The Problem:
In real life, all planets are spherical. This has always posed a major problem to mapmakers of any age because of the curvature of Earth. So how does one project a spherical image onto a 2D plane? Better yet, how does one take a 3D sphere's surface and map it onto a plane? (see picture link)
This is a simple Perlin fractal texture I mapped to a sphere. It is impossible to see all sides of the sphere because the sphere blocks the view. Thus, it would be practically useless to try to take a map from this sort of perspective.
My Solution:
To solve this problem, I will begin with a simple sphere. Normally, one can only see a portion of a sphere's surface. For the purposes of this project, I need to be able to see all of the surface at once. I will place the "camera" at the center of the sphere and take a picture.
This is a regular picture taken from inside the sphere. Notice that it is not possible to see all of the surface from this point of view, again making the method useless if one wanted to make a map of the entire planet.
It is commonly known what a panoramic picture is: a camera sits in the middle of a circle of people and rotates as it takes a picture. A spherical picture takes that same principle and applies it to height. This will allow me to see the entire surface of the sphere in one picture.
This is a picture inside the same sphere with a spherical picture. The distortion at the top and bottom is caused by that a sphere is mapped onto a 2D plane (the computer screen). The benefit from mapping this onto a sphere is that there is left-right continuity, which means that the left and right edges of the picture line up exactly.
For the development stage of this project, I will be using a spherical render to show my progress. Once I have the algorithm, I will render the sphere normally and show how the algorithm can be applied.