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One way to advance the science of computational geometry is§to make a comprehensive study of fundamental operations that§are used in many different algorithms. This monograph§attempts such an investigation in the case of two basic§predicates: the counterclockwise relation pqr, which states§that the circle through points (p, q, r) is traversed§counterclockwise when we encounter the points in cyclic§order p, q, r, p,...; and the incircle relation pqrs, which§states that s lies inside that circle if pqr is true, or§outside that circle if pqr is false. The author, Donald§Knuth, is one of the greatest computer scientists of our§time. A few years ago, he and some of his students were§looking at amap that pinpointed the locations of about 100§cities. They asked, "Which ofthese cities are neighbors of§each other?" They knew intuitively that some pairs of cities§were neighbors and some were not; they wanted to find a§formal mathematical characterization that would match their§intuition.This monograph is the result.
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