AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO F ^ k.^

Transcription

1 Computer a jap Animation Algorithms and Techniques Second Edition Rick Parent Ohio State University AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO F ^ k.^ Morgan Kaufmann is an imprint ofelsevier MORGAN KAUFMANN PUBLISHERS

2 Preface xix Chapter 1 Introductioh Perception The Heritage of Animation Early Devices The Early Days of "Conventional" Animation Disney Contributions of Others Other Media for Animation Principles of Animation Principles of Filmmaking Animation Production Sound Computer Animation Production Computer Animation Production Tasks Digital Editing Digital Video Digital Audio 25 IX

3 1.5 A Brief History of Computer Animation Early Activity (pre 1980) The Middle Years (The'80s) Animation Comes ofage (The mid-80's and beyond) Chapter Summary 35 References 35 Chapter 2 Technical Background Spaces and Transformations The Display Pipeline Homogeneous Coordinates and the Transformation Matrix Compound Transformation: Concatenating Transformation Matrices Basic Transformations Representing an Arbitrary Orientation Extracting Transformations from a Matrix Description of Transformations in the Display Pipeline Error Considerations Orientation Representation Fixed Angle Representation Euler Angle Representation Angle and Axis Representation Quaternion Representation Exponential Map Representation Chapter Summary 70 References 70 Chapter 3 Interpolating Values Interpolation The Appropriate Function Summary Controlling the Motion of a Point Along a Curve Computing Are Length Speed Control Ease-in/Ease-out 97

4 XI General Distance-Time Functions Curve Fitting to Position-Time Pairs Interpolation oforientations Interpolating Quaternions Working with Paths Path Following Orientation along a Path Smoothing a Path Determining a Path along a Surface Path Finding Summary Chapter Summary 129 References 129 Chapter 4 Interpolation-Based Animation Key-Frame Systems Animation Languages Artist-Oriented Animation Languages Füll Featured Programming Languages for Animation Articulation Variables Graphical Languages Actor-Based Animation Languages Deforming Objects Picking and Pulling Deforming an Embedding Space Three-dimensional Shape Interpolation Matching Topology Star-Shaped Polyhedra Axial Slices Map to Sphere Recursive Subdivision Summary Morphing (Two-dimensional) Coordinate Grid Approach Feature-Based Morphing Chapter Summary 183 References 183

5 Chapter5 Kinematic Linkages Hierarchical Modeling Data Structure for Hierarchical Modeling Local Coordinate Frames Forward Kinematics Inverse Kinematics Solving a Simple System by Analysis Thejacobian Numeric Solutions to Inverse Kinematics Summary Chapter Summary 215 References 215 Chapter 6 Motion Capture Motion Capture Technologies Processing the Images Camera Calibration Three-Dimensional Position Reconstruction Multiple Markers Multiple Cameras Fitting to the Skeleton Output from Motion Capture Systems Manipulating Motion Capture Data Processing the Signals Retargeting the Motion Combining Motions Chapter Summary 230 References 231 Chapter 7 Physically Based Animation Basic Physics A Review Simulating a Spring-mass-damper System 237

6 Xlll 7.2 Spring Meshes Flexible Objects Virtual Springs Particle Systems Particle Generation Particle Attributes Particle Termination Particle Animation Particle Rendering Particle System Representation Forces on Particles Particle Life Span Rigid Body Simulation Bodies in Free Fall Bodies in Collision Dynamics of Linked Hierarchies ÄÄ Summary Enforcing Soft and Hard Constraints Energy Minimization Space-Time Constraints Chapter Summary 283 References 283 Chapter 8 Fluids: Liquids & Gases Specific Fluid Models Models of Water Models of Clouds (by David Ebert) Models offire Summary Computational Fluid Dynamics General Approaches to Modeling Fluids CFD Equations Chapter Summary 321 References 322 Chapter 9 Modeling and Animating Human Figures Overview of Virtual Human Representation Representing Body Geometry 327

7 xiv Geometry Data Acquisition Geometry Deformation Surface Detail Layered Approach to Human Figure Modeling Reaching and Grasping Modeling the Arm The Shoulder Joint The Hand Coordinated Movement Reaching Around Obstacles Strength Walking The Mechanics of Locomotion The Kinematics of the Walk Using Dynamics to Help Produce Realistic Motion Forward Dynamic Control Summary Getting Dressed Up Cloth and Clothing Simple Draping Getting into Clothes Hair Chapter Summary 363 References 363 Chapter 10 Facial Animation The Human Face Anatomie Structure The Facial Action Coding System Facial Models Creating a Continuous Surface Model Textures Animating the Face Parameterized Models Blend Shapes 382

8 xv Muscle Models Expressions Summary Lip-Sync Animation Articulators of Speech Phonemes Coarticulation Prosody Chapter Summary 389 References 390 Chapter 11 Modeling Behavior Knowing the Environment Vision Memory Aggregate Behavior Primitive Behaviors Flocking Behavior Prey-Predator Behavior Modeling Intelligent Behavior Autonomous Behavior Expressions and Gestures Modeling Individuality: Personality and Emotions Crowd Management Emergent Behavior Statistically Modeled Behavior Internal structure Chapter Summary 417 References 417 Chapter 12 Special Models for Animation Implicit Surfaces Basic Implicit Surface Formulation Animation Using Implicitly Defined Objects Collision Detection 425

9 Deforming the Implicit Surface as a Result of Collision Level Set Methods Summary Plants A Little Bit of Botany L-Systems Animating Plant Growth Summary Subdivision Surfaces Chapter Summary 442 References 443 Appendix A Rendering Issues 445 A. 1 Double Buffering 446 A.2 Compositing 446 A.2.1 Compositing without Pixel Depth Information 449 A.2.2 Compositing with Pixel Depth Information 455 A.3 Displaying Moving Objects: Motion Blur 458 A.4 Drop Shadows 461 A.5 Billboarding and Impostors 466 A.6 Summary 467 References 468 Appendix B Background Information and Techniques 469 B.l Vectors and Matrices 469 B. 1.1 Inverse Matrix and Solving Linear Systems 471 B.1.2 Singular Value Decomposition 479 B.2 Geometrie Computations 480 B.2.1 Components of a Vector 480 B.2.2 Lengthofa Vector 481 B.2.3 Dot Product oftwo Vectors 481 B.2.4 Cross Product of Two Vectors 482 B.2.5 Vector and Matrix Routines 484

10 B.2.6 Closest Point between Two Lines in Three- Space 487 B.2.7 Area Calculations 488 B.2.8 The Cosine Rule 490 B.2.9 Barycentric Coordinates 490 B.2.10 Computing Bounding Shapes 491 Transformations 507 B.3.1 Transforming a Point Using Vector-Matrix Multiplication 507 B.3.2 Transforming a Vector Using Vector-Matrix Multiplication 507 B.3.3 Axis-Angle Rotations 508 B.3.4 Quaternions 509 Denevit and Hartenberg Representation for Linked Appendages 513 B.4.1 Denavit-Hartenberg Notation 513 B.4.2 A Simple Example 515 B.4.3 Including a Ball-and-Socket Joint 517 B.4.4 Constructing the Frame Description 518 Interpolating and Approximating Curves 519 B.5.1 Equations: Some Basic Terms 519 B.5.2 Simple Linear Interpolation: Geometrie and Algebraic Forms 521 B.5.3 Parameterization by Are Length 522 B.5.4 Computing Derivatives 523 B.5.5 Hermite Interpolation 523 B.5.6 Catmull-Rom Spline 524 B.5.7 Four-Point Form 528 B.5.8 Blended Parabolas 528 B.5.9 Bezier Interpolation/Approximation 530 B.5.10 De Casteljau Construction of Bezier Curves 531 B.5.11 Tension, Continuity, and Bias Control 531 B.5.12 B-Splines 534 B.5.13 Fitting Curves to a Given Set of Points 535 Randomness 537 B.6.1 Noise 537 B.6.2 Turbulence 540 B.6.3 Random Number Generator 540

11 B.7 Physics Primer 542 B.7.1 Position, Velocity, and Acceleration 542 B.7.2 Circular Motion 543 B.7.3 Newtons Laws of Motion 544 B.7.4 Inertia and Inertial Reference Frames 545 B.7.5 Center of Mass 545 B.7.6 Torque 545 B.7.7 Equilibrium: Balancing Forces 546 B.7.8 Gravity 546 B.7.9 Centripetal Force 547 B.7.10 Contact Forces 547 B.7.11 Centrifugal Force 549 B.7.12 Work and Potential Energy 550 B.7.13 Kinetic Energy 550 B.7.14 Conservation of Energy 550 B.7.15 Conservation ofmomentum 551 B.7.16 Oscillatory Motion 551 B.7.17 Damping 552 B.7.18 Angular Momentum 552 B.7.19 Inertia Tensors 553 B.8 Numerical Integration Techniques 554 B.8.1 Function Integration for Are Length Computation 554 B.8.2 Updating Function Values 556 B.8.3 Updating Position 560 B.9 Standards for Moving Pictures 561 B.9.1 In the Beginning, There Was Analog 561 B.9.2 In the Digital World 565 B.10 Camera Calibration 570 References 575 Index 577