Before we begin, I must ask you to keep the vocabulary at high school level.
These variables define the point the plane needs to be tangent to – the center of the circle is at the origin.
r - defines the radius of the sphere
Ø1 – defines the rotation in the x-z axis – can be from 0 to 2π
Ø2 – defines the rotation in the y axis – can be from 0 to π
I have found that I can convert that point on the sphere to Cartesian coordinates using equations.
These variables define the location of the point to be converted on the 2d plane that is tangent to the sphere.
d1 – is the x coordinate
d2 – is the y coordinate
Positive y for the 2d plane is in the vertical direction as much as possible (because the plane is tangent to the sphere), positive x is in the counterclockwise direction looking down on the sphere from positive y in 3d space (or to the right if the plane is on your side of the sphere).
The formulas I have made are:
At this point I hope you understand what I am trying to do and can point me to where I’ve gone wrong.