e-mail: lgarnier@u-bourgogne.fr
Keywords: Geometric modeling, Quadric primitives,
Dupin cyclides surfaces, Supercyclides, Bézier surfaces, Blending.
ABSTRACT
Dupin cyclides are algebraic surfaces introduced for the first
time in 1822 by the French mathematician Pierre-Charles Dupin.
They have a low algebraic degree and have been proposed as a
solution to a
variety of geometric modeling problems.
The circular curvature line's property facilitates the
construction of the cyclide (or the portion of a cyclide) that
blends two circular quadric primitives. In this context of
blending, the only drawback of cyclides is that they are not
suitable for the blending of elliptic quadric primitives. This
problem requires the use of non circular curvature
blending surfaces.
In this paper, we present another formulation of cyclides: Scaled
cyclides. A scaled cyclide is the image of a Dupin cyclide under
an affine scaling application. These surfaces are well suited for the
blending of elliptic quadrics primitives since they have
elliptical lines of curvature. We also show how one can convert a
scaled cyclide into a set of rational quadric Bézier patches.