Game Development Reference
In-Depth Information
k
P
φ
r
θ
j
i
Figure C.3. Spherical coordinates.
angle formed between the z axis and the line connecting P to the origin. The po-
lar angle φ always satisfies 0 φ π
≤≤
.
The Cartesian coordinates
x yz corresponding to a point having spherical
,,
coordinates
r θφ are given by
,,
x r φθ
y r φθ
zr φ
=
=
=
sin
cos
sin
sin
cos
.
(C.13)
The spherical coordinates
r θφ can be written in terms of the Cartesian coor-
,,
dinates
x yz as follows.
,,
(
)
2
2
2
rxyz
,,
=++
x
y
z
x
(
)
(
)
1
θ xyz
,,
=
sgn
y
cos
2
2
x
+
y
z
(
)
1
φ xyz
,,
=
cos
(C.14)
2
2
2
xyz
++
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