In this chapter we lay the geometric foundations that will serve as a basis for the topics that we shall meet later. The statements of projective geometry, in contrast to those of affine geometry, often allow a particularly simple formulation. The projective equivalence of polytopes and pointed polyhedra (Theorem 3.36) and Bézout’s Theorem (Theorem 8.27) on the number of intersections of two algebraic curves in the plane are good examples of this. We will also introduce the notion of convexity, which is an irreplaceable concept in linear computational geometry.
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