I want to find the Intersection Point and the normal vector of an intersection of a line and a solid of revolution.
I am currently programming some kind of lens simulator for my bachelor thesis, and i want to let the user define their own aspheric lenses by a function that gets rotated around the Y axis. To use the law of refraction I need to know the normal vector aswell as the intersection point of the line penetrating the solid of revolution.
I am thankful for every bit of help. Cheers
If you rotate the line around the symmetry axis, you get a surface which is a hyperboloid of one sheet.
The section of this hyperboloid by a plane through the axis is a hyperbola. So you need to find the intersection of the hyperbola with the profile curve of the lens.
The method to use depends on the type of the profile curve.