Publisher's Synopsis
Excerpt from The Voronoi Methods for Motion-Planning: I. The Case of a Disc
Proof. First consider any point x in Q; let p belong to Near(x). Claim that for any point 2 on the open line-segment joining p to x, Near(z) {p}. This is because, given q in Near(z), d(x, q) d(x, p) d(x, z) d(z, p) d(x, z) therefore xzq is a straight angle.
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