Geodesic
The Mean Width and Integral Geometric Properties of the Oloid
Journal for geometry and graphics, Tome 22 (2018) no. 2, pp. 149-161 Cet article a éte moissonné depuis la source Heldermann Verlag

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The oloid is the convex hull of two circles with equal radius in perpendicular planes so that the center of each circle lies on the other circle. We calculate the mean width of the oloid in two ways, first via the integral of mean curvature, and then directly. Using this result, the surface area and the volume of the parallel body are obtained. Furthermore, we derive the expectations of the mean width, the surface area and the volume of the intersections of a fixed oloid and a moving ball, as well as of a fixed and a moving oloid.
Classification : 53A05, 52A22, 52A15, 60D05
Mots-clés : Oloid, convex hull, integral of mean curvature, mean width, Steiner formula, parallel body, intrinsic volumes, principal kinematic formula 
@article{JGG_2018_22_2_JGG_2018_22_2_a0,
     author = {U. B\"asel },
     title = {The {Mean} {Width} and {Integral} {Geometric} {Properties} of the {Oloid}},
     journal = {Journal for geometry and graphics},
     pages = {149--161},
     year = {2018},
     volume = {22},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2018_22_2_JGG_2018_22_2_a0/}
}
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U. Bäsel . The Mean Width and Integral Geometric Properties of the Oloid. Journal for geometry and graphics, Tome 22 (2018) no. 2, pp. 149-161. http://geodesic.mathdoc.fr/item/JGG_2018_22_2_JGG_2018_22_2_a0/