## Computational Geometry in CThis is the newly revised and expanded edition of the popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. A new "Sources" chapter points to supplemental literature for readers needing more information on any topic. A novel aspect is the inclusion of working C code for many of the algorithms, with discussion of practical implementation issues. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The code in this new edition is significantly improved from the first edition, and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp. |

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### Contents

II | 1 |

III | 11 |

IV | 16 |

V | 24 |

VI | 27 |

VII | 32 |

VIII | 44 |

X | 47 |

XXXVII | 169 |

XXXVIII | 179 |

XXXIX | 182 |

XL | 191 |

XLI | 193 |

XLII | 194 |

XLIII | 199 |

XLIV | 201 |

XI | 51 |

XII | 56 |

XIII | 58 |

XIV | 63 |

XV | 64 |

XVI | 66 |

XVII | 68 |

XVIII | 69 |

XIX | 72 |

XX | 87 |

XXI | 88 |

XXII | 91 |

XXIII | 96 |

XXIV | 101 |

XXVI | 109 |

XXVII | 117 |

XXVIII | 146 |

XXIX | 149 |

XXX | 150 |

XXXI | 153 |

XXXII | 155 |

XXXIV | 157 |

XXXV | 161 |

XXXVI | 165 |

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### Common terms and phrases

adjacent angle arbitrary Area2 arrangement bool boundary cell Chapter collinear complexity computational geometry cone constructed convex hull convex polygon coordinates counterclockwise crossings cube data structure define Delaunay triangulation deleted Design an algorithm determined diagonal dual ear tip Edelsbrunner endpoints Equation example Exercise face floating-point halfplane horizontal implementation incremental algorithm independent set inside integer interior intersection point ladder Lemma length linear loop lower bound medial axis Minkowski sum monotone mountains monotone polygon motion planning moving nearest neighbor nodes nonconvex number of vertices O(n logn obstacles orthogonal polygon output partition plane pointer polyhedra polyhedron polytope problem programming proof query QuickHull random reachability region regular polytopes rightmost robot Section segment set of points shortest path shown in Figure sorting stack star polygons tangent tetrahedron Theorem three dimensions tPointi trapezoid tree two-dimensional typedef vector vertex visibility graph Voronoi diagram

### Popular passages

Page 351 - A. Aggarwal, LJ Guibas, J. Saxe, and PW Shor. A linear-time algorithm for computing the Voronoi diagram of a convex polygon. Discrete Comput.