Optimizing Refined Geometric Primitive's Leaflet Visibility for Interactive 3D Visualization via Geometric Algebra
Werner Benger, Dietmar Hildenbrand, Wolfgang Dobler · 2018
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.