Spherical Geometry
This section is added to aid the users for calculations
in the following sections and to explore the geometry involved in the unique coordinate system
that fits the mathematics of the pool balls. Spherical coordinate system defines any location
on a perfect sphere by using radius, latitudinal angle, and the longitudinal angle. It is very
similar to the way our globe defines an exact location on earth.
This animation illustrates variance in the radius, r.
This animation illustrates variance in the longitude, q (angle of ascension).
This animation illustrates variance in the latitude, f (angle of declination).
There are some restrictions and requirements for the three coordinates (r,
f, q) so that there is no variance in
defining the same location. These are as follow:
r > 0,
0 < q
< 2p,
0 < f
< p,
Point P is defined using spherical coordinate, (r, f,
q) Press each button to see its transformation.
How does one convert from spherical coordinates (r, f,
q) to rectangular coordinates, (x, y, z)?
To answer this question, a few equations are given for conversions:
x = rsinfcosq
y = rsinfsinq
z = rcosf
Sample Problem
What are the rectangular coordinates for spherical coordinates, (5, p,
p/2)?