Geodesic
A Class of Star-Shaped Bodies
Canadian mathematical bulletin, Tome 2 (1959) no. 3, pp. 175-180

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The more important properties of the class κ of all bounded convex bodies in E3 with non-empty interior include: uniform approximability by polyhedra, existence of volume and surface area, and Blaschke's selection principle, [l ], [2 ]. In this note we define and consider a class H of star-shaped bodies in E3, which enjoys many properties of κ, among them the above-mentioned ones, and is considerably larger. Roughly speaking, H consists of closed bounded sets in E3 with nonempty interior, whose boundary is completely visible from every point of a set with non-empty interior. It turns out that H is identifiable with the class of all real-valued positive functions on the sphere S3 which satisfy a Lipschitz condition. 
Melzak, Z.A. A Class of Star-Shaped Bodies. Canadian mathematical bulletin, Tome 2 (1959) no. 3, pp. 175-180. doi: 10.4153/CMB-1959-023-6
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     title = {A {Class} of {Star-Shaped} {Bodies}},
     journal = {Canadian mathematical bulletin},
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     year = {1959},
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     doi = {10.4153/CMB-1959-023-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1959-023-6/}
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