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.

Figure 11.1 An airplane that flies along the x-axis can change direction by turning to the left or right (yawing), pointing up or down (pitching), or simply spinning about its axis (rolling). 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 11.2 When v is orthogonal to ω, v and ω × v form a basis for the plane perpendicular to ω. 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 11.3 Wrapping a line onto a circle. 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 11.4 Wrapping a disk onto a sphere; all points of the circular edge of the disk are sent to the North Pole. 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 11.5 The set of all cosine-sine combinations of v and w wraps around the whole circle. 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 11.6 All cosine-sine combinations of two perpendicular unit vectors in the sphere again form a unit circle, called a great circle. 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 11.7 The blue path in the domain transforms to the short arc between π/4 and 3π/4 in the codomain, while the red one transforms to the long arc. 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 11.8 We have two rotation matrices, M1 and M2; the first corresponds to a pair of antipodal quaternions, ±q1, and the second to a different pair of antipodal quaternions, ±q2. Starting at q1, we choose whichever of q2 and −q2 is closer (in this case, −q2) and interpolate between them (as indicated by the thick red arc); we then can project the interpolated points to SO(3) to interpolate between M1 and M2. 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 11.9 We can compute the midpoint of the quadrilateral ABCD by finding the midpoints of AB and CD (marked by circles), and then the midpoint of the segment between them, or by doing the same process to the edges AD and BC (whose midpoints are marked by squares); the resultant quadrilateral midpoint (indicated by the diamond) is the same in both cases. This does not happen when we work with quaternions. 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 11.10 The object being viewed is imagined as lying in a large glass sphere. Moving a point on the surface of the sphere moves the object inside. 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 11.11 When the user clicks near the lower-right corner of the display, we can recover the 3-space coordinates of a corresponding point S of the imaging plane in 3-space; we’ll use this to determine where a ray from the eye through this point hits the virtual sphere. 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.