The 3D modeler, newbie and odd questions box

[probiner]

Hi
I do 3D modeling and lately i have been trying to make some more theoretic diagrams about the whole thing. Sometimes i try to go through ways where math and geometry are needed (or so i think) and my background is not up to it.
I'll use this thread to post some initial questions per post. If you can drop me a line or forward me to helping references i'll thank you.

Cheers

 

[probiner]

A - Mosaic Sphere

- The Objective -
So the usual sphere in 3D apps will make X sides incident in the pole and Y segments that are evenly distant. (How is this type of sphere called/designated?). Near the poles this sphere quads look very rectangular and some times that is not good.
So, what i would like to get is this type sphere, but where the quads are the most squarish/regular as possible. For this the parallels/segments distance will have to different, being smaller in the poles.

-Attempts-
Here's a comparison between the usual sphere and an eye balled Mosaic Sphere to explain the objective.

I also tryed to do the following using an expression like x^3, took the y values in a straigth line, Bend it 90º and the made a Lathe, to make a semi-sphere. It's not great, but looks just ok, because i think x^3 or something like this is not the right expression.

So i started to think which shape would be more close to a square between 2 angled guidelines. And it seems to me that a http://en.wikipedia.org/wiki/File:Quadrilateral_hierarchy.png" might be it.

So what function/expression would give me the heights of such polygons? If i could use such, i would just need to bend the Y values and make a Lathe to have this thing done properly.

Cheers

 

[coolul007]

Have you looked into geodesics/great circles making trinagles

 

[Unrest]

A - Mosaic Sphere
So, what i would like to get is this type sphere, but where the quads are the most squarish/regular as possible. For this the parallels/segments distance will have to different, being smaller in the poles.

I want to solve this exact same problem. I struggled with it once but didn't get far. Ideally for me, the y-values would be expressed as a function of x for one segment/strip from pole to equator.

The similar problem for a flat disk might be a help:
r = e^p
This gives you the radius of a point numbered by p. For example if p is
-5, -4, -3, -2, -1, 0
then r is
0.007, 0.018, 0.050, 0.14, 0.37, 1

Revolving this string of points about the origin produces a circle of radius 1 with the points being the corners of quads which are all exactly the same shape, but get smaller towards the center (r=0). Maybe if you bend one of these strips into a quarter-circle it will produce the desired result?

You have to have a hole in the center/pole because you'd need infinitely many similar quads to reach r=0.