Leaflets are a common technology used in web services to provide high resolution maps by providing them in tiles of incremental resolutions. While for 2D display an unique level of resolution is all that is needed, within a 3D perspective display a combination of resolution levels needs to be identified. Block-Structured Adaptive Mesh Refinement (AMR) utilizes an organisation of data similar to Leaflets, but deals with 3D or 4D volumetric blocks of data. Such a data organisation is very suitable for hierarchical organisation of big data. In this article we propose using the AMR data organisation for hierarchical structuring of arbitrary geometric primitives, i.e. point clouds, sets of lines, triangle meshes, volumes. Such data organisation allows for generic and performant data access of out-of-core data on demand, as relevant for navigation through big data. Ultimately identification of data block visibility is crucial for a fluid interactive experience. We propose an algorithm based on Conformal 5D Geometric Algebra to approximate bounding boxes via spheres and the view frustum as a cone to arrive on a visibility criteria used for priority sorting of candidate blocks.

Geometric Algebra is considered as a very intuitive tool to deal with geometric problems and it appears to be increasingly efficient and useful to deal with computer graphics solutions. For example, the Conformal Geometric Algebra includes circles, spheres, planes and lines as algebraic objects, and intersections between these objects are also algebraic objects. More complex objects such as conics, quadric surfaces can also be expressed and be manipulated using an extension of the conformal Geometric Algebra. However due to high dimension of their representations in Geometric Algebra, implementations of Geometric Algebra that are currently available do not allow efficient realizations of these objects. This paper presents a Geometric Algebra implementation dedicated for both low and high dimensions. The proposed method is a hybrid solution for precomputed code with fast execution and runtime computations with low memory requirement. More specifically, the proposed method combines a precomputed table approach with a recursive method using binary trees. Some rules are defined to select the most appropriate choice, according to the dimension of the algebra and the type of multivectors involved in the product. The resulting implementation is well suited for high dimensional spaces (e.g. algebra of dimension 15) as well as for lower dimensional space. This paper details the integration of this hybrid method as a plug-in into Gaalop, which is a very advanced optimizing code generator. This paper also presents some benchmarks to show the performances of our method, especially in high dimensional spaces.

Cactus is an open source problem solving environment designed for scientists and engineers. Its modular structure facilitates parallel computation across different architectures and collaborative code development between different groups. The Cactus Code originated in the academic research community, where it has been developed and used over many years by a large international collaboration of physicists and computational scientists. We discuss how the intensive computing requirements of physics applications now using the Cactus Code encourage the use of distributed and metacomputing, describe the development and experiments which have already been performed with Cactus, and detail how its design makes it an ideal application test-bed for Grid computing.