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We present a meshing and rendering framework for large unstructured tetrahedral meshes which is based on a collection of segments that form a multi resolution model. Each segment contains several thousand tetrahedra and covers either a part of the original tetrahedral mesh or a simplified version of the mesh. The mesh can be adapted locally at run time to viewing and classification parameters by replacing segments with other segments. Dependencies between segments are stored in a hierarchical graph and ensure a consistent mesh at any time. So, we extend the concept of multi-triangulations from triangle meshes to tetrahedral meshes and show how hierarchical segments can be constructed easily for huge tetrahedral meshes.The segments are stored in a simple, but efficient compressed format which not only saves disc space but also allows for an easy calculation of the incidency information between segments at decompression time. A visualization system exploits the multitriangulation to increase the interactivity of direct volume rendering, isosurface extraction and vector field visualization such that large meshes can be explored on standard PCs.

Figure 1: The left figure shows how the mesh is adapted to the view point (red circle). The middle picture shows a close-up view of the model. The border faces of the tetrahedral mesh indicate the level of detail overlaid by our point based rendering technique. The middle-right picture shows the point based technique supported by silhouettes. The right picture shows a typical volume image created by projected tetrahedra. AbstractInteractive exploration of huge tetrahedral meshes is required by many applications but the limitations of the current hardware do not allow for the full dataset to be rendered at interactive frame rates. Multi resolution representations are an important tool to adapt the tetrahedral mesh complexity to the current viewing parameters in real time rendering environments.We present a meshing framework that builds a compact multi resolution representation for large tetrahedral meshes. A preprocessing step simplifies the mesh into a binary vertex hierarchy which is used at run time to adapt the mesh to viewing parameters. Exploiting the redundancy in the connectivity information of the mesh enables us to store the vertex hierarchy compactly such that a vertex split or edge collapse can be performed by knowing incremental updates only.We integrated this multiresolution representation into a volume rendering environment that supports direct volume rendering as well as a new point based rendering approach.

In this chapter we survey recent developments in the area of compression of static and dynamic 3D meshes. In an introductory section we give a definition of meshes and define terms and notations related to meshes. Furthermore, we give an overview to coding techniques in general and describe the principles of mesh compression algorithms at a very informative level. The following two sections give an overview on single rate and progressive coding techniques for static and dynamic meshes, explaining them in more detail pointing out the main ideas of each encoding approach. We conclude each section with a discussion providing an overall picture of developments in the mesh coding area, highlighting advantages and disadvantages of presented approaches, and pointing out directions for future research.The development of compression algorithms for static meshes was mainly forced by the community of 3D graphics hardware accelerators. The goal in mind was to reduce the amount of bytes that need to be transferred from the main memory to the graphics card. Based on the pioneering work of Michael Deering, a variety of algorithms have been proposed that work well for both triangle and polygonal meshes.But not only the hardware community benefits from compression techniques. Modern scanning devices are able to produce huge point clouds which are converted to even bigger triangle soups by surface reconstruction algorithms. A famous example is the Digital Michelangelo project of Stanford that contains scans of some of the most famous sculptures of Michelangelo. The biggest model consists of 386,488,573 polygons. The compression of such huge static meshes not only increases the rendering performance but also decreases

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