If I have a sphere of known radius, R, centred at the origin and a plane with a known angle to the x and y axes (roll, φ, and pitch, θ), how can I find the coordinates of the points that this plane could be a tangent to the sphere assuming the plane can be translated.
I have done some research into spherical coordinates, however, I am required to know the azimuth and inclination to find the point on the sphere. I am not sure how to calculate these from the angle of the tangent plane to the x and y axes. From further research I believe rotation matrices may be the answer, but I am unsure how to apply them to this problem. Any help is much appreciated.
Many Thanks!
Use the roll and pitch angles to calculate the unit-length normal vector $\mathbf{N}$ of the plane. Then the point of tangency is $R\,\mathbf{N}$.
The roll and pitch angles are examples of "Euler angles", which you can look up here and in many other places. Euler angles are a mess because there are many different ways to define them. There are choices about which axes you rotate around and in which order. I can't really tell you how to calculate $\mathbf{N}$ from your two angles without some clear definition of what they mean.