Modeling, Evaluation, Editing, and Illumination of Three Dimensional Mazes and Caves for Computer Games DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Matthew J. Boggus Graduate Program in Computer Science and Engineering The Ohio State University 2012 Dissertation Committee: Roger Crawfis, Advisor Han-Wei Shen Richard Parent Copyright by Matthew J. Boggus 2012 Abstract Caves are commonly used as environments in computer games. As the popularity of open world games rises, so does the demand for expansive virtual environments. To ease this cost, many tools have been developed to create and edit content for games including terrain, plants, roads, buildings, and cities. The same is not true for caves. We present data structures and algorithms to create, evaluate, edit, and illuminate three dimensional models of caves for use in computer games. Game levels can be classified according to their spatial configuration: linear, maze, or open. Caves formed by the same geological process have similar features. These define parameters that can be used to partially or fully automate the creation of cave models of different spatial configurations. Additional information about the model such as its volume, number of branching paths, and number of connected components can be used by the designer in evaluating and editing the model to meet gameplay requirements. To assist in editing of cave models we propose a new data structure and framework and compare its use to existing modeling approaches. Physically based illumination of a cave typically results in low level lighting which is not suitable for games. We introduce a new illumination model based on radiant flux that can be used to ensure a sufficient amount of light is present throughout the cave. The new illumination model can also be adapted to assist in player navigation. Illuminating a scene according to distance to objects within it creates ii highlights that captures the player’s visual attention. A user study was done to evaluate the new technique. iii To Meg and my parents for their love and support. iv Acknowledgments This document could not have been completed without assistance from many individuals, and I am grateful for their help. First and foremost I would like to thank my advisor, Roger Crawfis, for his time and advice. I would also like to thank E. Scott Bair for providing domain knowledge in Geology. More generally, I am very grateful for the opportunity to work with the knowledgeable faculty, collaborative graduate students, and supportive staff in the Department of Computer Science and Engineering at The Ohio State University. I would also like to thank the Department of Computer Science and Engineering and The Computer Graphics Group at Ohio State for financial support in publishing this work. v Vita 2006................................................................B.A. Computer Science and Mathematics, Hiram College 2007................................................................University Fellow, The Ohio State University 2008-2011 ......................................................Graduate Teaching Associate, Department of Computer Science and Engineering, The Ohio State University 2012................................................................Visiting Instructor, Department of Computer Science, Oberlin College and Conservatory Publications Boggus, M. and Crawfis, R. 2010. Distance Field Illumination: a Rendering Method to Aid in Navigation of Virtual Environments, In Proceedings of the 6th International Symposium on Visual Communication, 501-510. Boggus, M. and Crawfis, R. 2010. Prismfields: A Framework for Interactive Modeling of Three Dimensional Caves, In Proceedings of the 6th International Symposium on Visual Communication, 213-221. Boggus, M. and Crawfis, R. 2010. Distance based illumination as a navigational aid. In Proceedings of the 2010 ACM SIGGRAPH Symposium on interactive 3D Graphics and Games (I3D '10). ACM, New York, NY, 1-1. Boggus, M. and Crawfis, R. 2009. Explicit Generation of 3D Models of Solution Caves for Virtual Environments, In Proceedings of the 2009 International Conference on Computer Graphics and Virtual Reality, Las Vegas, NV, 85-90. vi Boggus, M. and Crawfis, R. 2009. Procedural Creation of 3D Solution Cave Models, In Proceedings of the 20th IASTED International Conference on Modelling and Simulation, Banff, Alberta, 180-186. Fields of Study Major Field: Computer Science and Engineering vii Table of Contents Abstract ............................................................................................................................... ii Dedication .......................................................................................................................... iv Acknowledgments............................................................................................................... v Vita ..................................................................................................................................... vi List of Tables .................................................................................................................... xii List of Figures .................................................................................................................. xiii Chapter 1: Introduction ....................................................................................................... 1 Chapter 2: Related Works ................................................................................................... 9 2.1: Fun and Games ......................................................................................................... 9 2.2: Video Game Level Design ..................................................................................... 10 2.3: Speleology – the Study of Caves ........................................................................... 17 2.3.1: Solution Caves ................................................................................................. 19 2.3.2: Solution Cave Passages ................................................................................... 22 2.3.3: Solution Cave Patterns .................................................................................... 25 2.4: Cave Mapping and Modeling ................................................................................. 28 2.5: Terrain Modeling and Rendering ........................................................................... 32 viii 2.5.1: Heightfields ..................................................................................................... 32 2.5.2: Volume Elements ............................................................................................ 34 2.5.3: Run-length Encoded Terrain ........................................................................... 34 2.6: Illumination Models ............................................................................................... 37 2.7: Perception and Navigation in a Virtual Cave ......................................................... 40 Chapter 3: Linear and Branching Maze Cave Levels ....................................................... 43 3.1: Curve and Surface Modeling ................................................................................. 43 3.2: Single Passage Cave Modeling for Linear Levels ................................................. 46 3.2.1: Phreatic Passages ............................................................................................. 46 3.2.2: Vadose Passages .............................................................................................. 48 3.2.3: Combination Passages ..................................................................................... 51 3.2.4: Varying Passages ............................................................................................. 52 3.3: Cave Passage Modeling for Branching Maze Levels ............................................ 56 Chapter 4: Island Maze and Open Cave Levels ................................................................ 60 4.1: Terrain Modeling ................................................................................................... 60 4.2: Cave Model Construction Using Cave Patterns ..................................................... 70 4.3: Level Visualization and Evaluation ....................................................................... 80 4.3.1: Model Visualization ........................................................................................ 82 4.3.2: Level Analysis ................................................................................................. 86 ix Chapter 5: Modeling and Editing of Non-Planar 3D Caves ............................................. 94 5.1: Prismfield Framework ............................................................................................ 94 5.1.1: Prismfield Data Structure ................................................................................ 94 5.1.2: Prismfield Vertical Drilling ............................................................................. 97 5.1.3: Prismfield Horizontal Drilling ......................................................................... 99 5.1.4: Prismfield Framework Rendering ................................................................. 101 5.2: Implementation and Performance Results ..........................................................