6533b834fe1ef96bd129dfa1

RESEARCH PRODUCT

G1-Blend between a Differentiable Superquadric of Revolution and a Plane or a Sphere Using Dupin Cyclides

Sebti FoufouLionel GarnierYohan Fougerolle

subject

SuperellipsoidParametric surfacePlane (geometry)Mathematical analysisDupin cyclideGeometryBézier curveDifferentiable functionCurvatureComputational geometryMathematics

description

In this article, we present a method to perform G1-continuous blends between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. These blends are patches delimited by four lines of curvature. They allow to avoid parameterization problems that may occur when parametric surfaces are used. Rational quadratic Bezier curves are used to approximate the principal circles of the Dupin cyclide blends and thus a complex 3D problem is now reduced to a simpler 2D problem. We present the necessary conditions to be satisfied to create the blending patches and illustrate our approach by a number of superellipsoid/plane and superellipsoid/sphere blending examples.

yearjournalcountryeditionlanguage
2008-11-012008 IEEE International Conference on Signal Image Technology and Internet Based Systems
https://doi.org/10.1109/sitis.2008.73