Intersections of Surfaces of Revolution

Abstract

In this paper, we deal with surfaces of revolution and their intersections. We start with the surfaces of revolution RS that have their axis along the x3–axis and find intersections with a line, a plane, and then intersection of two such RS. Furthermore, we apply formulas for the intersection with a line to determine the visibility of RS. Later we develop formulas for the intersection of two surfaces of revolution that have their axis along different arbitrary straight lines, and, as a special case, the intersections of two spheres and intersections of general surface of revolution with a sphere and a surface given by an equation. We apply our own software to the graphical representation of all the results we present.