Efficient algorithms for compressing geometric data have been widely developed in the recent years, but they are mainly designed for closed polyhedral surfaces which are manifold or "nearly manifold". We propose here a progressive geometry compression scheme which can handle manifold models as well as "triangle soups" and 3D tetrahedral meshes. The method is lossless when the decompression is complete which is extremely important in some domains such as medical or finite element. While most existing methods enumerate the vertices of the mesh in an order depending on the connectivity, we use a kd-tree technique [Devillers and Gandoin 2000] which does not depend on the connectivity. Then we compute a compatible sequence of meshes which can be encoded using edge expansion [Hoppe et al. 1993] and vertex split [Popović and Hoppe 1997].The main contributions of this paper are: the idea of using the kd-tree encoding of the geometry to drive the construction of a sequence of meshes, an improved coding of the edge expansion and vertex split since the vertices to split are implicitly defined, a prediction scheme which reduces the code for simplices incident to the split vertex, and a new generalization of the edge expansion operation to tetrahedral meshes.

Given a triangulation T of n points in the plane, we are interested in the minimal set of edges in T such that T can be reconstructed from this set (and the vertices of T) using constrained Delaunay triangulation. We show that this minimal set is precisely the set of non locally Delaunay edges, and that its cardinality is less than or equal to n + i/2 (if i is the number of interior points in T), which is a tight bound.

The preprocessing of large meshes to provide and optimize interactive visualization implies a complete reorganization that often introduces significant data growth. This is detrimental to storage and network transmission, but in the near future could also affect the efficiency of the visualization process itself, because of the increasing gap between computing times and external access times. In this article, we attempt to reconcile lossless compression and visualization by proposing a data structure that radically reduces the size of the object while supporting a fast interactive navigation based on a viewing distance criterion. In addition to this double capability, this method works out-of-core and can handle meshes containing several hundred million vertices. Furthermore, it presents the advantage of dealing with any n-dimensional simplicial complex, including triangle soups or volumetric meshes, and provides a significant rate-distortion improvement. The performance attained is near state-of-the-art in terms of the compression ratio as well as the visualization frame rates, offering a unique combination that can be useful in numerous applications.

The application needs in 3D visualization culminate today, in particular in the field of geographic information systems (GIS), as evidenced by the popularity of applications like Google Earth or Google Map. Meanwhile, the popular success of mobile devices like smartphones or tablets and the explosion of cloud computing directly related to ubiquitous networks accelerates the gradual shift from the traditional desktop application development to web and specialized mobile application development. But if the latest technologies centered around HTML5 facilitate the development of rich internet applications (RIA), the gap in resources between a desktop computer and a smartphone requires still an important conceptual and algorithmic work when one aims to design web applications offering a user experience similar to desktop applications. In this paper, we propose a method of terrain simplification suitable for data compression and streaming, and therefore ideal for the GIS visualization in a web browser. Based on new parallel algorithms, this method was designed to exploit the multi-core architectures of the latest CPU and GPU, within the constraints of the latest HTML5 API (WebGL, WebSockets, WebCL). It offers the main advantage of working on irregular grids, which allows to modelize highly nonuniform terrains (containing for instance roads and buildings) that may be unprojectable (plain 3D and not only 2.5D).