Information Technology Reference
In-Depth Information
The relationship between the coordinates of original and rotated vector is given by:
cos
sin
sin
sin
cos
To complete the set of iteration equation, the variables U
i
, V
i
, W
i
are introduced
which are defined as:
cos
cos
sin
cos
sin
In matrix form these equations can be represented as follows:
1
·
1
·2
2
1
·2
·
·
·2
·2
1
1
Similarly
1
·
1
·2
2
1
·2
·
·
·2
·2
1
1
Also
1
·2
1
·2
From the above equation it is clear that four 2D CORDIC rotations are required for
a 3D rotation of a vector. Also the scale factor for Z
i+1
and W
i+1
is different from that
of U
i+1
, V
i+1
and Y
i+1
. They need to be compensated via pre-scaling of inputs or post
scaling of outputs with their respective constants K and K
2
whose values are given by:
3
Proposed Cartesian to Spherical Coordinate Converter
The proposed Cartesian to Spherical Coordinate Converter
is based
on scaling free
3D CORDIC algorithm. Third order approximation of Taylor series as in [10] is used
to derive the CORDIC equation.
The Taylor series expansion of sine and cosine of an angle is:
sin
2
3!
2
5!
2
cos
12!
2
4!
2
