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The problem of the existence of an equi-partition of a curve in R n has recently been raised in the context of computational geometry (see [2] and [3]). The problem is to show that for a (continuous) curve Γ : [0, 1] → R n and for any positive integer N, there exist points t 0 = 0 < t 1 <. .. < t N −1 < 1 = t N , such that d(Γ(t i−1), Γ(t i)) = d(Γ(t i),… (More)

Let P be a convex polytope in R d , d = 3 or 2, with n vertices. We present linear time algorithms for approximating P by simpler polytopes. For instance, one such algorithm selects k < n vertices of P whose convex hull is the approximating polytope. The rate of approximation, in the Hausdorff distance sense, is best possible in the worst case. An analogous… (More)

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