Blending Planes and Canal Surfaces Using Dupin Cyclides

We develop two different new algorithms of G1-blending between planes and canal surfaces using Dupin cyclides. It is a generalization of existing algorithms that blend revolution surfaces and planes using a plane called construction plane. Spatial constraints were necessary to do that. Our work consist in building three spheres to determine the Dupin cyclide of the blending. The first algorithm is based on one of the definitions of Dupin cyclides taking into account three spheres of the same family enveloping the cyclide. The second one uses only geometric properties of Dupin cyclide. The blending is fixed by a circle of curvature onto the canal surface. Thanks to this one, we can determine…