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 NURBS
sphere primitive.
The name says it all, however we also have a NURBS sphere
properties panel, which provides us with several rather
important settings used to build our NURBS sphere.
Start angle: default value = 0
End angle: default value = 360
The start and end angle values are used to determine where
your NURBS sphere will start and end. In the example below, the
start angle has been set to 20 degrees while the  end
angle has been left unchanged from its default value of 360.
These two settings provide you with the ability to not only
create a whole sphere, but also a segment. You could for
instance create a segment that has a start value of 340 degrees,
with an end angle of 360 degrees. This would produce a segment
20 degrees in width. As you can see, there is a rather large
range which these two setting provide you with. You are given
the ability to create a segment that starts at any angle and
ends at any angle. You could literally have a segment which is
only one degree in width!  As
we progress through the various other settings which are
available in the NURBS sphere options panel, you will begin to
see the power you have to create spheres of many different
shapes and sizes. Hopefully you will see how deceptive the NURBS
sphere primitive seems at first glance.
Ideally, you will spend some time testing different values in
these two settings and discover for yourself the different
combinations. At some point in time, we should discuss the
possibility of creating NURBS spheres which are non-objects. I
say this because there will be some settings you use that will
create a NURBS sphere that has no vertices and no faces. If you
find yourself in such a situation, remember that I have provided
you with the default values for each setting on the NURBS sphere
options panel. Return values to the default values in such a
situation. When you do create a sphere such as I have mentioned,
you will notice the values in the object info panel. The sphere
will actually be given a name, however it will not be visible
and the values for vertices and faces will show as 0 in the
object information panel. Just a word to the wise.
Top angle: default value = 180
Bottom angle: default value = 0
Just as the Start angle and the End angle affect vertical
size and shape of a NURBS sphere, the Top angle and Bottom   angle
affect horizontal size and shape of a NURBS sphere. As you can
see from the image on the right, setting the Top and Bottom
angles to 90 degrees produces a wafer. The image on the left
shows how the sphere develops shape as the values change.
As you can see, the Top angle covers degree range from 90-180
degrees. The Bottom angle covers degree range from 0-90 degrees.
The default values for these two settings will produce a whole
sphere. When you combine these two settings, with the previous
mentioned Start angle and End angle, you can produce some
interesting NURBS sphere objects. For the sake of argument we
will call them NURBS sphere objects. They are after all
constructed from the NURBS sphere primitive.
Latitude: default value = 4
Longitude: default value = 6
Both the Latitude and the Longitude values control the number
of segments your NURBS sphere primitives will be constructed
with. Latitude value has a minimum value of 1, while the
Longitude value has a minimum value of 2. Latitude value adds
horizontal segments, while Longitude value adds vertical
segments.
The image on the right shows a NURBS sphere primitive with a
Longitude value of 2 and a Latitude value of 1. With these two
settings, we have only 2 control-points on this entire NURBS
sphere primitive. Changing the Latitude value to 2 would produce
4 control-points on this NURBS sphere. Changing the value of the
Latitude value to 3 would produce 5 control-points on the NURBS
sphere. To make a long story short, add your Longitude and
Latitude values together to calculate the number of
control-points your NURBS sphere primitive will have.
The six settings covered so far from the NURBS sphere options
panel are perhaps the most important for you to become familiar
with. The remaining four settings are important as well, however
they do not have as dramatic an effect on the primitive as these
six settings have.
Closed arc: default = unchecked
This option works in tandem with the End angle setting.
Basically, with this option checked, cutting-out instead of
circular arc is used as a base for creation of the sphere
primitive. In other words, you can have two different types of
sphere primitives, closed or open. Again, this works in tandem
with the End angle setting. For instance,  using
the following settings in the NURBS sphere options panel:
Start angle = 0
End angle = 40
Top angle = 160
Bottom angle = 30
Latitude = 6
Longitude = 6
Leave Closed arc, Top cap, Bottom cap and One patch all
unchecked. The result will be the sphere primitive displayed on
the right in the image above. Changing only the Closed arc to
checked, will produce the sphere primitive shown on the left in
the image above. Of course the End angle must be less than 360
for the Closed arc setting to take affect. 
Top cap: default = checked
Bottom cap: default = checked
Both Top and Bottom cap settings determine if the sphere
primitive will be constructed with or without caps. As you
can see from the image on the right, we have set the primitive
to have no Top cap, however we set the primitive to have a
Bottom cap.
One patch: default = checked
With
this option checked, the NURBS sphere primitive is created as
one NURBS patch, instead of three patches (bottom cap, cloak and
top cap).
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