Washington University in St. Louis Washington University Open Scholarship All Theses and Dissertations (ETDs) Winter 12-1-2013 An Algorithm for Triangulating 3D Polygons Ming Zou Washington University in St. Louis Follow this and additional works at: https://openscholarship.wustl.edu/etd Part of the Computer Sciences Commons Recommended Citation Zou, Ming, "An Algorithm for Triangulating 3D Polygons" (2013). All Theses and Dissertations (ETDs). 1212. https://openscholarship.wustl.edu/etd/1212 This Thesis is brought to you for free and open access by Washington University Open Scholarship. It has been accepted for inclusion in All Theses and Dissertations (ETDs) by an authorized administrator of Washington University Open Scholarship. For more information, please contact
[email protected]. Washington University in St. Louis School of Engineering and Applied Science Department of Computer Science and Engineering Thesis Examination Committee: Tao Ju, Chair Robert Pless Yasutaka Furukawa AN ALGORITHM FOR TRIANGULATING 3D POLYGONS by Ming Zou A thesis presented to the School of Engineering and Applied Science of Washington University in partial fulfillment of the requirements for the degree of Master of Science December 2013 Saint Louis, Missouri copyright by Ming Zou 2013 Contents List of Tables ::::::::::::::::::::::::::::::::::::::: iv List of Figures :::::::::::::::::::::::::::::::::::::: v Acknowledgments :::::::::::::::::::::::::::::::::::: vii Abstract :::::::::::::::::::::::::::::::::::::::::: ix 1 Introduction :::::::::::::::::::::::::::::::::::::: 1 1.1 Background . .1 1.2 Contributions . .3 1.3 Related Work . .3 1.3.1 Triangulating a single polygon . .3 1.3.2 Triangulating multiple polygons . .4 2 Algorithm ::::::::::::::::::::::::::::::::::::::: 6 2.1 Single polygon . .6 2.2 Multiple polygons . .8 2.2.1 Domains . .9 2.2.2 Topologically correct triangulation . 10 2.2.3 Minimal sets .