Curves of intersection between surfaces of revolution, including cone, cylinder, sphere, hyperboloid and cyclid are computed exactly and efficiently with polynomials of fourth order or less. All combinations are considered and pathological conditions pose no problem. Applications include torch tip and axis pose computation in cutting and welding and collision avoidance among mechanism components and surrounding objects. Fig. is an example of intersection between hyperboloids with skewed axes.
P. Zsombor-Murray, Y. Liu
Intersection between hyperboloids of revolution.