By Medhat H. Rahim

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Citation Details

Title: three-D special effects: A Mathematical creation with OpenGL.(Book review)

Author: Medhat H. Rahim

Publication: institution technological know-how and arithmetic (Magazine/Journal)

Date: March 1, 2009

Publisher: university technological know-how and arithmetic organization, Inc.

Volume: 109 factor: three web page: 183(2)

Article kind: e-book review

Distributed via Gale, part of Cengage studying

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**Extra resources for 3-D Computer graphics. Mathematical introduction with OpenGL**

**Example text**

Even more important, the techniques discussed in this chapter have the advantage of being fairly easy for an artist or programmer to use and lend themselves to efﬁcient software and hardware implementation. In fact, modernday PCs typically include specialized graphics chips that carry out many of the transformations and interpolations discussed in this chapter. 1 Transformations in 2-Space We start by discussing linear and afﬁne transformations on a fairly abstract level and then see examples of how to use transformations in OpenGL.

The x- and y-coordinates determine the position of a vertex in the ﬁnal graphics image. The z-coordinates measure the distance to the object, although they can represent a “pseudo-distance,” or “fake” distance, rather than a true distance. Homogeneous coordinates are described later in this chapter. As we will see, perspective division consists merely of dividing through by a w value. Displaying. In this stage, the scene is rendered onto the computer screen or other display medium such as a printed page or a ﬁlm.

When we discuss perspective transformations, which are more general than afﬁne transformations, it will be necessary to have other values in the bottom row of the matrix. 9 shows an afﬁne transformation acting on an F. (a) Is this a linear transformation? Why or why not? (b) Give a 3 × 3 matrix that represents the afﬁne transformation. [Hint: In this case, the easiest way to ﬁnd the matrix is to split the transformation into a linear part and a translation. ] For the next exercise, it is not necessary to invert a 3 × 3 matrix.