Re: Geodesic Vs Polar

Hi,

2013/5/29 B. Isherwood <[email protected]>

> 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?
>



 Yes I'd agree to go the geodesic way, even though you can still get some
distortion with higher resolution spheres, while still lower than other
models.
You would have also an equator line by setting it up as two opposing
icosahedron, so it would be the line divinding them. For the day line you
could pick a vertex on the equator.



> 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?
>
>
>
>
Usually the gsoc program prefers this sort of thing, maybe through blogs.
So you could either post it in a blog or here or in both depending if you
want a more one directional communication "this is how i did it, why,
etc..." or want to ask questions. If you don't have a blog we could check
for hosting it like the blogs from the other years in the cs spaces.


>
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