The best one-volume introduction to point-based graphics ever, it addresses virtuallyevery aspect of computer graphics from a point-based perspective: acquisition, repre-sentation, modeling, animation, rendering–everything from the history of point-basedgraphics to the latest research results. A broad and deep book destined to be the standardreference for years to come, edited and written by leaders in the field.

Dr. Henry FuchsFederico Gil Professor, Department of Computer Science, University North Carolina,Chapel Hill

Point-based representations have recently come into prominence in computer graphicsacross a range of tasks, from rendering to geometric modeling and physical simulation.Point-based models are unburdened by connectivity information and allow dynamicallyadaptive sampling, according to the application needs. They are well-suited for modelingchallenging effects such as wide-area contacts, large deformations, or fractures. The lackof manifold connectivity and regularity among the samples, however, presents manynew challenges in point-based approaches and requires the development of new toolkitsto address them. This book, in a series of well-written chapters, covers all essentialaspects of using point-based representations in computer graphics, from the underlyingmathematics to data structures to GPU implementations—providing a state-of-the-artreview of the field.

Prof. Leonidas J. GuibasComputer Science Department, Stanford University

There is no simpler object than a zero dimensional point. Yet somehow, armed with mil-lions of such simple primitives, researchers have constructed complex 3D models thatwe can see and manipulate on the screen. Point-Based Graphics brings us the rich his-tory of work that has been done in this area of computer graphics. Editors Markus Grossand Hanspeter Pfister and their contributing authors present a complete set of all thedetailed work that has exploded over the past decade resulting in many of the imageswe see today. This book provides both the theoretical foundations as well as the practicalelements needed to build new applications with point-based graphics.

Michael F. CohenPrincipal Researcher, Microsoft Research

This book offers much more than what its title advertises. It provides not only anin-depth coverage of the new field of point-based graphics, but also a solid introductionto most modern techniques in computer graphics, from acquisition to rendering andanimation. Written by leading experts on the topic, chapters include the introduction

of fundamental tools as well as in-depth case studies of state-of-the-art algorithms.I learned a lot reading the book and I expect to use it often as a reference.

Fredo DurandAssociate Professor, Computer Science and Artificial Intelligence Laboratory, Mas-sachusetts Institute of Technology

Point-based graphics has seen a significant rebirth, which greatly changes the graphicsarena. This book, focusing on the major, recent advances in point-based graphics, pro-vides an excellent introduction and overview of the state of the art. It is particularlyimpressive for its breadth and depth, covering the foundations of the point primitive,modeling, processing, and rendering, as well as advanced topics, such as physics- basedanimation. Other distinctive features of the book are its world-renowned editors, MarkusGross and Hanspeter Pfister, and the high academic caliber of the contributors. Pro-fessionals and students alike will find the book intriguing and stimulating with soundand practical advice. It is a required reading for anyone who wants to keep pace withthe rapid progress in this re-emerging and important area of research.

Dr. Arie E. KaufmanDistinguished Professor & Chair, Computer Science Department, Stony BrookUniversity (SUNY), Stony Brook, NY

Point-Based Graphics

The Morgan Kaufmann Series in Computer Graphics

Point-Based GraphicsMarkus Gross and HanspeterPfister, Editors

Geometric Algebra for ComputerScience: An Object-orientedApproach to GeometryLeo Dorst, Daniel Fontijne, andStephen Mann

Visualization in MedicineBernhard Preim and Dirk Bartz

High Dynamic Range Imaging:Data Acquisition, Manipulation,and DisplayErik Reinhard, Greg Ward,Sumanta Pattanaik, and PaulDebevec

Complete Maya ProgrammingVolume II: An In-depth Guide to3D Fundamentals, Geometry, andModelingDavid A. D. Gould

MEL Scripting for MayaAnimators, Second EditionMark R. Wilkins and ChrisKazmier

Advanced Graphics ProgrammingUsing OpenGLTom McReynolds and DavidBlythe

Digital Geometry GeometricMethods for Digital PictureAnalysisReinhard Klette and AzrielRosenfeld

Digital Video and HDTVAlgorithms and InterfacesCharles Poynton

Real-Time Shader ProgrammingRon Fosner

Complete Maya Programming: AnExtensive Guide to MEL and theC++ APIDavid A. D. Gould

Texturing & Modeling: AProcedural Approach, ThirdEditionDavid S. Ebert, F. KentonMusgrave, Darwyn Peachey, KenPerlin, and Steven Worley

Geometric Tools for ComputerGraphicsPhilip Schneider and DavidH. Eberly

Understanding Virtual Reality:Interface, Application, and DesignWilliam B. Sherman and AlanR. Craig

Jim Blinn’s Corner: Notation,Notation, NotationJim Blinn

Level of Detail for 3D GraphicsDavid Luebke, Martin Reddy,Jonathan D. Cohen, AmitabhVarshney, Benjamin Watson, andRobert Huebner

Pyramid Algorithms: A DynamicProgramming Approach to Curvesand Surfaces for GeometricModelingRon Goldman

Non-Photorealistic ComputerGraphics: Modeling, Rendering,and AnimationThomas Strothotte and StefanSchlechtweg

Curves and Surfaces for CAGD:A Practical Guide, Fifth EditionGerald Farin

Subdivision Methods for GeometricDesign: A Constructive ApproachJoe Warren and Henrik Weimer

Computer Animation: Algorithmsand TechniquesRick Parent

The Computer Animator’sTechnical HandbookLynn Pocock and JudsonRosebush

Advanced RenderMan: CreatingCGI for Motion PicturesAnthony A. Apodaca and LarryGritz

Curves and Surfaces in GeometricModeling: Theory and AlgorithmsJean Gallier

Andrew Glassner’s Notebook:Recreational Computer GraphicsAndrew S. Glassner

Warping and Morphing ofGraphical ObjectsJonas Gomes, Lucia Darsa, BrunoCosta, and Luiz Velho

Jim Blinn’s Corner: Dirty PixelsJim Blinn

Rendering with Radiance: The Artand Science of LightingVisualizationGreg Ward Larson and RobShakespeare

Introduction to Implicit SurfacesEdited by Jules Bloomenthal

Jim Blinn’s Corner: A Trip Downthe Graphics PipelineJim Blinn

Interactive Curves and Surfaces:A Multimedia Tutorial on CAGDAlyn Rockwood and PeterChambers

Wavelets for Computer Graphics:Theory and ApplicationsEric J. Stollnitz, Tony D. DeRose,and David H. Salesin

Principles of Digital ImageSynthesisAndrew S. Glassner

Radiosity & Global IlluminationFrançois X. Sillion and ClaudePuech

Knotty: A B-Spline VisualizationProgramJonathan Yen

User Interface ManagementSystems: Models and AlgorithmsDan R. Olsen, Jr.

Making Them Move: Mechanics,Control, and Animation ofArticulated FiguresEdited by Norman I. Badler, BrianA. Barsky, and David Zeltzer

Geometric and Solid Modeling: AnIntroductionChristoph M. Hoffmann

An Introduction to Splines for Usein Computer Graphics andGeometric ModelingRichard H. Bartels, JohnC. Beatty, and Brian A. Barsky

Point-based GraphicsEdited by

MARKUS GROSS AND HANSPETER PFISTER

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About the Editors

DR. MARKUS GROSS

Dr. Gross is a professor of computer science, chair ofthe institute of computational science, and director ofthe Computer Graphics Laboratory of the Swiss FederalInstitute of Technology (ETH) in Zurich. His researchinterests include point-based graphics, physically-based modeling, multiresolution analysis, and virtualreality. He has published more than 130 scientificpapers on computer graphics and scientific visualiza-tion, and he authored the book “Visual Computing”,Springer, 1994. He holds various patents on core graphics

technologies. Gross has taught courses at major graphics conferences including ACMSIGGRAPH, IEEE Visualization, and Eurographics. He serves as a member of inter-national program committees of many graphics conferences and on the editorialboard of various scientific journals. Gross was a papers co-chair of the IEEE Visual-ization ’99, the Eurographics 2000, and the IEEE Visualization 2002 conferences. Hewas chair of the papers committee of ACM SIGGRAPH 2005. Gross received a Masterof Science in electrical and computer engineering and a PhD in computer graphicsand image analysis, both from the University of Saarbrucken, Germany. From 1990 to1994, Gross worked for the Computer Graphics Center in Darmstadt, where he estab-lished and directed the Visual Computing Group. He is a senior member of IEEE, amember of the IEEE Computer Society, a member of ACM and ACM Siggraph, anda member of the Eurographics Association. From 2002-2006 he was a member of theETH research commission. Gross serves in board positions of a number of interna-tional research institutes, societies and government organizations. He is chair of thetechnical advisory committee of Ageia Corporation. Gross co-founded Cyfex AG,Novodex AG, and LiberoVision AG.

viii

ABOUT THE EDITORS/CONTRIBUTORS ix

DR. HANSPETER PFISTER

Hanspeter Pfister is Associate Director and SeniorResearch Scientist at MERL—Mitsubishi ElectricResearch Laboratories—in Cambridge, MA. He is thechief architect of VolumePro, Mitsubishi Electric’s real-time volume rendering hardware for PCs. His researchinterests include computer graphics, scientific visualiza-tion, and graphics architectures. His work spans a rangeof topics, including point-based graphics, appearancemodeling and acquisition, computational photography,3D television, and face modeling. Hanspeter Pfisterreceived his Ph.D. in Computer Science in 1996 from theState University of New York at Stony Brook. He received

his M.S. in Electrical Engineering from the Swiss Federal Institute of Technology(ETH) Zurich, Switzerland, in 1991. Dr. Pfister has taught courses at major graph-ics conferences including SIGGRAPH, IEEE Visualization, and Eurographics. He hasbeen teaching introductory and advanced graphics ourses at the Harvard ExtensionSchool since 1999. He is Associate Editor of the IEEE Transactions on Visualizationand Computer Graphics (TVCG), chair of the IEEE Visualization and Graphics Tech-nical Committee (VGTC), and has served as a member of international programcommittees of major graphics conferences. Dr. Pfister was the general chair of theIEEE Visualization 2002 conference. He is senior member of the IEEE, and mem-ber of ACM, ACM SIGGRAPH, the IEEE Computer Society, and the EurographicsAssociation.

ABOUT THE CONTRIBUTORS

Adams, Bart Bart Adams received the M.Sc. Degree in Computer Engineering(magna cum laude) from the Katholieke Universiteit Leuven, Belgium in 2002. InOctober 2002 he joined the Computer Graphics Group of Prof. Philip Dutre andstarted a Ph.D. at the Computer Science Department of the Katholieke UniversiteitLeuven funded by the National Fund for Scientific Research, Belgium. His currentresearch focuses on the use of point-based surface representations and techniques forcomputer graphics applications and has lead to two publications so far at the annualACM SIGGRAPH conference. He has worked together with the Computer GraphicsLab at ETH Zurich on various projects and was a visiting scholar at Stanford Univer-sity in the summers of 2004 and 2005.

Adamson, Anders Anders Adamson is a research associate, teaching assistant andPhD student at the Department of Computer Science of the TU Darmstadt,

x ABOUT THE EDITORS/CONTRIBUTORS

Germany. He holds Dipl.-Informatiker (MSc) Degree in Computer Science. Hisresearch interests are the reconstruction and rendering of surfaces defined by points.

Alexa, Marc Marc Alexa is a Professor in the Faculty of Electrical Engineering andComputer Science at the Technical University of Berlin and heads the ComputerGraphics group. He is primarily interested in representing shapes and their deforma-tion, using point sampled geometry, implicit surfaces, explicit representations, andlinear spaces of base shapes. For his earlier work on morphing he received a PhD inComputer Science from Darmstadt University of Technology.

Amenta, Nina Nina Amenta is an Associate Professor of Computer Science at theUniversity of California at Davis. She got her PhD from the University of California atBerkeley, and was a post-doc at The Geometry Center at the University of Minnesota,and at Xerox Palo Alto Research Center (PARC), and an Assistant Professor at theUniversity of Texas at Austin. Professor Amenta studies computational geometry andcomputer graphics.

Barthe, Loıc Loıc Barthe is an assistant professor at the computer graphics depart-ment of IRIT/UPS Toulouse, France since September 2003. From September 2000to August 2003, he was a postdoctoral scholar first at IRIT/UPS Toulouse, then atCambridge University and finally at RWTH Aachen. Before, he received his PhD in2000 and hold a Master Degree in 1997. His is specially interested in shape represen-tation, interactive and intuitive modeling.

Botsch, Mario Mario Botsch is a post-doctoral research associate at the ComputerGraphics Laboratory of ETH Zurich, Switzerland. After he received his M.S. degreein mathematics in 1999 from the University of Erlangen-Nurnberg, Germany, heworked as research associate at the Max- Planck Institute for Computer Science inSaarbrucken, Germany, until 2000. He then joined the computer Graphics group atRWTH Aachen, Germany, as research associate and Ph.D. candidate in 2001, fromwhere he received his Ph.D. degree in Computer Science in July 2005.

Christensen, Per Per Christensen is a senior software developer in Pixar’sRenderMan group. His main research interest is efficient ray tracing and global illu-mination in very complex scenes. He received an M.Sc. degree in electrical engineer-ing from the Technical University of Denmark and a Ph.D. in computer science fromthe University of Washington.

Dachsbacher, Carsten Carsten Dachsbacher is a postdoctoral scholar at INRIA/Sophia-Antipolis, France (since May 2006). Before he has been at the ComputerGraphics Group of the University of Erlangen-Nuremberg, Germany. He received hisPh.D. degree (summa cum laude) in 2006 and his diploma (with honors) in com-puter science in 2002 from the University of Erlangen-Nuremberg, Germany. Hisresearch focuses on interactive, hardware-assisted computer graphics; in particular

ABOUT THE EDITORS/CONTRIBUTORS xi

he is working on interactive global illumination techniques, procedural models forrendering photo-realistic virtual terrains and point-based rendering.

Ertl, Thomas Thomas Ertl is a full professor of computer science at the Universityof Stuttgart, Germany and the head of the Visualization and Interactive Systems Insti-tute (VIS). He received a MS in computer science from the University of Colorado atBoulder and a PhD in theoretical astrophysics from the University of Tuebingen. Hisresearch interests include visualization, computer graphics, and human computerinteraction.

Guennebaud, Gael Gael Guennebaud is a postdoctoral scholar at the computergraphics department of IRIT/UPS Toulouse, France. He received his Ph.D. degreein 2005 and holds a Master Degree in 2002. His research interests include real-timerendering of complex scenes, point-cloud refinement and soft-shadow generation.

Kalaiah, Aravind Aravind Kalaiah received a Ph.D. from the University ofMaryland in 2005, a M.S. from Stony Brook University in 2000, and a B. Tech. degreefrom the Indian Institute of Technology, Bombay in 1998. His research interests arein point-based graphics, geometric modeling, and hardware accelerated rendering.Aravind is currently a Senior Engineer at Nvidia.

Keiser, Richard Richard Keiser is a research associate and PhD student at the com-puter science department of ETH Zurich, Switzerland. He holds a Masters Degreein Computer Science and specializes in physics based animations using particles anddeformable point-based surface modeling.

Klein, Thomas Thomas Klein received his MS in computer science from theUniversity of Stuttgart. He is a PhD Student at the Visualization and Interactive Sys-tems Group in Stuttgart. His research interests include volume rendering, hardware-accelerated graphics and point-based rendering.

Kobbelt, Leif P. Leif P. Kobbelt is a full professor of Computer Science and headof the Computer Graphics group at the RWTH Aachen University, Germany.His research interests include all areas of Computer Graphics and GeometryProcessing with a special focus on 3D model acquisition and optimization, high-quality shape editing, and the efficient handling of complex geometric models. Hepreviously worked at the Max-Planck Institute for Computer Science in Saarbrucken,Erlangen University, University of Wisconsin in Madison, and Karlsruhe University,where he got his Master and Ph.D. degrees.

Levoy, Marc Marc Levoy is a Professor of Computer Science and Electrical Engi-neering at Stanford University. He received degrees in Architecture from CornellUniversity in 1976 and 1978 and a PhD in Computer Science from the Universityof North Carolina in 1989. His research interests include computer-assisted car-toon animation, volume rendering (for which he won the SIGGRAPH Computer

xii ABOUT THE EDITORS/CONTRIBUTORS

Graphics Achievement Award in 1996), 3D scanning, light field sensing and display,computational imaging, and digital photography.

Matusik, Wojciech Wojciech is a research scientist at Mitsubishi Electric ResearchLabs. He received a B.S. in EECS from the University of California at Berkeley in 1997,M.S. in EECS from MIT in 2001, and Ph.D. in 2003. In 2004, he was named one of theworld’s top 100 young innovators by MIT’s Technology Review Magazine. Wojciech’sprimary research lies in computer graphics, data-driven modelling, computationalphotography, and new display technologies.

Muller-Fischer, Matthias Matthias Muller-Fischer received his Ph.D. on atomisticsimulation of dense polymer systems in 1999 from ETH Zurich and changed fieldsto macroscopic physically-based simulations during his post-doc 1999-2001 with theMIT Computer Graphics Group.

In 2002 he co-founded NovodeX, now a subsidiary of AGEIA Inc., the companydeveloping the world’s first Physics Processing Unit (PPU) for games. He currentlyworks for AGEIA as a principal software engineer responsible for the developmentof hardware accelerated simulation software for real-time effects such as fluids, clothand rigid body animation.

Pajarola, Renato Renato Pajarola received Dipl. Inf-Ing ETH and Dr. sc. techn.degrees in computer science from ETH Zurich in 1994 and 1998 respectively. Afterbeing a postdoctoral scholar at Georgia Tech for one year he was an Assistant Pro-fessor at University of California Irvine from 1999 to 2006 where he founded theComputer Graphics Lab. Since 2005 he has been a Professor in computer science atUniversity of Zurich where he leads the Visualization and MultiMedia Lab, and hisresearch interests include 3D graphics, multiresolution modeling, point based graph-ics, interactive scientific visualization, remote and parallel rendering.

Paulin, Mathias Mathias Paulin is an associate professor at the computer sciencedepartment of the universite Paul Sabatier, Toulouse, France since november 2004.He his a member of IRIT, a join institute between french CNRS, Universite PaulSabatier and National Polytechnical Institute of Toulouse. His habilitation, defendedin november 2004, was entittled “Rendering in computer graphics : from realismto real time”. His research interests include real time rendering of complex scenes,multi-model and multiresolution shape and appearance modeling and physics-basedlighting simulation.

Pauly, Mark Mark Pauly is an assistant professor at the computer science depart-ment of ETH Zurich, Switzerland, since April 2005. From August 2003 to March2005 he was a postdoctoral scholar at Stanford University, where he also held a posi-tion as visiting assistant professor during the summer of 2005. He received his Ph.D.degree (with highest distinction) in 2003 from ETH Zurich and his M.S. degree (with

ABOUT THE EDITORS/CONTRIBUTORS xiii

honors) in computer science in 1999 from the Technical University of Kaiserslautern,Germany. His research interests include geometry processing, multi-scale shapemodeling and analysis, physics-based animation, and computational geometry.

Peikert, Ronald Ronald Peikert is a senior researcher in the Institute of Computa-tional Science at ETH Zurich. He received his PhD in mathematics at ETH in 1985,and from 1988 to 1995 he was head of the scientific visualization group of the SwissCenter for Scientific Computing. His research interests include flow visualization,feature extraction techniques, and industrial applications of visualization.

Reina, Guido Guido Reina is a PhD Student at the Visualization and Interac-tive Systems Group in Stuttgart. He received his MS in computer science from theUniversity of Stuttgart. His research interests include molecular visualization,hardware-accelerated graphics, point-based rendering and volume rendering.

Rusinkiewicz, Szymon Szymon Rusinkiewicz is an assistant professor in the Com-puter Science Department at Princeton University. His work focuses on acquisitionand use of the reflectance and 3D shape of real-world surfaces, including the design ofscanning devices and data structures for efficient representation. He also investigatesalgorithms for processing of geometric and reflectance data, including registration,matching, completion, and sampling, as well as real-time rendering and perceptually-guided depiction.

Sadlo, Filip Filip Sadlo is a research associate and PhD student at the computer sci-ence department of ETH Zurich, Switzerland. He holds a masters degree in computerscience from ETH Zurich and his research topic is scientific visualization with focuson flow visualization.

Stamminger, Marc Marc Stamminger is a professor for computer graphics at theUniversity of Erlangen-Nuremberg, Germany, since 2002. After finishing his PhDthesis on finite element methods for global illumination in 1999, he was a PostDocat the MPI Informatik in Saarbrucken Germany, and at the INRIA Sophia-Antipolisin France. His current research interests are interactive computer graphics, globalillumination, and medical visualization.

Varshney, Amitabh Amitabh Varshney is a Professor of Computer Science at theUniversity of Maryland. He has served on several visualization and graphics confer-ence committees and journal editorial boards. Varshney received the NSF CAREERaward in 1995 and the IEEE Visualization Technical Achievement Award in 2004.Varshney received a B.Tech. in Computer Science from the Indian Institute of Tech-nology Delhi in 1989 and a M.S. and Ph.D. in Computer Science from the Universityof North Carolina at Chapel Hill in 1991 and 1994.

Wand, Michael Michael Wand is currently visiting assistant professor in the com-puter graphics laboratory at Stanford University. He has previously been member

xiv ABOUT THE EDITORS/CONTRIBUTORS

of the computer graphics group at University of Tubingen, Germany, from 2000 to2005 where he received a PhD in computer science in 2004. He has studied computerscience at University of Paderborn, Germany, where he received a Diploma in 2000.His current research interests include multi-resolution representations for complexgeometry and statistical data analysis techniques for geometry processing.

Weyrich, Tim Tim Weyrich received his Diploma degree in computer science fromthe University of Karlsruhe (TU), Germany in 2001. He is currently PhD student inthe Computer Graphics Laboratory of the Institute of Technology (ETH) in Zurich.His research interests are point-based graphics, 3D reconstruction, and appearancemodeling. He is member of ACM SIGGRAPH and GI.

Wicke, Martin Born in 1979, Martin Wicke studied Computer Science at theUniversity of Kaiserslautern, Germany. He currently works as a research associate andPh.D. Student at the Computer Graphics Laboratory at ETH Zurich, Switzerland. Hismain research interests are physics based modeling and animation.

Wurmlin, Stephan Dr. Stephan Wurmlin is currently a post-doctoral researcher inthe Computer Graphics Laboratory at ETH Zurich and head of the blue-c-II project.He received a PhD degree from ETH Zurich in 2004 on the design of the 3D videotechnology for the blue-c collaborative virtual reality system. His current researchinterests include 3D video, video-based rendering, point-based representations andrendering, virtual reality, and multimedia coding.

Wu, Jianhua Jianhua Wu is a research assistant and pursuing his Ph.D. Degree atComputer Graphics Group, RWTH Aachen University, Germany. He graduated in2002 with a Master Degree in computer science from Tsinghua University,Beijing, China. His research interests mainly focus on efficient surface representationsfor geometry processing and efficient geometric data structures for distributed andmobile multimedia communications.

Zwicker, Matthias Matthias Zwicker is an Assistant Professor with the Departmentof Computer Science and Engineering at the University of California, San Diego. Afterreceiving his Ph.D. from the Swiss Federal Institute of Technology Zurich in 2003,he was a Postdoctoral Associate with the Computer Graphics Group at the Mas-sachusetts Institute of Technology until 2005. His research interests include signalprocessing for computer graphics, geometry processing, and data-driven modelingand animation.

Contents

Foreword xxi

CHAPTER 1. INTRODUCTION 1Markus Gross and Hanspeter Pfister

1.1 Overview 1

1.2 Book Organization 3

1.3 Common Issues and Reoccurring Patterns 5

1.4 Acknowledgments 6

CHAPTER 2. THE EARLY HISTORY OF POINT-BASEDGRAPHICS 9

Marc Levoy

2.1 Sample-based Representations of Geometry 9

2.2 Image-order versus Object-order Visibility and Antialiasing 10

2.3 The Challenge Posed By Procedural Modeling 11

2.4 The Curious Case of Displacement Mapping 12

2.5 Points and Micropolygons to the Rescue 13

2.6 The Current Renaissance in Point Graphics 15

CHAPTER 3. ACQUISITION 19

3.1 Acquisition of Point-sampled Geometry 20

Szymon Rusinkiewicz3.1.1 Overview of the 3D Acquisition Pipeline 21

xv

xvi CONTENTS

3.1.2 Triangulation-based 3D Scanners 233.1.3 Other 3D Scanning Technologies 383.1.4 Scan Alignment 413.1.5 Conclusion 48

3.2 A Practical Low-cost Scanner for Geometry and Appearance 49

Filip Sadlo, Tim Weyrich, and Ronald Peikert3.2.1 Overview 493.2.2 System Overview 493.2.3 Calibration 51

3.2.4 Geometry Reconstruction 533.2.5 Texture Reconstruction 583.2.6 Results 633.2.7 Conclusion 66

3.3 Point-based 3D Photography 66

Wojciech Matusik and Hanspeter Pfister3.3.1 Overview 663.3.2 Previous Work 663.3.3 System Overview 683.3.4 Hardware Setup 693.3.5 Data Acquisition Process 703.3.6 Point-sampled Data Structure 773.3.7 Surface Light Fields 793.3.8 Relighting 823.3.9 Conclusion 93

CHAPTER 4. FOUNDATIONS AND REPRESENTATIONS 954.1 Surface Reconstruction 96

Nina Amenta4.1.1 Overview 964.1.2 Normal Estimation 974.1.3 Implicit Surface Methods 984.1.4 Voronoi Methods 1034.1.5 Surface Evolution Methods 1064.1.6 Conclusion 108

4.2 Moving Least Squares–based Surface Representations 109

Marc Alexa4.2.1 Overview 1094.2.2 Notation and Terms 1104.2.3 Interpolation and Approximation of Functional Data 1114.2.4 Normals 1184.2.5 Implicit Surfaces from Points and Offset Points 1194.2.6 Implict Surface from Points and Tangent Frames 1214.2.7 Conclusion 126

CONTENTS xvii

4.3 Sampling of Point Models 127

Jianhua Wu, Leif Kobbelt, and Mark Pauly4.3.1 Overview 1274.3.2 Decimation and Resampling Techniques 1284.3.3 Analysis and Comparison 1404.3.4 Multiresolution Representations 1434.3.5 Conclusion 147

4.4 Efficient Data Structures 148

Renato Pajarola4.4.1 Overview 1484.4.2 Spatial Data Organization 1494.4.3 Multiresolution and Level of Details 1564.4.4 Effective Representation 1564.4.5 Out-of-Core Representation 1614.4.6 Conclusion 165

4.5 Real-time Refinement 165

Gael Guennebaud, Loıc Barthe, and Mathias Paulin4.5.1 Overview 1654.5.2 One-ring Neighborhood Selection 1674.5.3 Refinement Algorithm 1724.5.4 Refinement of Sharp Features 1784.5.5 Implementation and Applications 1814.5.6 Conclusion 183

CHAPTER 5. DIGITAL PROCESSING 1875.1 Preprocessing and Filtering of Point Models 188

Tim Weyrich and Markus Gross5.1.1 Overview 1885.1.2 An Interactive Approach 1915.1.3 Underlying Techniques 1925.1.4 Outlier Removal 1955.1.5 Hole Filling and Smoothing 2005.1.6 Conclusion 206

5.2 3D Editing and Painting 207

Matthias Zwicker and Martin Wicke5.2.1 Overview 2075.2.2 Interaction Modes 2105.2.3 Surface Parameterization 2115.2.4 Resampling 2175.2.5 Surface Editing 2195.2.6 Painting with Virtual Brushes 2215.2.7 Conclusion 224

xviii CONTENTS

5.3 Shape Modeling 225

Mark Pauly and Leif Kobbelt5.3.1 Overview 2255.3.2 Boolean Operations 2265.3.3 Free-form Deformation 2345.3.4 Dynamic Sampling 2395.3.5 Conclusion 243

CHAPTER 6. RENDERING 2476.1 Splatting Fundamentals 248

Matthias Zwicker6.1.1 Overview 2486.1.2 Signal-processing Basics 2506.1.3 Frequency Analysis of Aliasing 2526.1.4 Resampling 2566.1.5 Gaussian Filters 2586.1.6 Surface Splatting 2616.1.7 Results and Comparison 2676.1.8 Conclusion 270

6.2 GPU Splatting 271

Mario Botsch and Leif Kobbelt6.2.1 Overview 2716.2.2 OpenGL and GPU Programming 2726.2.3 Splat Rasterization 2766.2.4 Splat Shading 2816.2.5 Antialiasing 2906.2.6 Comparison 2926.2.7 Conclusion 293

6.3 Ray Tracing of Point Models 294

Bart Adams and Anders Adamson6.3.1 Overview 2946.3.2 Ray-surface Intersection Algorithm 2956.3.3 Optimizations for Static and Deforming Point Clouds 3056.3.4 Implementation Tips 3096.3.5 Conclusion 312

6.4 Rendering of Very Large Models 313

Michale Wand6.4.1 Overview 3136.4.2 Point-based Multiresolution Rendering 3146.4.3 Rendering Costs, Quality, and Optimizations 3196.4.4 Example Implementation 3246.4.5 Conclusion 326

CONTENTS xix

6.5 Sequential Point Trees 327

Carsten Dachsbacher and Marc Stamminger6.5.1 Overview 3276.5.2 Sequentialization 3296.5.3 Rearrangement 3326.5.4 Better Error Measures 3346.5.5 Hybrid Point-polygon Rendering 3376.5.6 Implementation and Results 3386.5.7 Conclusion 339

CHAPTER 7. PHYSICS-BASED ANIMATION 341

7.1 Meshless Finite Elements 342

Matthias Muller-Fischer7.1.1 Overview 3427.1.2 Continuum Elasticity 3437.1.3 Meshless Discretization 3487.1.4 Moving Least Squares Interpolation 3507.1.5 Updating Strains and Stresses 3517.1.6 Computation of Forces Via Strain Energy 3517.1.7 Animation of Elastic Objects 3547.1.8 Plasticity 3557.1.9 Passive Surfel Advection 3577.1.10 Conclusion 357

7.2 Animation of Fracturing Material 358

Richard Keiser and Mark Pauly7.2.1 Overview 3587.2.2 Historical Background 3597.2.3 Modeling of Discontinuities 3617.2.4 Surface Model 3637.2.5 Crack Initiation and Propagation 3637.2.6 Topology Control 3657.2.7 Volumetric Sampling 3677.2.8 Fracture Control 3707.2.9 Simulation Pipeline 3727.2.10 Conclusion 372

7.3 Fluid Simulation 373

Martin Wicke, Richard Keiser, and Markus Gross7.3.1 Overview 3737.3.2 Simulation Methods 3737.3.3 Smoothed Particle Hydrodynamics 3757.3.4 Surface Representation 3817.3.5 Surface Tracking Using Point Samples 3837.3.6 Conclusion 386

xx CONTENTS

CHAPTER 8. SELECTED TOPICS 3898.1 Point-sampled 3D Video 390

Stephan Wurmlin and Markus Gross8.1.1 Motivation 3908.1.2 Dynamic Point Samples 3928.1.3 3D Video Recording 3928.1.4 Real-time 3D Video 3988.1.5 3D Video of Dynamic Scenes 4018.1.6 Conclusion 407

8.2 Statistical Representations 407

Amitabh Varshney and Aravind Kalaiah8.2.1 Motivation 4078.2.2 Related Work 4088.2.3 Statistical Point Geometry 4088.2.4 Statistical Rendering 4148.2.5 Conclusion 420

8.3 Visualization of Attributed 3D Point Datasets 420

Guido Reina, Thomas Klein, and Thomas Ertl8.3.1 Motivation 4208.3.2 A Framework for Point Glyph Visualization 4238.3.3 Visualization of Isotropic Particles 4258.3.4 Visualization of Anisotropic Particles on the GPU 4278.3.5 Visualization of Complex Glyphs on the GPU 4318.3.6 Conclusion 435

8.4 Point Clouds and Brick Maps for Movie Productions 435

Per H. Christensen8.4.1 Motivation 4358.4.2 Pixar’s RendermanTM 4368.4.3 Baking 3D Information as Point Clouds 4378.4.4 Subsurface Scattering 4438.4.5 Point-based Approximate Ambient Occlusion 4478.4.6 Point-based Approximate Global Illumination 4518.4.7 Photon Maps and Radiosity Point Clouds 4538.4.8 Brick Maps 4568.4.9 Single-bounce Global Illumination 4638.4.10 The Radiosity Atlas for Global Illumination 4658.4.11 Volume Data 4708.4.12 Conclusion 473

Bibliography 475

Index 515

About the CD-ROM 527

Foreword

In any established field, doing something “different” presents a challenge. Even incomputer graphics, an area that evolves rapidly, the notion of treating simple pointsas primitive modeling and display elements did not get off to a fast start. Nevertheless,every good idea has its time. Two timely factors that promote the idea of point-basedgraphics are procedural shape definition and automated shape acquisition. The for-mer has the flexibility to produce as many or as few points as needed to accuratelyrepresent itself. The latter naturally produces a massive flood of points. The sheercomplexity of such models begs for a representation that is inherently simple. Pointsare simple. However, effectively acquiring, editing, animating, rendering, and other-wise processing points requires a non-intuitive understanding of the representationsand processes. That’s why this book is necessary.

Twenty years ago, when my students were experimenting with point-based repre-sentations of surfaces and volumes, they repeatedly asked “what would happen if wetried this crazy idea?” As demonstrated in this text, today’s discussions are conductedwith more rigor and sophistication. While points themselves may be simple, a com-plete understanding of how they are processed and how collections of them should beinterpreted requires sophisticated explanations. And there is no single “best” methodfor processing such point collections. The explanations in this book are broad; theauthors cover a range of applications and techniques, and they cover these thoroughly.

The approaches described in this book may once have been considered outside themainstreambyexperiencedgraphicspractitioners.Theeditorsandcontributorsthem-selves, however, are among the best and brightest in mainstream computer graphicsresearch. To bring their expertise to bear on a single coherent volume is no small feat.

There are undoubtedly a few of us that enjoy ideas just because of their inherentbeauty. Having migrated to computer graphics from a background in signal process-ing, I have a certain attachment to point-based graphics methods. Because of thisinterest, I have tracked the work of many of the book’s contributors for several years.

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xxii FOREWORD

Their perseverance and ingenuity are an inspiration. Seeing their work collected inone place is a tremendous personal pleasure. More importantly for the reader, thistext is a unique and valuable resource for those who wish to understand and makeuse of point-based graphics technology.

Turner WhittedMicrosoft Research

Point-Based Graphics