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
the points
of the dataset (selected on the basis of a maximum error criterion) into the existing
triangulation and updates the triangulation itself to satisfy Delaunay
constraints. |
| 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
Enrico
Puppo of
the University of Genova .
)Abstract
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.
, Figs:
)Abstract
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
Abstract
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.