Techniques for the simplification of volume datasets (represented via tetrahedra meshes) have been devised.
|Simplification in TAn v.1||
The first release of the TAn
system supports the simplification of tetrahedra meshes by adopting a
Delaunay-based refinement approach. The algorithm starts with a very
simple initial mesh (a single tetrahedra); it operates by incrementally inserting
of the dataset (selected on the basis of a maximum error criterion) into the existing
triangulation and updates the triangulation itself to satisfy Delaunay
|Mesh simplification via edge collapse||
Simplification can be performed on tetrahedra meshes by adopting the classical edge-collapse approach. A new approach for the integrated evaluation of the error introduced by both the modification of the domain and the approximation of the scalar field defined on the volume dataset. Different techniques to evaluate the approximation error or to produce a sound prediction are proposed and evaluated.
This simplification approach is at the base of the TAn v.2 system, but has been implemented as an independent software module.
Finally, a simplification tool (ECSiT v1.0) for managing tetrahedral meshes without scalar field values has been implemented and it is available on our downloads page. It adopts edge collapse and the simplification is driven by just the geometry and topology of the tetrahedral mesh.
Most of these researches are carried out in cooperation with Leila De Floriani and
the University of Genova .
The techniques for reducing the size of a volume dataset by preserving both the geometrical/topological shape and the information encoded in an attached scalar field are attracting growing interest. Mesh simplification can be efficiently implemented on simplicial decompositions, both in 2D and 3D. Given the framework of incremental 3D mesh simplification based on edge collapse, the paper proposes an approach for the integrated evaluation of the error introduced by both the modification of the domain and the approximation of the field of the original volume dataset. We present and compare various techniques to evaluate the approximation error or to produce a sound prediction. A flexible simplification tool has been implemented, which provides different degree of accuracy and computational efficiency for the selection of the edge to be collapsed. Techniques for preventing a geometric or topological degeneration of the mesh are also presented.
A system to represent and visualize scalar volume data at multiple resolution is presented. The system is built on a multiresolution model based on tetrahedral meshes with scattered vertices that can be obtained from any initial dataset. The model is built off-line through data simplification techniques, and stored in a compact data structure that supports fast on-line access. The system supports interactive visualization of a representation at an arbitrary level of resolution through isosurface and projective methods. The user can interactively adapt the quality of visualization to requirements of a specific application task, and to the performance of a specific hardware platform. Representations at different resolutions can be used together to enhance further interaction and performance through progressive and multiresolution rendering.
Multiresolution Modeling and Rendering of Volume Data based on Simplicial Complexes
A scattered volumetric dataset is regarded as a sampled version of a scalar field defined over a three-dimensional domain, whose graph is a hypersurface embedded in a four-dimensional space. We propose a multiresolution model for the representation and visualization of such dataset, based on a decomposition of the three-dimensional domain into tetrahedra. Multiresolution is achieved through a sequence of tetrahedralizations that approximate the scalar field at increasing precision. The construction of the model is based on an adaptive incremental approach driven by the local coherence of the scalar field.
The proposed model allows an efficient extraction of compact isosurfaces with adaptive resolution levels as well as the development of progressive and multiresolution rendering approaches. Experimental evaluations of the proposed approach on different scattered datasets are reported.