Graphics Reference
In-Depth Information
Rotate frame
cos β
sin β
0
R 1
β
.
=
sin β
cos β
0
0
0
1
Translate and rotate frame
cos β
sin β
t x cos β
t y sin β
R 1
β
T 1
.
t x ,t y =
sin β
cos βt x sin β
t y cos β
0
0
1
8.6.2 Summary of Multivector Transforms
Frame rotor
R β =
cos β
+
sin β e 12 .
Translate frame
p =
p
t
=
(x
t x ) e 1 +
(y
t y ) e 2 .
Rotate frame
R β p
p =
=
( cos β
+
sin β e 12 )(x e 1 +
y e 2 ).
Translate and rotate frame
p =
sin β e 12 ) (x
t y ) e 2 .
R β ( p
t )
=
( cos β
+
t x ) e 1 +
(y
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