Floating Body, Illumination Body, and Polytopal Approximation
نویسنده
چکیده
Let K be a convex body in Rd and Kt its floating bodies. There is a polytope that satisfies Kt ⊂ Pn ⊂ K and has at most n vertices, where n ≤ e vold(K \Kt) t vold(B d 2 ) . Let Kt be the illumination bodies of K and Qn a polytope that contains K and has at most n (d−1)-dimensional faces. Then vold(K t \K) ≤ cd vold(Qn \K), where n ≤ c dt vold(K t \K).
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