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 36.1 The yellow wall is illuminated only by light reflected from the hidden red polygon. Removing it will cause the yellow wall to be illuminated only by light from the blue surface.

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 36.2 V(P, A) = 1 because there is no occluder. V(P, B) = 0 because a wall is in the way. V(P, C) = 0 because, even though P can see C through the window, the window is an occluder as far as mathematical “visibility” is concerned. Likewise, V(P, D) = 0, even though P sees a reflection of D in the mirror.

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 36.3 Visibility parameterized by distance along a ray.

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 36.4 (Top) Self-occlusion from insufficient numerical precision or offset values causes the artifacts of shadow acne and speckling in indirect illumination terms such as mirror reflections. (Bottom) The same scene with the shadow acne removed.

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 36.5 Finite precision leads to self-occlusions. “Bumping” the outgoing ray biases the representation error in a direction less likely to produce artifacts by favoring the points above the surface as the ray origin.

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 36.6 The quantitative invisibility of two points is the number of surface intersections on the segment between them. The quantitative invisibility of B with respect to A is 2 in this figure. The depth complexity of a ray is the total number of surface intersections along the ray. The ray from A through B has depth complexity 3 in this figure.

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 36.7 A ray tangent to an intersected surface.

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 36.8 The splitting plane for a single internal BSP node divides this scene composed of five spheres into two half-spaces.

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 36.9 Tracing a ray through a scene containing disks stored in a 2D BSP tree. Highlighted portions of space correspond to the node at which the algorithm is operating in each step. Iteration proceeds depth-first, preferring to descend into the geometrically closer of the two children at each node.

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 36.10 Packets of rays with similar direction and origin may perform similar traversals of a BSP tree. Processing them simultaneously on a parallel architecture can amortize the memory cost of fetching nodes and leverage vector registers and instructions. Rays that diverge from the common traversal (illustrated by dashed lines) reduce the efficiency of this approach.

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 36.11 Two people using an early “rendering engine” to make a picture of a lute.

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 36.12 Rendering of a scene (left), and a visualization of its depth buffer (right).

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 36.13 The points in (x, z bufferValue) space that are exactly representable under fixed-point, reverse-mapped fixed-point, and floating-point schemes. Fixed-point representations result in wildly varying depth precision with respect to screen-space x (or y).

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 36.14 Comparison of precision versus depth for various z-buffer representations: 24-bit fixed point (green) is obviously strictly more accurate than 16-bit fixed point (blue); 16-bit floating point is more accurate than 16-bit fixed point when far from the camera (on the right), but has less precision very near to the camera (on the left). The blue and green curves are lines in log-log space, but would appear as hyperbolas in a linear plot. The red floating-point line is jagged because floating-point spacing is uniform within a single exponent and then jumps at the next exponent; the red curve is a smoothed trendline.

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 36.15 Three convex polygons that cannot be rendered properly using the painter’s algorithm due to their mutual overlaps. At each point, a strict depth ordering exists, but there is no correct ordering of whole rectangles.

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 36.16 The red input polygon is clipped against the convex blue boundary polygon; the result is the boundary of the yellow shaded area.

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 36.17 Two cameras facing to the right, toward spheres. The long lines depict the rays from the center of projection to the silhouette of the sphere, which is where the backfacing and frontfacing surfaces meet. The top camera is near a sphere, so most of the sphere’s surface is backfacing. The bottom camera is distant from its sphere, so only about half of the sphere’s surface is backfacing.

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 36.18 Backface culling allows a ray to intersect the correct one of the two coincident airglass and glass- air interfaces of a glass ball surrounded by air.

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 36.19 (Left) View inside Fred Brooks’ bedroom. There are two open doors and a mirror between them. The resultant portals are outlined in white and the mirrors are outlined in red. (Right) Schematic of visible regions for the observer from the top image. Note how the sight lines to the mirror give rise to a reflected visibility frustum that passes behind the viewer. (Courtesy of David Luebke ©1995 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 36.20 A pixel is a rectangular region of the framebuffer. A primitive is the geometric shape to be rendered, such as a triangle. A fragment is the portion of a primitive that lies within a pixel. A sample is a point within a pixel. Coverage and shading are computed at samples (although possibly not at the same samples). The color of a pixel is determined by a resolve operation that filters nearby samples, for example, averaging all sample values within a pixel.

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 36.21 The triangle has binary visibility 1 on the pixels marked with solid blue and 0 on the pixels that are white. A binary value cannot accurately represent the triangle’s visibility on the pixels along the triangle’s slanted sides that are marked in light green. Attempting to compute binary visibility at those pixels necessarily produces aliasing.

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 36.22 Depiction of the storage allocated for a single pixel under 16x CSAA [You06]. The large box on the left depicts the coverage samples. Each color sample contains a 2-bit integer that indexes into the four slots in the color table depicted by the smaller box on the right. When a fifth unique color is required, one of the four color samples is replaced. Thus, CSAA is heuristic and cannot guarantee correctness when many different surfaces color a pixel. (Courtesy of NVIDIA)

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 36.23 Partial occlusion of the lens leads to partial occlusion of the single point P at point Q.