## Computational Geometry: Algorithms and ApplicationsComputational geometry emerged from the ?eld of algorithms design and analysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The success of the ?eld as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains—computer graphics, geographic information systems (GIS), robotics, and others—in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or dif?cult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simpli?ed many of the previous approaches. In this textbook we have tried to make these modern algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self-study. |

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### Contents

2 | |

Line Segment Intersection | 19 |

Polygon Triangulation | 45 |

Linear Programming | 63 |

Orthogonal Range Searching | 95 |

4 | 102 |

7 | 109 |

Point Location | 121 |

4 | 180 |

Delaunay Triangulations | 191 |

More Geometric Data Structures | 219 |

Convex Hulls | 243 |

Binary Space Partitions | 259 |

Robot Motion Planning | 283 |

Quadtrees | 307 |

Visibility Graphs | 323 |

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### Common terms and phrases

3-dimensional associated structure beach line bound boundary breakpoints BSP tree canonical subsets Chapter compute configuration space construction contains convex hull convex polygon corresponding data structure defined Delaunay triangulation denote disjoint doubly-connected edge list endpoint face facets Figure geometric graph half-edge half-plane Hence input inside interior intersection point interval tree kd-tree leaf Lemma lies line segments linear program mesh Minkowski sum motion planning number of edges number of reported O(nlogn objects obstacles partition tree pgoal pixel planar point location point q point set pointer problem prove pseudodiscs pstart quadtree query algorithm query point query range range queries range searching range tree recursive region robot search path search structure Section segment tree set of points shortest path square subdivision subtree sweep line Theorem total number trapezoidal map vertex vertical line visibility graph visible Vor(P Voronoi cell Voronoi diagram xmid y-coordinate