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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
774 Chapter 17 Rotations
17.2.9 Interpolation
Quaternions are quite amenable to interpolation. Once again, the standard operation
that is used is spherical linear interpolation (slerp). Given quaternions p and q with
acute angle θ between them, slerp is defined as
slerp(t; p, q) = p(p
q)
t
for t [0, 1]. Note that slerp(0; p, q) = p and slerp(1; p, q) = q. It is not immedi-
ately clear how to compute slerp in the form specified by the definition. An equivalent
definition is
slerp(t; p, q) =
sin((1 t)θ)p + sin (t θ )q
sin(θ)
If p and q are thought of as points on a unit circle, this formula is a parameterization
of the shortest arc between them. If a particle ...
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Publisher Resources

ISBN: 9781482267303