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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
16.7 Differential Equations 749
A
1
= F(t
i
, X
i
)
A
2
= F(t
i
+ h/2, X
i
+ hA
1
/2)
A
3
= F(t
i
+ h/2, X
i
+ hA
2
/2)
A
4
= F(t
i
+ h, X
i
+ hA
3
)
X
i+1
= X
i
+
h
6
(A
1
+ 2A
2
+ 2A
3
+ A
4
)
t
i+1
= t
i
+ h
Runge-Kutta with Adaptive Step
For some data sets, it is possible to dynamically adjust the step size h to reduce the
total number of steps to get to a desired final time. The following algorithm is fifth
order and adjusts the step size accordingly.
1. Take two half-steps:
A
1
= F(t
i
, X
i
)
A
2
= F(t
i
+ h/4, X
i
+ hA
1
/4)
A
3
= F(t
i
+ h/4, X
i
+ hA
2
/4)
A
4
= F(t
i
+ h/2, X
i
+ hA
3
/2)
X
inter
= X
i
+
h
12
(A
1
+ 2A
2
+ 2A
3
+ A
4
)
and
B
1
= F(t
i
+ h/2, X
inter
)
B
2
= F(t
i
+ 3h/4, X
inter
+ hB
1
/4)
B
3
= F(t
i
+ 3h/4, X
inter
+ hB
2
/4)
B
4
= F(t
i
+ h, X
inter
+
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Publisher Resources

ISBN: 9781482267303