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3D Game Engine Design, 2nd Edition
book

3D Game Engine Design, 2nd Edition

by David Eberly
November 2006
Intermediate to advanced content levelIntermediate to advanced
1040 pages
26h 31m
English
CRC Press
Content preview from 3D Game Engine Design, 2nd Edition
32 Chapter 2 The Graphics System
which can be solved to obtain
d = D
.
(X P)
The point of projection is therefore defined by
Y P = (D
.
(X P))D = DD
T
(X P)
Equivalently, the projection is
Y = DD
T
X +
I DD
T
P (2.39)
which is of the form Y = MX + B, therefore orthogonal projection onto a line is
an affine transformation. Unlike our previous examples, this transformation is not
invertible. Each point on a line has infinitely many points that project to it (an entire
plane’s worth), so you cannot unproject a point from the line unless you have more
information. Algebraically, the noninvertibility shows up in that M =DD
T
is not an
invertible matrix.
Orthogonal ...
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Publisher Resources

ISBN: 9781482267303