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 25.1 A triangle strip is represented by a stream of vertex indices; every group of three adjacent indices describes another triangle in the strip. The communication attributable to a typical triangle is therefore just a single vertex index, rather than three vertex indices.

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 25.2 Polygonal meshes used to represent a cube, a teapot, and a smooth, wavy surface.

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 25.3 A small mesh with interior edges drawn in green and boundary edges drawn in blue. The red edge, which is not adjacent to any faces, is a “dangling” edge and is not allowed in our meshes.

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 25.4 The red vertex marked with a dot in the top mesh is an interior vertex; the one in the bottom mesh is a boundary vertex.

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 25.5 Each of these fails to be a surface mesh in some way.

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 25.6 Two oriented adjacent faces, (2, 3, 7) and (7, 3, 4). The oriented edge (3, 7) is in the boundary of the first face, while (7, 3) is in the boundary of the second.

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 25.7 The point P is on the same side of the plane J as C, and therefore may be in the triangle ABC. If it passes corresponding tests for planes containing the edges BC and CA, we know it’s in the triangle.

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 25.8 The star of a simplex consists of all simplices containing it.

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 25.9 The 1-ring of V is drawn in large red dots; the 2-ring in smaller green dots.

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 25.10 The star of the top vertex is drawn in brown; the 1-ring, which forms an octagon in the middle level, in red. The 2-ring, at the bottom drawn in bright green, is connected into a figure-eight shape.

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 25.11 (Top) A mesh with bad self-intersections. (Middle) A mesh in which a vertex of the pink face at the right lies in the middle of an edge of the green face at the top right. (Bottom) The red vertex marked with a dot is a T-junction.

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 25.12 A see-through view of the torso and arm of a simple robot character.

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 25.13 In this simple model of Earth, a small disk around the North Pole projects injectively onto a disk in the horizontal tangent plane to the North Pole.

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 25.14 Projection from the mesh onto any plane passing through the central red vertex will not be injective. The large green vertices are closer to the eye; the small aqua ones are farther away.

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 25.15 The slices of a torus are smooth (blue) except at the min, max, and the two “critical” levels where the slices are figure-eights (red).

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 25.16 The front wall of a building, seen from above. Notice the narrow embossed portion of the wall in the center. The sides of this embossment will reflect light from the east or west, while the rest of the wall will not.

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 25.17 The BRDF of the wall, drawn for light coming from the east, south, and west.

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 25.18 Two irregularly shaped objects overlap; when we simplify each one, getting rid of small details, the space between the objects remains as a small detail, unrecognized by our simplification process.

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 25.19 A curve, represented in a wavelet basis, consists of large- and small- scale features. The small-scale features—the “character” of the curve—can be edited without affecting the large-scale shape, and vice versa. (Courtesy of Adam Finkelstein and David H. Salesin, ©1994 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 25.20 The edge from u to v has been collapsed to a single new vertex, which is labeled w. The two triangles that meet this edge have disappeared, and the four non-uv edges have collapsed into two edges. The set of triangles shown is called the neighborhood of the edge.

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 25.21 An edge-collapse can be made gradually, by interpolating from the original positions of u and v part of the way toward the final position w.

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 25.22 The value of “spring” energy: If we try to fit the six data points on a circle (marked with small dots) using a triangle with short edges, the green triangle (top) is a reasonably good solution. If we remove the short-edge constraint, the red triangle (bottom) is a “perfect” fit, even though it violates our expectations.

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 25.23 Knowing function values at grid points, we can estimate zero-crossings (black dots) by linear interpolation, and then connect the dots, in each cell, to estimate the level curve at level zero.

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 25.24 We can estimate gradients at the zero- crossings as well. Fitting a surface to the point-and- direction data gives a different estimate of the level-set.

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 25.25 The normals at the two zero-crossings determine two lines, which intersect at a new point X.

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 25.26 (Following [Ju04], Figure 3.) Ju’s model-repair method. (a) A model, embedded in a fine grid. (b) The grid edges that intersect the model, stored in an oct tree. Each cell touches an even number of such edges. (c) Signs at grid points (indicated by light or dark shading) generated from the set of intersection edges. (d) The model reconstructed by contouring the sign data.

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 25.27 The U-shaped polygon soup generates several edges, but there’s no way to consistently assign signs to the grid cells so that each intersection edge exhibits a sign change. Cells with good labelings—most of the ones meeting the polyline—are in green. The problem arises at cells (in orange at the ends of the polyline) with an odd number of intersection edges.

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 25.28 The vertex v i is surrounded by a ring of vertices, one of which is v j ; the angles on either side of v j are called α and β. The cotangents of these angles are used in defining the weight of v j in the cotangent Laplacian vector at v i.

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 25.29 We start with a source and a target mesh, shown at left, a triangle-by-triangle correspondence between them (in this case, the correspondence is the fairly obvious one), and a deformation of the source mesh, shown at the top right. The deformation transfer algorithm provides a transformation of the target mesh that’s analogous to the deformation of the source mesh. (Courtesy of Robert Sumner and Jovan Popović.)

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 25.30 The sort order of the blue and red polygons is immaterial because of backface culling; the blue polygon obscures the green from some viewpoints, but the green never obscures the blue.

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 25.31 Drawing the rooftop regions of the building in increasing numerical order, and using backface culling, will prevent overdraw no matter what the viewpoint.

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 25.32 An eight-triangle building block.