Research on Generic Interactive Deformable 3D Models —Focus on the Human Inguinal Region— ; Research Thesis for Master in Computing
Total Page：16
File Type：pdf, Size：1020Kb
MASTER IN COMPUTING (VISUALIZATION,VIRTUAL REALITY, AND GRAPHIC INTERACTION) Research on Generic Interactive Deformable 3D Models —Focus on the Human Inguinal Region— ; Research Thesis for Master in Computing Thesis Student: Marc Musquera Moreno [[email protected]] Thesis Director: Antonio Sus´ınS´anchez(MA1-UPC) [[email protected]] Thesis Reader: Isabel Navazo Alvaro (LSI-UPC) [[email protected]] Spring 2008; v1:1 Acknowledgements ! You will never find time for anything. If you want the time, you must make it. - Charles Buxton First, I would like to thank my Thesis Director Dr. Antonio Susin for guiding me through this awesome research project in physically-based animation. Many thanks also to Prof. Isabel Navazo for her help, interest, collaboration as Thesis Reader, in addition of her support in burocratic tasks during this project. Also, I would like to thank the staff of the Master teachers, specially Profs. Carlos Andujar´ and Pere Pau Vazquez´ for their unvaluable help on voxelization and shader programming respectively, and my Master mates, Ricardo (I still remember we helping us each other with Mac peculiarities in front of PC), Quim and Jordi, for the good mo- ments and friendly environment during all the Master. My most sincere gratitude also to Laia, who has corrected from Toulouse, where she is achieving her PhD, the state of the art part in terms of making the text more comprehensive and easier to understand. Thanks also to Alba for doing the same with the introduction part. And, overcoat, my most sincere gratitude for my three most closer people, who have supported me and have helped me improving my life while they were adapting their own to mine: my dear parents Joan and Montse, of course —I don’t know what could I do without them—, and my particular jewel, Gemma, who has wanted to share with me these complex times, and have lived my good research moments as long as also sup- ported me in the bad ones all the time. The love from you three have been essential for the success of this project. I Table of Contents * AcknowledgementsI Table of Contents III List of Figures VII List of TablesXI List of Codes XIII PROJECT’S FIRST CONTACT 1 Project Abstract3 1.1 Overview...................................... 3 1.2 Focusing on the research thesis aims...................... 4 1.2.1 Interests and research fields....................... 4 1.2.2 Final result................................. 5 1.2.3 A non-interactive simulator....................... 5 2 Objectives and Research Contribution Overview7 2.1 Motivations and interests ............................ 7 2.1.1 Physically-based computing animation................ 7 2.1.1.1 Computer Animation typologies .............. 7 2.1.1.2 The 3D computer animation................. 8 2.1.1.3 Kinds of 3D computer animation. Focus on physically- based animation........................ 8 2.1.2 Human musculature studies ...................... 9 2.1.2.1 Introduction to Human Body Modeling and Animation. 9 2.1.2.2 Evolution of Human Animation............... 10 III IV Table of Contents 2.1.2.3 Main goal for this project................... 11 2.1.3 Surgery simulation............................ 12 2.1.3.1 Virtual surgery’s brief overview............... 12 2.1.3.2 This project’s approach and developed work . 12 2.2 Research fields and contributions........................ 13 2.2.1 Deformable models over static meshes................. 13 2.2.1.1 Objectives............................ 13 2.2.1.2 Methodology Overview.................... 13 2.2.2 Multiresolution meshes ......................... 14 2.2.2.1 Idea and motivation...................... 14 2.2.2.2 A little brief scheme about remeshing steps . 14 2.2.3 Surgery on a 3D object.......................... 15 2.2.3.1 A virtual scalpel for cutting ................. 15 2.2.3.2 Proposal for this project.................... 16 THE STATE OF THE ART 3 Volumetric Model from a Polygonal Mesh 19 3.1 Polygonal Meshes................................. 19 3.1.1 Introduction to Polygonal Meshes. The Triangle Meshes . 19 3.1.2 The Face-Vertex Mesh Format...................... 20 3.2 Mesh Voxelization................................. 20 3.2.1 The volumetric models. The voxelization process.......... 20 3.2.1.1 Introduction to the voxel space ............... 20 3.2.1.2 The 3D discrete topology................... 21 3.2.2 The Problem: Triangle VS Voxel..................... 22 3.2.2.1 Introduction .......................... 22 3.2.2.2 The test’s simplest case: gigantic meshes in low-grid vox- elmaps ............................. 22 3.2.2.3 Test’s generic case: voxelization of any mesh at any LOD. Alternative techniques .................... 24 3.3 The search tree structures applied to voxelization............... 28 3.3.1 Reasons for using trees.......................... 28 3.3.2 The most common Search Trees Structures .............. 28 3.3.2.1 Binary Space Partition Tree —BSP-Tree—.......... 29 3.3.2.2 Kd-Tree............................. 29 3.3.2.3 Quadtree (2D) and Octree (3D)................ 30 4 Polygonal Mesh Reconstruction: Multiresolution Meshes 31 4.1 Introduction to Multiresolution Meshes.................... 31 4.1.1 The need of a multiresolution mesh capability............ 31 Research on Generic Interactive Deformable 3D Models Table of Contents V 4.1.2 The IsoSurfaces.............................. 32 4.2 VoxelMap Refilling. The Model Carving.................... 32 4.2.1 Space Carving............................... 33 4.2.2 Voxel Carving............................... 33 4.3 IsoSurface Extraction Algorithms........................ 34 4.3.1 IsoSurface extraction as multiresolution mesh construction . 34 4.3.2 Marching Cubes ............................. 34 4.3.2.1 Overview............................ 34 4.3.2.2 Advantages and disadvantages............... 36 4.3.2.3 The isosurface-voxel intersection case LUT. Shortcomings 36 4.3.3 Marching Tetrahedron.......................... 37 4.3.3.1 Overview and shortcomings................. 37 4.3.3.2 The Marching Tetrahedra LUT . 38 5 3D Object Model Animation/Deformation 41 5.1 Point-Oriented Deformation........................... 41 5.1.1 The Point-Sampled Geometry...................... 41 5.1.2 Point-sampled deformation....................... 42 5.2 Geometric Deformation ............................. 43 5.2.1 Global or local deformation operators................. 43 5.2.1.1 Reminder: the jacobian matrix JF of a function F . 43 5.2.1.2 Method Overview....................... 44 5.2.1.3 Global and local operators.................. 44 5.2.1.4 Examples of global operator deformations......... 44 5.2.2 Free Form Deformation —FFD—.................... 47 5.2.2.1 Introduction to FFD ...................... 47 5.2.2.2 Methodology details ..................... 48 5.2.2.3 Grid of Control Points..................... 48 5.2.2.4 Capabilities and limitations ................. 49 5.2.3 Interactive Axial Deformations —AXDF— .............. 49 5.2.3.1 Method Overview....................... 49 5.2.3.2 Algorithm Details....................... 50 5.2.3.3 Advantages and lacks of AXDF . 51 5.2.4 Deformation by Wires.......................... 51 5.2.4.1 Introduction and wire definition............... 51 5.2.4.2 Algorithm overview...................... 52 6 Physically-Based Deformations 53 6.1 Introduction to deformation based on physics ................ 53 6.1.1 Overview of time stepping deformation algorithms......... 53 6.1.1.1 Accuracy VS speed performance............... 53 6.1.2 A simple particle P as the deformation system............ 54 6.1.2.1 State Vector and Vector Field of a simple particle . 54 Master Thesis in Computer Graphics by Marc Musquera Moreno VI Table of Contents 6.1.2.2 The time step ∆t. The numerical integrator concept. The Euler numerical integrator.................. 54 6.1.2.3 The integration system scheme ............... 55 6.1.2.4 The most used ODE integrators ............... 55 6.1.2.5 Accuracy and stability of numerical integrators . 56 6.1.2.6 Movement restrictions .................... 58 6.2 Dynamic Deformable Model Systems ..................... 59 6.2.1 Introduction to deformable systems.................. 59 6.2.1.1 Definition of Particle System................. 59 6.2.1.2 The deformable models as dependent-particle system. The continuum elasticity...................... 60 6.2.2 Points of View of a Physical Simulation. Solver Typologies . 61 6.3 Physical Simulation based on Lagrangian POV descriptions......... 62 6.3.1 Mesh Based Methods........................... 62 6.3.1.1 Finite Element Method —FEM—............... 62 6.3.1.2 Finite Differences Method .................. 64 6.3.1.3 Boundary Element Method.................. 64 6.3.1.4 Mass-Spring Systems..................... 65 6.3.2 Mesh Free Methods............................ 68 6.3.2.1 What are Mesh Free Methods ................ 68 6.3.2.2 Smoothed Particle Hydrodynamics —SPH— . 68 6.3.2.3 Meshless Deformations based on Shape matching . 69 6.3.3 The Hybrid Approaches......................... 69 6.3.3.1 Overview of the hybrid simulation approaches . 69 6.3.3.2 Pump it Up........................... 69 6.3.3.3 Mass-Spring with Volume Conservation.......... 70 6.4 Physical Simulation based on Eulerian POV descriptions .......... 71 6.4.1 Overview ................................. 71 6.4.2 Fluid Simulation ............................. 71 6.4.2.1 The Navier-Stokes equations for fluids........... 71 6.4.2.2 The yielding idea of display and computation . 72 6.4.2.3 A small summary of variants and proposals . 72 7 Topological Changes on Polygonal Meshes