Compression and Streaming of Polygon Meshes by Martin Isenburg A dissertation submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Computer Science. Chapel Hill 2005 Approved by: Jack Snoeyink, Advisor Craig Gotsman, Reader Peter Lindstrom, Reader Dinesh Manocha, Committee Member Ming Lin, Committee Member ii iii ABSTRACT MARTIN ISENBURG: Compression and Streaming of Polygon Meshes (Under the direction of Jack Snoeyink) Polygon meshes provide a simple way to represent three-dimensional surfaces and are the de-facto standard for interactive visualization of geometric models. Storing large polygon meshes in standard indexed formats results in files of substantial size. Such formats allow listing vertices and polygons in any order so that not only the mesh is stored but also the particular ordering of its elements. Mesh compression rearranges vertices and polygons into an order that allows more compact coding of the incidence between vertices and predictive compression of their positions. Previous schemes were designed for triangle meshes and polygonal faces were triangulated prior to compression. I show that polygon models can be encoded more compactly by avoiding the initial triangulation step. I describe two compression schemes that achieve better compression by encoding meshes directly in their polygonal representation. I demonstrate that the same holds true for volume meshes by extending one scheme to hexahedral meshes. Nowadays scientists create polygonal meshes of incredible size. Ironically, com- pression schemes are not capable|at least not on common desktop PCs|to deal with giga-byte size meshes that need compression the most. I describe how to compress such meshes on a standard PC using an out-of-core approach. The compressed mesh allows streaming decompression with minimal memory requirements while providing seamless connectivity along the advancing decompression boundaries. I show that this type of mesh access allows the design of IO-efficient out-of-core mesh simplification algorithms. In contrast, the mesh access provided by today's indexed formats complicates sub- sequent processing because of their IO-inefficiency in de-referencing (in resolving all polygon to vertex references). These mesh formats were designed years ago and do not take into account that a mesh may not fit into main memory. When operating on large data sets that mostly reside on disk, the data access must be consistent with its layout. I extract the essence of our compressed format to design a general streaming format that provides concurrent access to coherently ordered elements while documenting their coherence. This eliminates the problem of IO-inefficient de-referencing. Furthermore, it allows to re-design mesh processing tasks to work as streaming, possibly pipelined, modules on large meshes, such as on-the-fly compression of simplified mesh output. iv v ACKNOWLEDGMENTS Five years have passed since I arrived in Chapel Hill and each one of them has been great. While I am super happy that my dissertation is now complete, I am also a little bit sad that my time here is coming to an end. Whenever asked why I had not yet defended my thesis, my supervisor would answer \Martin is just having too much fun." But he never mentioned that in fact he was to blame for that. After all, he was the one who made sure that those years were so much fun. So let me set the record straight. As a visiting student at UBC in 1996 I enrolled in the \Computational Geometry" class that was taught by then associate professor Jack Snoeyink. He excited all of us about the material and the final course project with Marie-Claude was my first \real research experience" with polygon meshes. Shortly afterward, Jack took me, academically speaking, under his wing. First, he helped me to get into the Masters program at UBC, then became my thesis advisor, and eventually brought me along to UNC, where he would ultimately guide me to complete my doctorate. Jack gave me the best guidance a student could hope for. He always had an open door when I needed advise but also let me do my thing when I was on a roll; yet he was immediately available when I ran into an unforeseen obstacle, wanted to share an exciting result, or simply needed reassurance that I was on the right track. He always encouraged me to pursue all opportunities, be it working for a summer in industry, spending time in other research labs, or attending academic meetings. He also knew to motivate me with the occasional conference trip to more \exotic" places. Jack always kept a good balance between hard work and good fun. There was time for a game of foosball, an ultimate match, or an evening in the brew pub. His support extended well beyond academic affairs. He helped me move from Vancouver to Chapel Hill, sent someone to the airport to pick me up, registered and drove me to the \unavoidable" GRE test in Greensboro, and much more. He also sprang into action to save our SIGGRAPH 2000 presentation virtually in the last minute with a high-speed cab ride back the hotel. Yes, I was having fun. Thank you for all this, Jack! vi There are two other people who directly contributed to the work presented here. Ste- fan Gumhold single-handedly implemented the Out-of-Core Mesh described in Chap- ter 7 and Peter Lindstrom wrote most of the streaming simplification algorithms de- scribed in Chapter 8 and the out-of-core mesh re-ordering tools from Chapter 9. I also want to thank Craig Gotsman who invited me to work for half a year with Stefan Gumhold at the Technion in Haifa in 2000. This cooperation was quite synergetic and resulted in a fun paper. I enjoyed many espressos that \Chaim" prepared for me in his office with his high-tech coffee maker. I also thank Pierre Alliez and Olivier Deviller who welcomed me to their group at INRIA Sophia-Antipolis and helped me in a thousand ways to get settled there. They are ultimately to blame that I now speak some basic French. I also thank Peter Lindstrom for being so excited about streaming and for inviting me to California for six month of enjoyable joint-work. Peter also did an excellent job in reviewing this manuscript and finding many little mistakes. Big thanks go to Anveesh, Miguel, and Adrian who lived for six month with my mattress in their hallway, to Michael North who stood with my name on a sign at RDU airport when I first arrived, to Zachi Karni who was a good friend during my time in Israel, to Ming for challenging me repeatedly with pointed questions during my defense, to Dinesh for not being too angry about me reading the \Daily Tar Heel" during his lectures, to Janet Jones for loaning me her antique furniture and for infinite patience despite my chronic slack with filing paperwork, to my co-workers at EAI, Intel, and Nvidia for making my work experiences in the \real-world" so enjoyable, to all the baristas around town that kept my research going with numerous free coffee refills, to my fellow students with whom I spent fun times in the department and in local coffee shops, bars, and parties around Chapel Hill and Carrboro, to Scott who has been a true friend and a great roommate in 20B Davie Circle for fun roadtrips and those \burned" week-old Driade pastries that kept me going under SIGGRAPH submission stress, to my childhood friends Marcus and Oliver for supplying me with hometown gossip, to all my fellow hikers on backpacking and hot spring trips in California and Oregon, to Henna who ironed the tie that made me look so distinguished during my defense talk, and to the five highly-educated scientists that it took to get it properly tied. And finally, big thanks go to my mom, my dad, and my sister for their everlasting love and support from far away. Sometimes weeks went by without a note from me during the crazy rush to meet some conference deadline. But they would always be there for me to relieve some of that stress, to share joyous moments of accomplishment, and to come for the occasional visit no matter where I happened to be. vii CONTENTS LIST OF FIGURES xi LIST OF TABLES xiii 1 Introduction 1 1.1 Compression . 3 1.2 Streaming . 5 1.3 Overview . 8 2 Mesh Compression 11 2.1 Preliminaries . 14 2.2 Arithmetic Coding . 14 2.3 Connectivity Compression . 15 2.4 Coding Planar Graphs . 17 2.5 Coding Triangle Mesh Connectivity . 20 2.6 Optimal Coding of Planar Triangulations . 25 2.7 Extensions to Polygonal Connectivity . 27 3 Edge-based Connectivity Coding 29 3.1 Encoding and Decoding . 30 3.2 Compression . 33 3.3 Quadrilateral Grids . 34 3.4 Coding Triangular and Quadrangular Meshes . 35 3.5 Coding Stripified Triangle Meshes . 36 3.5.1 Triangle Strips . 37 3.5.2 Encoding Connectivity and Stripification . 38 3.5.3 Encoding the Stripification separately . 42 3.6 Summary . 42 viii 3.7 Hindsights . 45 4 Degree-based Connectivity Coding 47 4.1 Coding with Vertex and Face Degrees . 48 4.2 Compressing with Duality Prediction . 50 4.2.1 Compressing Face Degrees . 52 4.2.2 Compressing Vertex Degrees . 53 4.2.3 Compressing Offsets and Indices . 53 4.3 Coding Non-Manifold Meshes . 53 4.4 Reducing the Number of Splits . 55 4.5 Counts and Invariants . 56 4.6 Results . 58 4.7 Splits and Split Offsets .