A closed-form solution for the flat-state geometry of cylindrical surface intersections bounded on all sides by orthogonal planes

Presented herein is a closed-form mathematical solution for the construction of an orthogonal cross section of intersecting cylinder surface geometry created from a single planar section. The geometry in its 3-dimensional state consists of the intersection of two cylindrical surfaces of equal radii which is bounded on all four sides by planes orthogonal to the primary cylinder axis. A multivariate feature of the geometry includes two directions of rotation of a secondary cylinder with respect to a primary cylinder about their intersecting axes. See Figs. 1 and 2 for the definition of the two variable directions of rotation of the secondary cylinder with respect to the primary cylinder.