More on the spheres

Hello Christian and Stefano,

Okay so I am going to change my focus on the terrain mapping to something
more continuous. I think that the original polar coordinate idea will
probably work on the higher resolutions of the sphere without too much
trouble. However mapping you gave me still contains warping, it is very
interesting and I will look at it in more detail shortly, however I am not
sure how you would actually map terrain on that grid since the level curves
seem actually rather complicated, and that is an approach I haven't
considered until now.

Stefano as for your concerns about the complexity of the use of a truncated
icosahedron; I am a little confused, since there are LOD concerns and by
definition an icosahedron is a 20 sided figure so perhaps you can lead me
to what meant. However the math required to build the current truncated
icosahedron is actually very simple, essentially I am keeping track of a
list of constants for the sphere they are as follow:
Resolution, Radius, Angle of incidence for the hexagon (there are two of
these for when it is rotated by 90 degrees), Angle of incidence for the
pentagon (there are 6 of these for the different orientations on the axes),
the current phi and theta of the drawing location.

Also all of the relationships are constant by the nature of geodesic domes,
therefore about 40% of the actions are simple additions (which are then
followed by the trig functions for the position of the vertex). The math is
no more process heavy than a polar sphere, since both of them require
3-dimensional trigonometry and working with the truncated icosahedron
allows me to control the warping a lot easier. I will be the first to admit
that the anti-warping measures will be mildly math intensive but that
shouldn't be too much of a concern. I intend to have the final version
rendered in long triangle strips at the end as to take full use of graphics
hardware (I am currently using triangle fans for convenience, but the final
version will be in triangle strips).

I have updated my blog with the work from today, and hopefully in a day or
two I can amalgamate everything into a fully built sphere. I forgot to make
a crystalspace account (and to check my e-mail until now), and will do that
today in the later morning, and let you know Stefano.

The fully functioning mesh will be working shortly, thanks for the heads up
about how to add the plugin that will save me time so I can concentrate on
other aspects that are cooler than just simply interfacing.

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