## 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. |

### What people are saying - Write a review

User Review - Flag as inappropriate

i need some more information about T algorithm

User Review - Flag as inappropriate

This book is good but if had a solution guide for it's exercises, it would be perfect.

### Contents

I | 2 |

II | 3 |

III | 9 |

IV | 11 |

V | 14 |

VI | 16 |

VII | 19 |

VIII | 20 |

LX | 191 |

LXI | 193 |

LXII | 196 |

LXIII | 199 |

LXIV | 205 |

LXV | 208 |

LXVI | 214 |

LXVII | 215 |

IX | 29 |

X | 33 |

XI | 39 |

XII | 40 |

XIII | 41 |

XIV | 45 |

XV | 46 |

XVI | 49 |

XVII | 55 |

XVIII | 59 |

XIX | 60 |

XX | 63 |

XXI | 64 |

XXII | 66 |

XXIII | 71 |

XXIV | 76 |

XXV | 79 |

XXVI | 82 |

XXVII | 86 |

XXVIII | 89 |

XXIX | 91 |

XXX | 95 |

XXXI | 96 |

XXXII | 99 |

XXXIII | 105 |

XXXIV | 109 |

XXXV | 110 |

XXXVI | 111 |

XXXVII | 115 |

XXXVIII | 117 |

XXXIX | 121 |

XL | 122 |

XLI | 128 |

XLII | 137 |

XLIII | 140 |

XLIV | 143 |

XLV | 144 |

XLVI | 147 |

XLVII | 148 |

XLVIII | 151 |

XLIX | 160 |

L | 163 |

LI | 167 |

LII | 170 |

LIII | 173 |

LIV | 175 |

LV | 177 |

LVI | 179 |

LVII | 185 |

LVIII | 186 |

LIX | 188 |

LXVIII | 219 |

LXIX | 220 |

LXX | 226 |

LXXI | 231 |

LXXII | 237 |

LXXIII | 239 |

LXXIV | 243 |

LXXV | 244 |

LXXVI | 246 |

LXXVII | 250 |

LXXVIII | 253 |

LXXIX | 254 |

LXXX | 256 |

LXXXI | 257 |

LXXXII | 259 |

LXXXIII | 261 |

LXXXIV | 263 |

LXXXV | 264 |

LXXXVI | 268 |

LXXXVII | 271 |

LXXXVIII | 278 |

LXXXIX | 279 |

XC | 283 |

XCI | 284 |

XCII | 286 |

XCIII | 290 |

XCIV | 297 |

XCV | 299 |

XCVI | 303 |

XCVII | 305 |

XCVIII | 307 |

XCIX | 308 |

C | 309 |

CI | 315 |

CII | 318 |

CIII | 320 |

CIV | 323 |

CV | 324 |

CVI | 326 |

CVII | 330 |

CVIII | 331 |

CIX | 332 |

CX | 335 |

CXI | 336 |

CXII | 343 |

CXIII | 346 |

CXIV | 352 |

CXV | 353 |

357 | |

377 | |

### Other editions - View all

### Common terms and phrases

2-dimensional beach line BINARY SPACE PARTITIONS bound boundary BSP tree canonical subsets Chapter computational geometry conﬁguration space construction contains convex hull convex polygon corresponding data structure deﬁned deﬁnition Delaunay triangulation denote diagonal disc disjoint doubly-connected edge list efﬁcient endpoint event point face facets farthest-point Voronoi Figure ﬁnd ﬁnding ﬁrst Geom geometric graph half-edge half-planes Hence input interior intersection point kd-tree leaf Lemma lies line segments linear program mesh Minkowski sum motion planning number of reported O(nlogn objects obstacles optimal partition tree planar plane sweep point location point q pointer problem prove pseudodiscs pstart quadtree query algorithm query point random range queries range searching range tree recursive region robot search path search structure Section SEGMENT INTERSECTION segment tree set of points shortest path simple polygon split storage subdivision subtree sweep line Theorem total number trapezoidal map vertex Voronoi diagram y-coordinate

### Popular passages

Page 374 - Halperin, and MH Overmars. The complexity of the free space for a robot moving amidst fat obstacles. Comput. Geom. Theory Appl., 3:353-373, 1993.

Page 357 - Geom., 19:315-331, 1998. [2] PK Agarwal, M. de Berg, J. Matousek, and O. Schwarzkopf. Constructing levels in arrangements and higher order Voronoi diagrams. SIAM J. Comput., 27:654667, 1998.

### References to this book

Geometric Methods and Applications: For Computer Science and Engineering Jean H. Gallier Limited preview - 2001 |

Full-Chip Nanometer Routing Techniques Tsung-Yi Ho,Yaowen Zhang,Sao-Jie Chen No preview available - 2007 |