Wrapping ellipses around a convex skeleton

Abstract

Let F and G denote two closed convex curves in the (X,Z)-plane and in the (Y,Z)-plane, correspondingly, that are symmetric about the Z-axis and cross at two points. Let S denote the solid that results from wrapping (X Y)-parallel ellipses around F and G. SurprisinglyS need not be convex (though all intersections with planes containing the Z-axis are!). We analyze under which condition the solid S is convex, and provide one necessary and one sufficient criterion that are easy to use in practice.

Keywords:

• Convexity
• solid modelling

^∗ This work was partially supported by the Deutsche Forschungsgemeinschaft, grant K1 655/1-2.

^∗ This work was partially supported by the Deutsche Forschungsgemeinschaft, grant K1 655/1-2.

Notes

^∗ This work was partially supported by the Deutsche Forschungsgemeinschaft, grant K1 655/1-2.