1. Many of the figures from this book may be reproduced free of charge in scholarly articles, proceedings, and presentations, provided only that the following citation is clearly indicated: “Reproduced with the permission of the publisher from Computer Graphics: Principles and Practice, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley. Copyright 2014 by Pearson Education, Inc.” Reproduction for any use other than as stated above requires the written permission of Pearson Education, Inc. Reproduction of any figure that bears a copyright notice other than that of Pearson Education, Inc., requires the permission of that copyright holder.

2. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.1 An animation is a sequence of frames.

3. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.2 A series of key poses extracted from dense motion capture data [SYLH10] that have been visualized by rendering a virtual actor in those poses. (Courtesy of Moshe Mahler and Jessica K. Hodgins.)

4. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.3 Hundreds of complex shapes fall into a pile in this rigid-body simulation of Newtonian mechanics [WTF06]. This kind of simulation is leveraged extensively to present “what if?” scenarios for both entertainment and engineering applications. The primary challenges are efficiency and numerical stability. (Courtesy of Ron Fedkiw and Rachel Weinstein Petterson, © 2005 ACM, Inc. Reprinted by permission.)

5. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.4 Motion capture systems, such as the InsightVCS system pictured, record the three-dimensional motion of a real actor and then apply those motions to avatars in the virtual scene. (Courtesy of OptiTrack.)

6. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.5 Video tooning creates an animation from live-action footage [WXSC04]. This kind of algorithm is an important open-research topic and a great project, but it is not discussed further in this chapter. (Courtesy of Jue Wang and Michael Cohen. Drawn and performed by Lean Joesch-Cohen. © 2004 ACM, Inc. Reprinted by permission.)

7. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.6 Sample-and-hold interpolation of position over time of a point on a character’s hand.

8. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.7 Linear interpolation of position over time of a point on a character’s hand.

9. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.8 Piecewise-cubic interpolation of position over time of a point on a character’s hand using a spline.

10. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.9 One frame (bottom) and a superimposed detail of a sequence of frames (top) of animation depicting the flight of a cannonball as computed by procedural physics.

11. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.10 Selecting the key poses to navigate a character through these corridors is a problem at the interface between computer graphics and artificial intelligence (based on figure from [AVF04], which discusses AI-based methods for motion planning.).

12. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.11 Schematic of how interlacing is exploited to adapt 24 Hz film frames for 60 Hz interlaced broadcast to NTSC televisions under the 3:2 pulldown algorithm. In the center columns, the odd and even source film frames have been repeated three and two times, respectively. (Created by Eric Lee.)

13. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.12 Top row: a fence made of black posts on a white background imaged with increasing spatial resolution. Bottom row: a moving sphere imaged with increasing temporal resolution. Increasing the number of samples better captures the underlying scene, in space or time. Here a regular sampling pattern is used for each.

14. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.13 Undersampling in time with regular (a.k.a. uniform, statistically dependent) samples within each pixel (left) produces ghosting. Undersampling with stochastic (a.k.a. independent, random) samples produces noise (right) [AMMH07]. (Courtesy of Jacob Munkberg and Tomas Akenine-Möller)

15. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.14 The Dynamic Canvas algorithm [CTP + 03] produces background-paper detail at multiple scales that transform evocatively under 3D camera motion. (Courtesy of Joelle Thollot, “Dynamic Canvas for Non-Photorealistic Walkthroughs,” by Matthieu Cunzi, Joelle Thollot, Sylvain Paris, Gilles Debunne, Jean-Dominique Gascuel and Fredo Durand, Proceedings of Graphics Interface 2003.)

16. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.15 The view-dependent tufts on the trees, grass, and bushes are rendered with graftals that move coherently between adjacent frames of camera animation. (Courtesy of the Brown Graphics Group, © 2000 ACM, Inc. Reprinted by permission.)

17. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.16 An interpolated leg position between key poses found by one of the earliest inverse kinematics algorithms. (Courtesy of A.A. Maciejewski, © 1985 ACM, Inc. Reprinted by permission.)

18. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.17 Four images of animated characters autonomously performing complex tasks requiring motion planning. (Courtesy of the Graphics Lab at Carnegie Mellon University. © 2004 ACM, Inc. Reprinted by permission.)

19. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.18 Complex global flocking behaviors (top) emerge in Reynolds’s seminal “boids” animation system [Rey87] from simple, local rules for each virtual bird (bottom). (© 1987 ACM, Inc. Included here by permission.) (Courtesy of Craig Reynolds, © 1987 ACM, Inc. Reprinted by permission.)

20. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.19 A complex traversal requiring both pathfinding and general motion planning [SH07]. (Courtesy of Jessica Hodgins and Alla Safonova © 2007 ACM, Inc. Reprinted by permission.)

21. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.20 Forces due to gravity between two bodies.

22. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.21 Force of gravity on a small object near a planet.

23. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.22 Buoyancy on an object with volume v i submerged in a fluid with density ρ.

24. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.23 Spring force between two bodies.

25. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.24 The normal force prevents penetration. It is in the direction of the adjacent surface’s normal and has magnitude dependent on all other forces.

26. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.25 Kinetic friction has magnitude proportional to the normal force magnitude and direction opposite velocity (in the plane of the surface).

27. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.26 Drag forces are caused by friction between an object and the surrounding fluid, and by the pressure built up in the fluid by the object’s relative motion and friction within the fluid. Drag forces are hard to model accurately and efficiently because the fluid’s behavior is complex and highly dependent on the object’s shape at all scales.

28. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.27 Cannonball path in time-state space.

29. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.28 Visualization of D for the state space of one 1D particle under some arbitrary forces.

30. From Computer Graphics, Third Edition, by John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley (ISBN-13: 978-0-321-39952-6). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 35.29 A flow curve through a tangent field, and two attempts to follow it in discrete steps.