Tubelike joints: A classical geometry perspective Original Research Article

Canal surfaces are envelopes of 1-parameter families of spheres. Via a one to one correspondence between spheres and planes of 3D and points of 5-dimensional space, 1-parameter families of spheres correspond to curves in this space. Tables 1 and 2 present how to translate objects (spheres, planes, conics, circles, etc.) and relationships (tangency, orthogonality, coplanarity, cosphericity, etc.) from the 3D into the 5-dimensional context.