6533b827fe1ef96bd1285ab9

RESEARCH PRODUCT

Blending Planes and Canal Surfaces Using Dupin Cyclides

Lucie DruotonRemy BesnardRémi LangevinHerve MarcellierLionel Garnier

subject

Surface (mathematics)GeneralizationComputer sciencePlane (geometry)Dupin cyclideGeometrySPHERESMathematics::Differential GeometrySymmetry (geometry)Curvature

description

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 a cyclide symmetry plane used for the blend. Each algorithm uses one of the two symmetry planes of a cyclide constructed with the centres of three spheres or orthogonal to the first plane and to the one containing the circle of curvature of the canal surface.

yearjournalcountryeditionlanguage
2011-01-01
https://doi.org/10.1007/978-3-642-22027-2_33