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Virtual Prototyping with Surface Reconstruction and Freeform Geometric Modeling Using Level-Set Method

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Virtual Prototyping with Surface Reconstruction and Freeform Geometric Modeling Using Level-Set Method Scholars' Mine Doctoral Dissertations Student Theses and Dissertations Fall 2008 Virtual prototyping with surface reconstruction and freeform geometric modeling using level-set method Weihan Zhang Follow this and additional works at: https://scholarsmine.mst.edu/doctoral_dissertations Part of the Mechanical Engineering Commons Department: Mechanical and Aerospace Engineering Recommended Citation Zhang, Weihan, "Virtual prototyping with surface reconstruction and freeform geometric modeling using level-set method" (2008). Doctoral Dissertations. 1984. https://scholarsmine.mst.edu/doctoral_dissertations/1984 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. VIRTUAL PROTOTYPING WITH SURFACE RECONSTRUCTION AND FREEFORM GEOMETRIC MODELING USING LEVEL-SET METHOD by WEIHAN ZHANG A DISSERTATION Presented to the Faculty ofthe Graduate School of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING 2008 Approved by Ming C. Leu, Advisor Frank W. Liou Michael G. Hilgers Robert G. Landers Robert B. Stone 111 PUBLICATION DISSERTATION This dissertation includes the following four articles: Pages 50-72 have been published in ASME JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING, 2007, 7(3), pp. 203-210. Pages 73-106 have been accepted for publication in ASME JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Pages 107-119 have been accepted for publication in CIRP ANNUALS­ MANUFACTURING TECHNOLOGY. Pages 120-142 are prepared for submission to the INTERNATIONAL JOURNAL OF COMPUTER AIDED-DESIGN. IV ABSTRACT More and more products with complex geometries are being designed and manufactured by computer aided design (CAD) and rapid prototyping (RP) technologies. Freeform surface is a geometrical feature widely used in modern products like car bodies, airfoils and turbine blades as well as in aesthetic artifacts. How to efficiently design and generate digital prototypes with freeform surfaces is an important issue in CAD. This paper presents the development of a Virtual Sculpting system and addresses the issues of surface reconstruction from dexel data structures and freeform geometric modeling using the level-set method from distance field structure. Our virtual sculpting method is based on the metaphor of carving a solid block into a 3D freeform object using a 3D haptic input device integrated with the computer visualization. This dissertation presents the result of this study and consists primarily of four papers. The first paper presents the development of a novel contour generation algorithm for the purpose of visualizing the sculpted dexel models and interfacing with other CAD/CAM/CAE systems. To improve the sampling quality of the dexel model used in the virtual sculpting system, the second paper develops a triple-dexel structure and a novel surface reconstruction method from triple-dexel data. The developed surface reconstruction method is faster than the voxel­ based method, and the reconstructed surface model is more accurate than surface reconstructed from voxel representation using the marching cube algorithm. To enhance the modeling capability of the virtual sculpting system, additional free form modeling operations including deformation, smoothing and imprint are developed using the user's gesture inputs based on the level-set method. The developed operations generate a water­ tight mesh model effective for freeform geometric modeling. v ACKNOWLEDGMENTS I would like to express my sincere respect and gratitude to my research advisor, Professor Ming C. Leu, for his guidance and support through my academic study and research. During the research work for this dissertation, Dr. Leu shared his knowledge in many areas, provided inspiration and was ready to help whenever I needed his advice. I am fortunate to have such a kind, knowledgeable and passionate advisor in my academic life. My thanks also go to Professors Frank W. Liou, Michael G. Hilgers, Robert G. Landers, Robert B. Stone and Shun Takai for their valuable suggestions as members of my dissertation committee. I am also grateful to all the people from the Virtual Reality and Rapid Prototyping Laboratory, whom I had the pleasure to work with. I thank my colleagues, especially, Xiaobo Peng, for his input to my work, for the collaborating in the Virtual Sculpting Project. I thank my parents for their understanding, confidence, and encouragement while I am concentrating in my research work. Finally, I would like to thank my girlfriend, Chengchun Tsai, for her endless love and support, limitless patience, and for her efforts and endurance for my study. VI TABLE OF CONTENTS Page PUBLICATION DISSERTATION OPTION ................................................................... iii ABSTRACT ....................................................................................................................... iv ACKNOWLEDGMENTS ................................................................................................... v LIST OF ILLUSTRATIONS ............................................................................................ xii LIST OF TABLES ............................................................................................................. xv SECTION 1. INTRODUCTION ...................................................................................................... 1 1.1. MOTIVATION .................................................................................................... 1 1.2. RESEARCH OBJECTIVE AND ISSUES .......................................................... 3 1.3. RELATED WORK .............................................................................................. 4 1.3 .1. Virtual Prototyping Techniques ............................................................... .4 1.3.2. Geometric Representations ....................................................................... 7 1.3.2.1 Single-dexel model ....................................................................... 7 1.3.2.2 Triple-dexel model ....................................................................... 9 1.3.2.3 Voxel model ............................................................................... 11 1.3.2.4 Implicit model. ............................................................................ 11 1.3.2.5 Distance field model ................................................................... 11 1.3.2.6 Implicit surface and volumetric modeling techniques ................ 13 1.3.3. Surface Reconstruction for Virtual Prototyping ..................................... 18 1.3.3.1 Surface reconstruction from dexel model.. ................................. 19 1.3.3.2 Surface reconstruction from planar contours .............................. 20 1.3.3.3 Surface reconstruction from volumetric models ........................ 22 2. RESEARCH TASKS AND MAIN RESULTS ....................................................... 23 2.1. SURFACE RECONSTRUCTION FROM DEXEL DATA .............................. 23 2.1.1. Contour Reconstruction from Dexel Model.. .......................................... 23 2.1.2. Surface Reconstruct from Planar Contours ............................................. 26 2.1.3. Surface Reconstruction from Triple-Dexel Model ................................. 26 2.1.4. Contour Combination .............................................................................. 28 Vll 2.1.5. Surface Reconstruction from Three Orthogonal Slices of Contours ...... 29 2.1.6. Computational Complexity Analysis ...................................................... 30 2.1.7. Surface Error Analysis ............................................................................ 30 2.1.8. System Integration .................................................................................. 32 2.2. STUDY OF DISTANCE FIELD BASED FREEFORM MODELING ............ 32 2.2.1. Generation ofDistance Field Model from Triple-Dexel Model ............. 32 2.2.2. Hand Gesture Modeling .......................................................................... 34 2.2.3. Shape Modeling Using Level-Set Method .............................................. 35 2.2.4. Deformation Operation ........................................................................... 37 2.2.5. Smoothing Operation .............................................................................. 37 2.2.6. Performance Evaluation .......................................................................... 38 3. MAJOR RESEARCH CONTRIBUTIONS .............................................................. 39 3.1. SURFACE RECONSTRUCTION FROM DEXEL MODELS ........................ 39 3.2. DISTANCE FIELD GENERATION FROM TRIPLE-DEXEL MODEL ........ 40 3.3. LEVEL-SET METHOD BASED FREE FORM OPERATIONS ..................... .40 BIBLIOGRAPHY ......................................................................................................... 42 PAPER I. A NOVEL CONTOUR GENERATION ALGORITHM FOR SURFACE RECONSTRUCTION FROM DEXEL DATA ............................................... 50 ABSTRACT ...................................................................................................... 50 1. INTRODUCTION .......................................................................................
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