6533b834fe1ef96bd129cdcf
RESEARCH PRODUCT
Iterative construction of Dupin cyclides characteristic circles using non-stationary Iterated Function Systems (IFS)
Lucie DruotonRémi LangevinLionel Garniersubject
Pure mathematicsEnvelope of spheresMathematical analysisDupin cyclideDupin cyclideTangent[ INFO.INFO-GR ] Computer Science [cs]/Graphics [cs.GR]Singular point of a curveComputer Graphics and Computer-Aided DesignIndustrial and Manufacturing Engineering[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]Computer Science ApplicationsCircleIterated function systemDefinite symmetric bilinear formConic sectionSpace of spheresSubdivisionPoint (geometry)Mathematics::Differential GeometryPoint at infinityEnvelope (mathematics)Mathematicsdescription
International audience; 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 J.C. Fiorot. As we subdivide conic arcs, these algorithms are better than the previous algorithms developed by Garnier and Gentil.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-10-31 |