# Choosing a Sphere

### \Appropriate for a planet

Choosing what type of sphere to use was no easy task. I needed a sphere that had an even distribution of
detail and a high level of control over the resolution of the mesh.

## UV Sphere

The default option is an UV sphere, which is evenly divided into rows and columns. This allows for a high
level of granularity of control over the mesh's detail, which is one half of the equation. However, this
type of sphere has the problem of having a higher density of vertices and faces near the poles of the
sphere. This would not work well for my purposes as I don't want the planet to have higher levels of
details near the poles.

## Ico Sphere

The second option would be to use an ico sphere, which has equally sized triangles. This gives me an even
distribution of detail across the sphere. However, due to the nature of equally subdividing triangles, I can
only increase the number of faces by a factor of four. This gives me very little granularity and control of
how detailed the sphere is.

## Normalized Sphere

The third option is to start with a cube, and then normalize each vertices position from the center. This
creates a sphere has a very even distribution of detail, with only slightly higher level of detail near the
seams where the sides of the cube have come together. It also gives me a high granularity of detail as I can
divide the sides of the cube into as many faces as I'd like. The only downside is that there can be some
small artifacts along the seam lines where the sides of the cube meet.

## Conclusion

Using a normalized sphere has turned out great. It satisfied all of my requirements and the math needed to
create it was fairly simple. The small artifacts along the seam lines, where some vertices just don't quite
connect, are all but invisible once noise is applied and the sphere is deformed. I did find a solution that
solves this problem, which is to merge vertices that are really close to each other, connecting the small
gaps. However, merging nearby vertices takes about 500 milliseconds of compute time on my powerful desktop
computer. This performance hit is certainly not worth the small benefit of eliminating a rare and difficult
to spot artifact.