Geometric Fundamentals

  • Michael Joswig
  • Thorsten Theobald
Part of the Universitext book series (UTX)


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.


Projective Space Ideal Point Projective Geometry Projective Transformation Affine Plane 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Michael Joswig
    • 1
  • Thorsten Theobald
    • 2
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Institut für Mathematik, FB 12Johann Wolfgang Goethe-UniversitätFrankfurt am MainGermany

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