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Boissonnat J.D., Yvinec M. — Algorithmic Geometry
Boissonnat J.D., Yvinec M. — Algorithmic Geometry



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Название: Algorithmic Geometry

Авторы: Boissonnat J.D., Yvinec M.

Аннотация:

The design and analysis of geometric algorithms has seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD. The goal of this book is twofold: first to present a coherent and systematic treatment of the foundations; second to present algorithmic solutions to problems that are simple to state but which nevertheless are applicable in practical situations. The prerequisites for using the book are few which will make it ideal for teaching advanced courses in computational geometry.


Язык: en

Рубрика: Computer science/Алгоритмы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 544

Добавлена в каталог: 16.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accelerated algorithm      88 495
Acceptable line      236
Ackermann's function      7 367
adjacency      141 252
Adjacency, graph      177 202 267
Admissible path      498
Affine, combination      134
Affine, diagram      455
Affine, hull      134
Affine, independence      134
Algorithm, accelerated      88 495
Algorithm, adaptive      5
Algorithm, divide-and-conquer      35 208 371 383 416 507
Algorithm, dynamic      99 193 227 446 508
Algorithm, incremental      182 274 308 342 343 357
Algorithm, lazy      128
Algorithm, off-line      67
Algorithm, on-line      77 348 375 414 446 447 489
Algorithm, output-sensitive      38 245
Algorithm, randomized      65
Algorithm, sweep      37 488
Alternating sequence      367
Amortized analysis      6
Analysis, amortized      6
Analysis, backward      58 93
Analysis, randomized      6 67 79 105 190 201
Annulus of minimum area      245
Arrangement of hyperplanes      333 366
Arrangement of segments      365
Arrangement of triangles      387
Arrangement, convex hull of      360
Arrangement, projective      356
Arrangement, simple      333
Arrangement, zone      337 360
Art Gallery Problem      297
Backward analysis      58 93
Ball, intersection      445
Ball, topological      253
Ball, union      445
Biregion      93 107 203
Bisection      245
Bisector of line segments      484 508
Bisector, $L_1$      464
Bisector, hyperbolic      471 475
Bisector, perpendicular      423
Bitangent      210 227
Boundary of a complex      252
Boundary, non-trivial      382 383
Canonical triangulation      171 357
Caratheodory's theorem      168
Cell of an arrangement      371 404 417
Cell, complex      253 333 423 455
Co-cube      463
COMPLEX      251
Complex of cells      253 333 423 455
Complex of simplices      253
Complex, Delaunay      433
Complex, homogeneous      252
Complex, pure      252
Complex, regular      474
Complexity, average-case      4
Complexity, output-sensitive      5
Complexity, worst-case      4
Conflict      47
Conflict, graph      67
Conflict, list      73
Conformal triangulation      509
CONSTRAINED TRIANGULATION      277 312 508
Convex hull      131 134
Convex hull of a polygon      222
Convex hull of an arrangement      360
Convex hull of objects      382
Convex hull of two 3-polytopes      213
Convex hull, divide-and-conquer      212
Convex hull, dynamic      193 227
Convex hull, incremental      182
Convex hull, lower      173
Convex hull, on-line      186
Convex hull, output-sensitive      237 245
Convex hull, upper      173
Convex, function      59
Convex, set      134
Curve      44 93 384
Curve of moments      153 265
Cyclic polytope      153
Davenport — Schinzel sequences      367
Decision tree      10
Decomposition in convex parts      292 391
Decomposition of a lower envelope of triangles      397
Decomposition of a polygon      90 95 285
Decomposition of a polyhedral region      315
Decomposition of line segments      41 71 84 114
Decomposition of line segments, complete      42 92
Decomposition of line segments, dynamic      125
Decomposition of line segments, lazy      128
Decomposition of line segments, simplified      43
Decomposition of surfaces      417
Decomposition of triangles      388 408 416
Decomposition, geodesic      297
Decomposition, hierarchical      297
Decomposition, simplicial      319
Dehn — Sommerville relations      150 169 170 356
Delaunay, complex      433
Delaunay, triangulation      434
Delaunay, triangulation, flipping      439 446 447
Determinant      161 172
Determinant of a region      101 490
Determinant, van der Monde      153
Diagram for the $L_1$ metric      475
Diagram for the $L_\infty$ metric      475
Diagram, affine      455
Diagram, higher order power diagram      454
Diagram, power      452 455
Diagram, weighted      457 461 474
Diameter      228
DICTIONARY      16 25
Dictionary, augmented      16 25
Dictionary, persistent      30 359
Disk      269
Disk, motion planning      497
Distance $L_1$      463
Distance $L_\infty$      466
Distance in hyperbolic space      470
Distance, point to segment      482
Distance, polygonal      507
Distance, polyhedral      475
Distance, quadratic      456
Divide-and-conquer      35 416
Divide-and-conquer, a single cell      383
Divide-and-conquer, convex hull      208 212
Divide-and-conquer, lower envelope of functions      371
Divide-and-conquer, lower envelope of triangles      416
Divide-and-conquer, union of polygons      45
Divide-and-conquer, Voronoi diagram      507
Domain of a complex      252
Domain of influence      48
Domain, feasible      232
Duality      142 268
Duality, hyperbolic diagram      476
Dynamic, algorithm      99
Dynamic, convex hull      193 227
Dynamic, decomposition of segments      125
Dynamic, perfect hashing      26 29
Dynamic, Voronoi diagram      446 508
Edge of a complex      251
Edge of a polytope      135
EMST (Euclidean minimum spanning tree)      447
Euler characteristic      258 270
Euler relation      147 170 173 258 269 270
Event queue      37
Exterior of a polygon      256
Exterior of a polyhedron      257
Extreme points      202 235
Face of a complex      251
Face of a polytope      134 135
Face of a Voronoi diagram      457 464 466 470 482
Face of an arrangement      356 366 388
Face, inner      404
Face, outer      404
Face, popular      404
Face, proper      135
Face, singular      253
Facet of a polytope      135
Feasible domain      232
Function Ackermann      7 367
Function, convex      59
Function, hash function      29
General position for hyperplanes      146 333
General position for points      146
General position for spheres      453
General position, $L_1$-general      475
General position, $L_2$-general      424 482
General position, $L_\infty$-general      467 475
Geodesic decomposition      297
Gift-wrapping      213
Graph      16
Graph of adjacencies      177 202 267
Graph of conflicts      67
Graph of incidences      176 267
Graph of influence      78
Graph of influence (augmented)      101
Greatest empty rectangle      473
Hashing, hash functions      29
Hashing, perfect dynamic      26 29
Helly's theorem      168
Hierarchical decomposition      297
Hierarchical representation      228 293
history      96
Homogeneous complex      252
Hull, affine      134
Hull, convex      131 134
Hull, lower      173
Hull, upper      173
Hyperbolic bisector      475
Hyperbolic duality      476
Hyperbolic space      470 476
Hyperbolic Voronoi diagram      470 508
Hyperplane, arrangement      333
Hyperplane, radical      430
Hyperplane, supporting      135 169
incidence      141 252
Incidence, graph      176 267 269
Incremental arrangement      342 343 357
Incremental convex hull      182
Incremental triangulation      274 308
Independence, affine      134
Influence, domain      48
Influence, graph      78
Influence, graph (augmented)      101
Inner face      404
Inner vertex      62
Interior of a polygon      256
Interior of a polyhedron      257
Interior of a polytope      134
Interior of a sphere      425
Intersection of balls      445
Intersection of convex polygons      229
Intersection of half-spaces      173 203 245
Intersection of line segments      38
Intersection of polygonal regions      44
Intersection, miscellaneous      229
Jordan's Theorem      268
k-set      347 361
k-th element (selection of)      45
Lazy decomposition of segments      128
Lazy sweeping      290
Level in arrangements of hyperplanes      346 361 362
Level in arrangements of lines      361
Level in arrangements of simplices      417
Level in arrangements of triangles      417
Level in arrangements, surface of      346
Linear programming      231
LIST      14
Localization in a planar map      293
Lower envelope of cones      473
Lower envelope of functions      368
Lower envelope of half-lines      371
Lower envelope of line segments      370 381
Lower envelope of simplices      416
Lower envelope of surfaces      416
Lower envelope of triangles      393
Lower hull      173
LP-type problems      247
Mapping, projective      157
Maximal polytope      172
Maximum inscribed sphere      247
Minimum enclosing circle      246 445
Minkowski sum      174
moment      56
Moment, curve      153 265
Moment, theorem      57
Monotone polygon      279
Motion planning of a disk      497
Motion planning of a manipulator      384
Motion planning of a polygon      382 508
Motion planning of a polyhedron      418
Nearest neighbor      444 445
Nearest neighbor, on-line      445
Nearest neighbor, queries      444
Non-local subset of regions      59
Non-trivial boundary      382 383
Object      47
Off-line algorithm      67
On-line, $\leq$ k-levels      348
On-line, a single cell      375 414
On-line, algorithm      77
On-line, convex hull      186
On-line, decomposition of line segments      84
On-line, Delaunay triangulation      446 447
On-line, Voronoi diagram      432 446 489
Onion peeling      228
Orientation in a projective space      161
Orientation of a 2-triangulation      257
Orientation, clockwise and counter-clockwise      206 207
Orientation, direct and indirect      206 207
Orthogonal spheres      428
Outer face      404
Outer vertex      62
Output-sensitive, complexity      5
Output-sensitive, convex hull      237 245
Output-sensitive, segment intersections      38
Output-sensitive, triangulation      312
Paraboloid      172 426
Pencil of spheres      468
Perpendicular bisector      423
Persistent dictionary      30 359
Planar map      269
Poincare disk      476
Poincare half-space      470
Polarity with respect to a paraboloid      172 427
Polarity, image      142
Polarity, polytope      143
Polarity, projective      157
Polarity, transformation      141
Polygon      256
Polygon, convex hull of      222
Polygon, decomposition of      90 95
Polygon, intersection      44
Polygon, monotone      279
Polygon, star-shaped      294
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