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.

 

[blue_raver22]

Hello there,

As a fellow scientist and 3D modeler, I understand the importance of utilizing math and geometry in our work. It can certainly be challenging, especially for those of us who may not have a strong background in those subjects. However, I applaud your efforts in trying to incorporate these aspects into your diagrams.

I would be happy to help with any questions you may have. In terms of references, I recommend checking out online resources such as Khan Academy or Coursera for tutorials and courses on math and geometry. You can also reach out to other 3D modelers or scientists who have experience in this area for guidance and advice.

Keep up the great work and don't hesitate to ask any questions you may have. We are all constantly learning and it's important to seek out help when needed. Best of luck with your diagrams!

Sincerely,