Iterative construction of Dupin cyclide characteristic circles using non-stationary Iterated Function Systems (IFS)

作者：Druoton L; Garnier L^*; Langevin R

来源：Computer-Aided Design, 2013, 45(2): 568-573.

DOI：10.1016/j.cad.2012.10.042

• Circle
• Definite symmetric bilinear form
• Subdivision
• Dupin cyclide
• Envelope of spheres
• Space of spheres

A Dupin cyclide can be defined, in two different ways, as the envelope of an one-parameter family of oriented spheres. Each family of spheres can be seen as a conic in the space of spheres. In this paper, we propose an algorithm to compute a characteristic circle of a Dupin cyclide from a point and the tangent at this point in the space of spheres. Then, we propose iterative algorithms (in the space of spheres) to compute (in 3D space) some characteristic circles of a Dupin cyclide which blends two particular canal surfaces. As a singular point of a Dupin cyclide is a point at infinity in the space of spheres, we use the massic points defined by Fiorot. As we subdivide conic arcs, these algorithms are better than the previous algorithms developed by Gamier and Gentil.

• 出版日期2013-2
• 单位中国地震局