Cyclides in pure blending I Original Research Article

In this paper, we study blends between natural quadrics using both Dupin ring cyclides and parabolic cyclides. We present a new definition of a pure cyclide blend that we believe will help ensure the blend surface is useful to a designer. This definition will force the construction of nonsingular cyclide blends, deliberately excluding cyclide joins and singular surfaces. Further, we study the implications of the cyclide blend definition on the position of the quadrics in a blend and on the properties of the blending cyclideʹs extreme circles. This is the first part of a two part paper.