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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.

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: ). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 23.1 (Top) A Bézier patch drawn with the collection of curves t S(s, t) for several values of s between 0 and 1. (Middle) The same patch, drawn with the curves s S(s, t) for several values of t. (Bottom) The same surface, drawn colored by height. In the top two drawings, the control mesh Q ij (0 ≤ i, j ≤ 3) is shown.

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: ). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 23.2 A spherical blob made from six “rectangular” patches that meet three at a vertex.

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: ). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 23.3 A mesh where one vertex v has n adjacent vertices e 1, e 2, … e n, at the ends of the edges, leaving v.

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: ). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 23.4 The new vertex is connected to each new edge point; the new edge points are connected to the face points for adjacent faces.

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: ). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 23.5 For a quad mesh, the face vertices from the previous level of subdivision are opposite v in each quad.

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: ). Copyright © 2014 by Pearson Education, Inc. All rights reserved. Figure 23.6 (Top) The initial mesh consists of the integer lattice with one point raised. (Middle) The first and second levels of subdivision. (Bottom) The cubic B-spline basis function whose control points are the vertices of the original control mesh, for comparison.