of the mesh. None of the
algorithms requires a global parameterization or patch layouting in
a preprocessing step but uses local parameterizations only. We also
show how this general framework can be put into practice and sketch
several application scenarios. In particular we will show how the
users can adapt the involved algorithms in a way that the resulting
remesh meets their personal requirements