Dupin cyclide blends between non-natural quadrics of revolution and concrete shape modeling applications

• A general algorithm for the blending of 3D non-natural quadrics of revolution.
• Two Dupin cyclide patches and an intermediate cylinder are used for the blending.
• The 3D blending is reduced to a 2D direct computation of two cyclide patches.
• Several examples of algebraic and non-algebraic surface blendings are presented.
• Two complete shape modeling applications for designing concrete objects are provided.

In this work, we focus on the blending of two quadrics of revolution by two patches of Dupin cyclides. We propose an algorithm for the blending of non-natural quadrics of revolution by decomposing the blending operation into two complementary sub-blendings, each of which is a Dupin cyclide-based blending between one of the two quadrics and a circular cylinder, thus enabling the direct computation of the two Dupin cyclide patches and offering better flexibility for shape composition. Our approach uses rational quadric Bézier curves to model the relevant arcs of the principal circles of Dupin cyclides. It is quite general and we have successfully used it for the blending of several non-natural surfaces of revolution, such as paraboloids, hyperboloids, tori, catenaries, and pseudospheres. Two complete examples of 3D shape modeling, representing a satellite antenna and a hippocampus are presented to show how quadrics and Dupin cyclide patches can be combined to model concrete objects.

Figure optionsDownload high-quality image (187 K)Download as PowerPoint slide