I was wondering if a solution to this problem that doesn't involve coordinate space transformations.
I have two points in 3d space, and am interested in locations where the difference of the distances to the two points is constant. These locations form a hyperboloid.
I also have a line through 3d space. This line and the two previously-mentioned points are all coplanar. My goal is to find the places where the line intersects the hyperboloid.
One solution is to translate and rotate the coordinate system so that the common plane lies on two of the major axes, and then solving the problem in 2D. However, I was wondering if there was a more direct way to calculate this.
Thanks!