Foundations of physically based modeling and animation

451 Pages·2017·13.794 MB·English

by  House, Donald, Keyser, John C

FOUNDATIONS OF PHYSICALLY BASED
MODELING AND ANIMATION
FOUNDATIONS OF PHYSICALLY BASED
MODELING AND ANIMATION
DONALD H. HOUSE
Clemson University
School of Computing
Clemson, South Carolina, U.S.A.
JOHN C. KEYSER
Texas A&M University
Department of Computer Science and Engineering
College Station, Texas, U.S.A.
The ball and blocks cover image is courtesy of Alex Beatty.
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Library of Congress Cataloging-in-Publication Data
Names: House, Donald, 1945- author. | Keyser, John C., 1972- author.
Title: Foundations of physically based modeling and animation / Donald H. House, and John C. Keyser.
Description: Boca Raton : Taylor & Francis, a CRC title, part of the Taylor & Francis imprint, a member
of the Taylor & Francis Group, the academic division of T&F Informa, plc, [2017]
Identifiers: LCCN 2016039625 | ISBN 9781482234602 (acid-free paper)
Subjects: LCSH: Computer animation. | Physics in art.
Classification: LCC TR897.7 .H68 2017 | DDC 777/.7--dc23
LC record available at https://lccn.loc.gov/2016039625
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In memory of my father
Henry Allen House
—Donald H. House
For my family
—John C. Keyser
Contents
List of Figures
List of Tables
Preface
SECTION I Foundations
CHAPTER 1 ■ Introduction
1.1 WHAT IS PHYSICALLY BASED ANIMATION?
1.2 DYNAMIC VERSUS DISCRETE EVENT SIMULATION
1.3 MATHEMATICAL NOTATION CONVENTIONS
1.4 TOOLKITS AND COMMERCIAL SOFTWARE
1.5 STRUCTURE OF THE BOOK
CHAPTER 2 ■ Simulation Foundations
2.1 MODELS AND SIMULATIONS
2.2 NEWTON’S LAWS OF MOTION
2.3 DROPPING A BALL IN 1D
2.4 DIFFERENTIAL EQUATIONS OF MOTION
2.5 A BASIC SIMULATION LOOP
2.6 NUMERICAL APPROXIMATION
2.7 3D MOTION IN AIR
2.7.1 Tracking Three Dimensions
2.7.2 Air Resistance
2.7.3 Wind
2.8 SUMMARY
CHAPTER 3 ■ Follow the Bouncing Ball
3.1 COLLISIONS WITH PLANES
3.1.1 Collision Detection
3.1.2 Collision Determination
3.1.3 Updating the Simulation Loop
3.2 COLLISION RESPONSE
3.2.1 Elasticity
3.2.2 Friction
3.2.3 Putting It All Together
3.3 IMPLEMENTING A BOUNCING BALL
3.3.1 Numerical Precision
3.3.2 Resting Conditions
3.4 POLYGONAL GEOMETRY
3.5 POINT-POLYGON COLLISION
3.6 A SPECIAL CASE: TRIANGLE INTERSECTION
3.7 SUMMARY
SECTION II Particle-Based Models
CHAPTER 4 ■ Particle Systems
4.1 WHAT IS A PARTICLE SYSTEM?
4.2 RANDOM NUMBERS, VECTORS, AND POINTS
4.3 PARTICLE GENERATORS
4.4 PARTICLE SIMULATION
4.4.1 Organization of the Computation
4.4.2 Deactivating Particles
4.4.3 Collisions
4.4.4 Geometry
4.4.5 Efficient Random Numbers
4.5 PARTICLE RENDERING
4.5.1 Points and Streaks
4.5.2 Sprites
4.5.3 Geometry
4.5.4 Volume Rendering
4.6 SUMMARY
CHAPTER 5 ■ Particle Choreography
5.1 ACCELERATION OPERATORS
5.1.1 Gravitational Attractors
5.1.2 Random Accelerations
5.1.3 Drag and Undrag
5.1.4 Velocity Limiters
5.2 VELOCITY OPERATORS
5.2.1 Affine Velocity Operators
5.2.2 Vortices
5.3 COLLISION AVOIDANCE
5.3.1 Potential Fields
5.3.2 Steering
5.4 SUMMARY
CHAPTER 6 ■ Interacting Particle Systems
6.1 STATE VECTORS
6.1.1 State Vectors for Single Particles
6.1.2 State Vectors for Interacting Particles
6.1.3 Implementation
6.2 EXPANDING THE CONCEPT OF STATE
6.3 SPATIAL DATA STRUCTURES
6.3.1 Uniform Spatial Grids
6.3.2 Octrees
6.3.3 kd-Trees
6.4 ASTRONOMICAL SIMULATION
6.4.1 Clustering
6.4.2 A Simple Algorithm Using a Uniform Grid
6.4.3 An Adaptive Algorithm Using an Octree
6.5 FLOCKING SYSTEMS
6.5.1 Core Algorithm
6.5.2 Distance and Field-of-View
6.5.3 Acceleration Prioritization
6.5.4 Steering around Obstacles
6.5.5 Turning and Banking
6.6 SUMMARY
CHAPTER 7 ■ Numerical Integration
7.1 SERIES EXPANSION AND INTEGRATION
7.2 VERLET AND LEAPFROG INTEGRATION
7.2.1 Basic Verlet Integration
7.2.2 Velocity Verlet Integration
7.2.3 Leapfrog Integration
7.3 RUNGE-KUTTA INTEGRATION
7.3.1 First- and Second-Order Runge-Kutta
7.3.2 Fourth-Order Runge-Kutta
7.4 IMPLEMENTATION OF HIGHER-ORDER INTEGRATORS
7.4.1 State Vector Algorithm
7.4.2 Collision Detection with Higher-Order Integrators
7.5 STABILITY AND ACCURACY OF THE INTEGRATORS
7.5.1 Exponential Decay and Sinusoidal Oscillation
7.5.2 Integration of Exponential Decay
7.5.3 Integration of Sinusoidal Oscillation
7.5.4 Performance of the RK Methods
7.5.5 Damping to Avoid Instability
7.6 ADAPTIVE TIMESTEPS
7.7 IMPLICIT INTEGRATION
7.7.1 Direct Solutions of Implicit Formulations
7.7.2 Jacobians and Linearizing Functions
7.7.3 Root-Finding Solutions of Implicit Formulations
7.7.4 Accuracy and Stability of Implicit Formulations
7.8 SUMMARY
CHAPTER 8 ■ Deformable Springy Meshes
8.1 DAMPED SPRINGY CONNECTORS
8.1.1 Mathematics of a Damped Spring
8.2 SPRINGY MESHES
8.2.1 Strut—A 3D Structural Element for a Springy Mesh
8.2.2 Building a Springy Mesh Using Struts
8.2.3 Air Resistance and Wind
8.2.4 Simulation of a Springy Mesh
8.2.5 Structural Rigidity
8.3 TORSIONAL SPRINGS
8.3.1 Torque
8.3.2 Computation of Torque from a Torsional Spring
8.3.3 Computation of the Vertex Forces from a Torsional Spring
8.3.4 Simulation of a Mesh with Torsional Springs
8.4 CHOOSING GOOD PARAMETERS
8.5 COLLISIONS
8.5.1 Types of Collisions
8.5.2 Determining Collisions
8.5.3 Collision Response for Springy Objects
8.6 LATTICE DEFORMERS
8.7 CLOTH MODELING
8.8 SUMMARY
SECTION III Rigid Bodies and Constrained Dynamics
CHAPTER 9 ■ Rigid Body Dynamics
9.1 RIGID BODY STATE
9.2 PROPERTIES OF RIGID BODIES
9.2.1 Center of Mass
9.2.2 Moment of Inertia
9.3 RIGID BODY MOTION
9.3.1 Torque
9.3.2 Updating Rigid Body State
9.3.3 Quaternion Representation
9.4 IMPLEMENTATION
9.5 SUMMARY
CHAPTER 10 ■ Rigid Body Collisions and Contacts
10.1 COLLISIONS OF RIGID BODIES
10.1.1 Frictionless Collision with a Static Object
10.1.2 Frictionless Collision of Two Moving Objects