Geodesic Vs Polar

Hello Stefano

So I will just explain the logistical differences

Geodesics:

Essentially a geodesic dome or sphere is a structure that is built from
equilateral triangles where all the corners are projected onto an outer
sphere. So for this project since all the vertices are separated by exactly
the same distance and have exactly the same angle of attack all of the
cells will even and therefore in theory should remove all distortions. I am
going to link a gif from wikipedia so you can see what I mean.

http://en.wikipedia.org/wiki/File:G%C3%A9ode_V_3_1.gif

The main problem is this form of sphere requires a recursive building
procedure and there is no defined equator or dateline, meaning the
divisions appear to be less organized

Polar Coordinates:

Polar coordinates have an LOD issue and that is the farther you are from
the poles the more more stretched the cells you are working with are. The
main advantage of polar coordinate systems are they are simple to use for
less complicated structures such as plain spheres since the appearance.
Essentially you can think of a polar sphere as a series of circles drawn 1
after the other rotating around a single point, because the poles of the
sphere are closer to the rotational axis the distance between each circle
is less than they would be at the equator.

This form leaves well to matching up with and XYZ system by replacing it
with a phi, radius, theta system, this is the main advantage, since I can
map directly from the existing terrain functions with a very small amount
of work. However the cost will be stretching at the poles. I am linking an
image that illustrates this problem.

http://content.answcdn.com/main/content/img/McGrawHill/Encyclopedia/images/CE160600FG0020.gif

As you can see the longitudinal lines begin to stretch out as you approach
the equator.

I am leaning towards developing a geodesic version over the polar version,
however it is the difficulty of converting the XYZ of the terrain
generators to the geodesic one seems daunting, however I think that I will
solve this problem by figuring out how to layout the geodesic sphere as a
flat 2D plane finding the relation to the proper XYZ plane.

So which system do you think will be preferable?

One last thing, when it comes to geometric programming I tend to make a lot
of notes, I think it would be easier for me to keep on track if I were to
send my notes every couple of days and perhaps you can comment on them and
give advice?

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