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 6.1 Very high-level overview of WPF’s 3D geometry pipeline.

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 6.1 Overhead view of pyramid.

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 6.3 WPF’s 3D right-handed coordinate system situated in a desert scene.

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 6.4 Tabular representation of the geometric specification of a single-triangle mesh.

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 6.5 Identification of the front side of a mesh triangle via counterclockwise ordering of vertices.

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 6.6 First triangle’s front side rendered using a uniformly yellow material.

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 6.7 First triangle’s back side, invisible due to lack of specification of a material for the back side.

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 6.8 First triangle’s back side, rendered using a uniformly red material.

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 6.9 Tabular representation of geometric specification of a two-triangle mesh.

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 6.10 Renderings of the partial pyramid in two distinct orientations, in an environment containing only ambient light.

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 6.11 Rays emanating from a point light source in the scene, striking points on a planar surface at an infinite variety of angles.

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 6.12 Rays emanating from a directional light source, infinitely distant from the planar surface, striking the surface’s points at identical angles.

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 6.13 Our desert scene’s coordinate system with annotation showing the direction of the rays emanating from the directional light source.

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 6.14 The angle θ, defined as the angle between the incoming light direction ray ℓ and the surface normal n.

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 6.15 Brightness computed by Lambert’s cosine law for three values of θ.

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 6.16 Rendering of the pyramid with directional lighting, with θ close to 90° for the right-most visible face.

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 6.17 Rendering of the pyramid with directional lighting, with θ approximately 70° for the rightmost visible face.

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 6.18 Flat-shaded rendering of a dolphin mesh model, with three triangles highlighted to demonstrate the concept of the key vertex.

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 6.19 Flat-shaded rendering of a cone with 16 sides.

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 6.20 Flat-shaded rendering of a cone with 64 sides, reducing (but not eliminating) the obvious faceting.

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 6.21 Flat-shaded rendering of the classic “Utah” teapot model.

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 6.22 Gouraud-shaded rendering of the same teapot model.

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 6.23 Comparison of flat shading and Gouraud shading, two different techniques for determining intensity values between the vertices at which lighting calculations were performed.

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 6.24 Calculating a vertex normal in 2D, as an average of the normals of the two adjacent line segments.

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 6.25 Calculating a vertex normal in 3D, as an average of the surface normals of all triangles sharing the vertex.

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 6.26 Tabular representation of geometric specification of a two-triangle mesh with reuse of shared vertices (the apex and the shared base vertex).

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 6.27 Assignment of indices to the vertices in our pyramid model.

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 6.28 Gouraud shaded pyramid, produced in WPF by specifying that the two triangles share vertices V 0 and V 2, causing their vertex normals to be the average of the surface normals of the two triangles.

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 6.29 Square 64 × 64 image of a tan-hued pattern to simulate a sandy desert floor.

31. 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 6.30 Floating-point texture coordinate system applied to the sand-pattern image, with the origin located at the upper-left corner.

32. 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 6.31 Mapping world-coordinate vertices on the two-triangle model of the desert floor to corresponding texture coordinates.

33. 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 6.32 Sand texture overstretched to cover the entire desert floor.

34. 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 6.33 Square image of a brick pattern.

35. 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 6.34 Result of stretching one copy of the brick texture onto each wall.

36. 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 6.35 Result of tiling multiple copies of the brick texture onto each wall.

37. 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 6.36 Image of a sky image.

38. 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 6.37 Renderings of a teapot, showing the contribution of each of the three components generated by the Phong lighting equation: (a) ambient, (b) diffuse, (c) specular, and (d) result generated by summing the contributions.

39. 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 6.38 Phong’s original technique for computing specular reflection, depicted in a context in which the camera position is very close to the reflection ray.

40. 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 6.39 Phong’s original technique for computing specular reflection, depicted in a context in which the camera position is not close to the reflection ray. The significant difference in the value of cos δ makes an even greater difference when it’s raised to a large power, so the specular term is nearly zero for this view.

41. 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 6.40 WPF’s rendering of the camel constructed via hierarchical modeling, with joints for legs and neck animation.

42. 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 6.41 Scene graph of the camel-leg model. Here, and below, we use a beige background to highlight a portion of the graph that is being used as a component or submodel.

43. 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 6.42 Rendering of the foot model, at its canonical position at the origin.

44. 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 6.43 Rendering of the shin model, at its canonical position at the origin.

45. 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 6.44 Rendering of a first draft of a lower-leg model, constructed by composing the two subcomponents without moving them from their canonical positions at the origin of the coordinate system.

46. 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 6.45 Rendering of the lower-leg model, now corrected via application of a modeling transformation on the shin subcomponent.

47. 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 6.46 Rendering of the lower-leg model from a second point of view.

48. 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 6.47 Rendering of the complete leg model.

49. 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 6.48 Result of specifying a 37º rotation at the knee joint, annotated with a red line through the joint, parallel to the x-axis, showing the axis of rotation.

50. 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 6.49 Scene graph of a camel constructed without reusable components, allowing individual control of each joint.

51. 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 6.50 Reducing the storage cost by reusing a lower-leg submodel, with no loss of flexibility in joint control.

52. 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 6.51 Reducing the storage cost by reusing a model for the left-side legs and a separate model for the right-side legs, with great loss of flexibility in joint control.

53. 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 6.52 Modeling a caravan by reusing a single camel model, a highly scalable approach at the cost of excessive synchronized leg movement.