I am fooling around with creating my own spheres from a points array, so I
took a look at the performance of sphere() with "show edges" turned on. I
noticed that it doesn't show edges for the top and bottom of the sphere...
so then I took a look at the output of cylinder() and cube() modules.
However if you create the same object with linear_extrude() using either
circle() or square() as the primitive, the display in F5 shows all the
triangles of the mesh.
This inconsistency isn't really a big thing to me, but it doesn't give me
much insight into how a sphere is formed... specifically how is the diameter
for the top and bottom of the sphere determined? I had thought that a sphere
might be topped and bottomed by a cone construction, but that doesn't seem
to be the case.
If you superimpose a cube over a sphere of the same size, you can also see
that there is inaccuracy at the top and bottom of the sphere which only
becomes more pronounced if you scale a sphere (i.e. construct spheres at the
size you ultimately require, don't scale).
So I'm thinking that the sphere generator I create should go for the cone
top and bottom so that the tip of the cone lies exactly on the measurement
specified, or do you folks think that's being overly picky? If I don't go
for the cone, then where should the truncation of the height dimension fall?
Just wanted the thoughts of the community on this.
Here's some code that displays the behaviour I've been talking about (just
remember to turn on "show edges")

$fn = 30;

cylinder(r = 5, h = 5);

translate([15,0,0])
linear_extrude(5)
circle(5);

translate([0,15,0]) {
cube([10,10,10], center = true);

translate([15,0,0])
	linear_extrude(10)
		square([10,10], center = true);

}

translate([35,10,0]) {
sphere(10);
#cube([20,20,20], center = true);
}

--
Sent from: http://forum.openscad.org/

You can look at:

https://github.com/thehans/FunctionalOpenSCAD/blob/master/functional.scad

For a sphere construction.  It matches up pretty well to the one in
OpenSCAD.

There are some drawbacks to that approach - the same project has some
alternative sphere constructions.

--
Sent from: http://forum.openscad.org/

You can look at:

https://github.com/thehans/FunctionalOpenSCAD/blob/master/functional.scad

For a sphere construction.  It matches up pretty well to the one in
OpenSCAD.

The same project has some alternative sphere constructions.

--
Sent from: http://forum.openscad.org/

Isn't it simpler to simply add more polygons to the sphere?

sphere(100,$fn=10); //Looks like crap

translate([240,0,0])
sphere(100,$fn=50); //Looks pretty good

translate([480,0,0])
sphere(100,$fn=500); //Looks smooth

--
Sent from: http://forum.openscad.org/

The sphere polyhedral model in OpenSCAD is based on a subdivision by
meridians and parallels. The number of adjacencies of a vertex in that
subdivision (in quads) is four except for the top vertex of the cones at
the top and bottom of the polyhedron. For high values of $fn, two vertices
have high number of adjacencies, the adjacent triangles are narrow and with
about the same normal. This may cause inaccuracies and issues on boolean
operations. Other sphere subdivisions, like the geodesic one, would be
preferable: they have low number of adjacencies, a few "fat" triangle
shapes and a better vertex distribution on the sphere surface. However,
some people argue that this should be done in user space.