Cyclides in pure blending II Original Research Article

In this the second of a two part paper, we continue our study of pure blends between natural quadrics using both Dupin ring cyclides and parabolic cyclides. Note, we make a distinction between blends and joins. If and only if conditions for the existence of cyclide blends and constructive proofs of their correctness are given in each quadric/quadric case. Easily implementable tests are given for these conditions. The relationship of the existence of cyclide blends to the common inscribed sphere condition is examined. Finally, an example that contains at least one of each type of cyclide blend is presented.