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

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 3.2 A different Du ̈ rer rendering approach.

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 3.3 The coordinate system for the Du ̈ rer woodcut: The origin is at the screw eye, labeled E, and the y- and z-coordinate axes are shown there. The picture frame lies in the plane z = 1, parallel to the plane of the wall, z = 0. The x-coordinate arrow is horizontal, lying in the plane of the wall, approximately in the direction of the shading lines on the wall, while the z-coordinate arrow is horizontal and perpendicular to the wall. Due to the effects of perspective, the x-direction and z-direction appear almost parallel, but pointing in opposite directions, at the screw eye. The point T is the point in the frame of the drawing plane (z = 1) closest to the screw eye. The z-direction points from the screw eye toward T, making the xyz-coordinates of T be (0, 0, 1).

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 3.4 The point P = (x, y, z) is on our object. The string from P to the eye, E, will pass through the window frame at some location P ʹ = (x ʹ, y ʹ, z ʹ ). Note that z ʹ = 1 ʹ, because we chose our coordinates to make that happen.

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 3.5 Two similar triangles overlaid on the picture in the x = 0 plane. The vertical edges of the small red and large blue triangles have lengths y ʹ and y, respectively. What are the lengths of their horizontal edges?

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 3.6 The labels for the vertices and edges of our cube model. Edge indices are in circles. The eyepoint and frame from the Du ̈ rer woodcut are also included, although we have chosen to adjust their relative positions by placing the frame in this case so that it extends from −½ to ½ in both x and y. Thus, we’re viewing the cube “at eye level” rather than “from above,” as Du ̈ rer viewed the lute.

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 3.7 The result of the rendering algorithm, (a) shown in place (i.e., drawn in the frame), with rays from the eye to the four near corners of the cube shown, projecting those corners onto the picture plane, and (b) seen directly, with the surrounding square (which ranges from −½ to ½ in both x and y) drawn to give context.

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 3.8 The result of the Du ̈ rer program: a wire-frame cube, shown in perspective, on a background that looks like graph paper. The axes on the graph paper are part of the GraphPaper itself, set up by the test bed, and are not drawn by the Du ̈ rer rendering part of the program.