EUROGRAPHICS 2018/ T. Ritschel and A. Telea Tutorial Voxel DAGs and Multiresolution Hierarchies: From Large-Scale Scenes to Pre-computed Shadows Ulf Assarsson 1 , Markus Billeter 2 , Dan Dolonius 1 , Elmar Eisemann 2 Alberto Jaspe 3 , Leonardo Scandolo 2 , Erik Sintorn 1 1 Chalmers University of Technology, Sweden 2 Delft University of Technology, The Netherlands 3 CRS4 Visual Computing, Italy Abstract In this tutorial, we discuss voxel DAGs and multiresolution hierarchies, which are representations that can encode large volumes of data very efficiently. Despite a significant compression ration, an advantage of these structures is that their content can be efficiently accessed in real-time. This property enables various applications. We begin the tutorial by introducing the concepts of sparsity and of coherency in voxel structures, and explain how a directed acyclic graph (DAG) can be used to represent voxel geometry in a form that exploits both aspects, while remaining usable in its compressed from for e.g. ray casting. In this context, we also discuss extensions that cover the time domain or consider an advanced encoding strategies exploiting symmetries and entropy. We then move on to voxel attributes, such as colors, and explain how to integrate such information with the voxel DAGs. We will provide implementation details and present methods for efficiently constructing the DAGs and also cover how to efficiently access the data structures with e.g. GPU-based ray tracers. The course will be rounded of with a segment on applications. We highlight a few examples and show their results. Pre-computed shadows are a special application, which will be covered in detail. In this context, we also explain how some of previous ideas contribute to multi-resolution hierarchies, which gives an outlook on the potential generality of the presented solutions. CCS Concepts •Computing methodologies → Ray tracing; Visibility; Volumetric Models; Course Schedule Opening Elmar Eisemann 5m Introduction Ulf Assarsson & Elmar Eisemann 25m Advanced DAG Encodings Alberto Jaspe 20m Attribute Compression Dan Dolonius & Ulf Assarsson 30m DAG Construction Erik Sintorn 20m DAG Ray-tracing Markus Billeter 20m Applications/Demos (all) 10m Compressed Shadow Volumes Erik Sintorn 20m Compressed Shadow Maps Leonardo Scandolo 20m Conclusion and Q&A (all) 10m 1. Overview We begin the course by a brief welcome, introducing the schedule and briefly outlining the content and purpose of the course. The course consists of seven presentations, plus a short demo session where we highlight applications and results. Each presentation is further outlined in Section 2. Presentations are either 20 or 30 min- utes. Finally, we conclude the course with a brief Q&A. The table below lists the individual parts with their main speakers. The open- ing, break and conclusion are shown in italic. We expect that all participants of the Eurographics conference will be able to follow this course, as it will introduce all necessary concepts. 2. Outline The course consists of three parts; the first part introduces the meth- ods, the second details the implementations, while the third part re- volves around applications with a focus on precomputed shadows. 2.1. Introduction Voxel DAGs and Multiresolution Hierarchies We begin by in- troducing binary voxel grids as a representation for geometry and discuss two of the important properties: sparsity and coherency. On the GPU for large-scale volumes sparse voxel octrees (SVOs) have proven very useful to enable a sparse encoding [GMIG08, CNLE09, CNSE10, LK10]. SVOs achieve their compression by avoiding stor- ing information in empty space. Coherency can be exploited to fur- ther compress SVOs by finding similarities and compressing these. In practice, identical subtrees in an SVO are identified, and merged by pointing to a single common instance. This transforms the SVO c  2018 The Author(s) Eurographics Proceedings c  2018 The Eurographics Association. DOI: 10.2312/egt.20181028