Front Cover -- Computer Animation: Algorithms and Techniques -- Copyright -- Dedication -- Contents -- Preface -- Overview -- Organization of the Book -- Acknowledgments -- References -- About the Author -- Chapter 1: Introduction -- 1.1. Motion perception -- 1.2. The heritage of animation -- 1.2.1. Early devices -- 1.2.2. The early days of ``conventional ́́animation -- 1.2.3. Disney -- 1.2.4. Contributions of others -- 1.2.5. Other media for animation -- 1.3. Animation production -- 1.3.1. Principles of animation -- Simulating physics -- Designing aesthetically pleasing actions -- Effectively presenting action -- Production technique -- 1.3.2. Principles of filmmaking -- Three-point lighting -- 180 rule -- Rule of thirds -- Types of shots -- Tilt -- Framing -- Focus the viewer's attention -- 1.3.3. Sound -- 1.4. Computer animation production -- 1.4.1. Computer animation production tasks -- 1.4.2. Digital editing -- In the old days -- Digital on-line nonlinear editing -- 1.4.3. Digital video -- 1.4.4. Digital audio -- Digital musical device control -- Digital audio sampling -- 1.5. A brief history of computer animation -- 1.5.1. Early activity (pre-1980) -- 1.5.2. The middle years (the 1980s) -- 1.5.3. Animation comes of age (the mid-1980s and beyond) -- 1.6. Summary -- References -- Chapter 2: Technical Background -- 2.1. Spaces and transformations -- 2.1.1. The display pipeline -- 2.1.2. Homogeneous coordinates and the transformation matrix -- 2.1.3. Concatenating transformations: multiplying transformation matrices -- 2.1.4. Basic transformations -- 2.1.5. Representing an arbitrary orientation -- Fixed-angle representation -- 2.1.6. Extracting transformations from a matrix -- 2.1.7. Description of transformations in the display pipeline -- Object space to world space transformation -- World space to eye space transformation.

Perspective matrix multiply -- Perspective divide -- Image to screen space mapping -- 2.1.8. Error considerations -- Accumulated round-off error -- Orthonormalization -- Considerations of scale -- 2.2. Orientation representation -- 2.2.1. Fixed-angle representation -- 2.2.2. Euler angle representation -- 2.2.3. Angle and axis representation -- 2.2.4. Quaternion representation -- Basic quaternion math -- Representing rotations using quaternions -- Rotating vectors using quaternions -- 2.2.5. Exponential map representation -- 2.3. Summary -- References -- Chapter 3: Interpolating Values -- 3.1. Interpolation -- 3.1.1. The appropriate function -- Interpolation versus approximation -- Complexity -- Continuity -- Global versus local control -- 3.1.2. Summary -- 3.2. Controlling the motion of a point along a curve -- 3.2.1. Computing arc length -- The analytic approach to computing arc length -- Estimating arc length by forward differencing -- Adaptive approach -- Estimating the arc length integral numerically -- Adaptive Gaussian integration -- Find a point that is a given distance along a curve -- 3.2.2. Speed control -- 3.2.3. Ease-in/ease-out -- Sine interpolation -- Using sinusoidal pieces for acceleration and deceleration -- Single cubic polynomial ease-in/ease-out -- Constant acceleration: parabolic ease-in/ease-out -- 3.2.4. General distance-time functions -- 3.2.5. Curve fitting to position-time pairs -- 3.3. Interpolation of orientations -- 3.3.1. Interpolating quaternions -- 3.4. Working with paths -- 3.4.1. Path following -- 3.4.2. Orientation along a path -- Use of the Frenet frame -- Camera path following -- 3.4.3. Smoothing a path -- Smoothing with linear interpolation of adjacent values -- Smoothing with cubic interpolation of adjacent values -- Smoothing with convolution kernels -- Smoothing by B-spline approximation.

3.4.4. Determining a path along a surface -- 3.4.5. Path finding -- 3.5. Chapter summary -- References -- Chapter 4: Interpolation-Based Animation -- 4.1. Key-frame systems -- 4.2. Animation languages -- 4.2.1. Artist-oriented animation languages -- 4.2.2. Full-featured programming languages for animation -- 4.2.3. Articulation variables -- 4.2.4. Graphical languages -- 4.2.5. Actor-based animation languages -- 4.3. Deforming objects -- 4.3.1. Picking and pulling -- 4.3.2. Deforming an embedding space -- Two-dimensional grid deformation -- Polyline deformation -- Global deformation -- FFD -- Composite FFDs-sequential and hierarchical -- Animated FFDs -- Deformation tools -- Moving the tool -- Moving the object -- Animating the FFD control points -- 4.4. Three-dimensional shape interpolation -- 4.4.1. Matching topology -- 4.4.2. Star-shaped polyhedra -- 4.4.3. Axial slices -- 4.4.4. Map to sphere -- 4.4.5. Recursive subdivision -- 4.5. Morphing (two-dimensional) -- 4.5.1. Coordinate grid approach -- 4.5.2. Feature-based morphing -- 4.6. Chapter summary -- References -- Chapter 5: Kinematic Linkages -- 5.1. Hierarchical modeling -- 5.1.1. Data structure for hierarchical modeling -- A simple example -- 5.1.2. Local coordinate frames -- 5.2. Forward kinematics -- 5.3. Inverse kinematics -- 5.3.1. Solving a simple system by analysis -- 5.3.2. The Jacobian -- A simple example -- 5.3.3. Numeric solutions to IK -- Solution using the inverse Jacobian -- Adding more control -- Alternative Jacobian -- Avoiding the inverse: using the transpose of the Jacobian -- Procedurally determining the angles: cyclic coordinate descent -- 5.3.4. Summary -- 5.4. Chapter summary -- References -- Chapter 6: Motion Capture -- 6.1. Motion capture technologies -- 6.2. Processing the images -- 6.3. Camera calibration -- 6.4. Three-dimensional position reconstruction.

6.4.1. Multiple markers -- 6.4.2. Multiple cameras -- 6.5. Fitting to the skeleton -- 6.6. Output from motion capture systems -- 6.7. Manipulating motion capture data -- 6.7.1. Processing the signals -- 6.7.2. Retargeting the motion -- 6.7.3. Combining motions -- 6.8. Chapter summary -- References -- Chapter 7: Physically Based Animation -- 7.1. Basic physics-a review -- 7.1.1. Spring-damper pair -- 7.2. Spring animation examples -- 7.2.1. Flexible objects -- Mass-spring-damper modeling of flexible objects -- A simple example -- 7.2.2. Virtual springs -- 7.3. Particle systems -- 7.3.1. Particle generation -- 7.3.2. Particle attributes -- 7.3.3. Particle termination -- 7.3.4. Particle animation -- 7.3.5. Particle rendering -- 7.3.6. Particle system representation -- Updating particle system status -- 7.3.7. Forces on particles -- 7.3.8. Particle life span -- 7.4. Rigid body simulation -- 7.4.1. Bodies in free fall -- A simple example -- A note about numeric approximation -- Equations of motion for a rigid body -- Orientation and rotational movement -- Center of mass -- Forces -- Momentum -- Inertia tensor -- The equations -- 7.4.2. Bodies in collision -- Colliding bodies -- Particle-plane collision and kinematic response -- The penalty method -- Testing polyhedra -- Impulse force of collision -- Computing impulse forces -- Friction -- Resting contact -- 7.4.3. Dynamics of linked hierarchies -- Constrained dynamics -- The Featherstone equations -- 7.5. Cloth -- 7.5.1. Direct modeling of folds -- 7.5.2. Physically based modeling -- 7.6. Enforcing soft and hard constraints -- 7.6.1. Energy minimization -- Three useful functions -- Useful constraints -- Point-to-fixed-point -- Point-to-point -- Point-to-point locally abutting -- Floating attachment -- Floating attachment locally abutting -- Energy constraints are not hard constraints.

7.6.2. Space-time constraints -- Space-time particle -- Numerical solution -- 7.7. Chapter summary -- References -- Chapter 8: Fluids -- 8.1. Specific fluid models -- 8.1.1. Models of water -- Still waters and small-amplitude waves -- The anatomy of waves -- Modeling ocean waves -- Finding its way downhill -- Summary -- 8.1.2. Modeling and animating clouds -- Anatomy of clouds and cloud formation -- Cloud models in CG -- 8.1.3. Modeling and animating fire -- Procedurally generated image -- Particle system approach -- Other approaches -- 8.1.4. Summary -- 8.2. Computational fluid dynamics -- 8.2.1. General approaches to modeling fluids -- Grid-based method -- Particle-based method -- Hybrid method -- 8.2.2. CFD equations -- Conservation of mass -- Conservation of momentum -- 8.2.3. Grid-based approach -- Stable fluids -- Density update -- The velocity update -- The simulation -- 8.2.4. Particle-based approaches including smoothed particle hydrodynamics -- 8.3. Chapter summary -- References -- Chapter 9: Modeling and Animating Human Figures -- 9.1. Overview of virtual human representation -- 9.1.1. Representing body geometry -- Polygonal representations -- Patch representations -- Other representations -- 9.1.2. Geometry data acquisition -- 9.1.3. Geometry deformation -- 9.1.4. Surface detail -- 9.1.5. Layered approach to human figure modeling -- Rigging -- 9.2. Reaching and grasping -- 9.2.1. Modeling the arm -- 9.2.2. The shoulder joint -- 9.2.3. The hand -- 9.2.4. Coordinated movement -- 9.2.5. Reaching around obstacles -- 9.2.6. Strength -- 9.3. Walking -- 9.3.1. The mechanics of locomotion -- Walk cycle -- Run cycle -- Pelvic transport -- Pelvic rotation -- Pelvic list -- Knee flexion -- Ankle and toe joints -- 9.3.2. The kinematics of the walk -- 9.3.3. Using dynamics to help produce realistic motion -- 9.3.4. Forward dynamic control.

9.3.5. Summary.