
Reference Systems and Coordinate Transformations 55
To compute the 3D spherical coordinate from the 3D Cartesian coordinate
the transformation equations are given by
ρ =
p
x
2
+ y
2
+ z
2
(3.23)
Φ = arctan(
y
x
) (3.24)
Φ = arccos(
x
p
x
2
+ y
2
) (3.25)
Φ = arcsin(
y
p
x
2
+ y
2
) (3.26)
θ = arctan(
p
x
2
+ y
2
z
) (3.27)
To compute the spherical coordinates from cylindrical coordinates the trans-
formation equations are given by
ρ =
p
r
2
+ h
2
(3.28)
Φ = Φ (3.29)
θ = arctan(
r
h
) (3.30)
To compute the cylindrical coordinates from Cartesian coordinates the
transformation equation are given by
r =
p
x
2
+ y
2
(3.31)
θ = arctan(
y
x
) + π(−x)sgny (3.32)
h = z (3.33)
3.8 Datum Transformation
As assumed by most ...