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Bergh J., Teillaud M. (Ed) — Effective Computational Geometry for Curves and Surfaces
Bergh J., Teillaud M. (Ed) — Effective Computational Geometry for Curves and Surfaces



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Название: Effective Computational Geometry for Curves and Surfaces

Авторы: Bergh J., Teillaud M. (Ed)

Аннотация:

The intent of this book is to settle the foundations of non-linear computational geometry. It covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology.

Each chapter provides a state of the art, as well as a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and efficient in practice.

References to open source software and discussion of potential applications of the presented techniques are also included.

This book can serve as a textbook on non-linear computational geometry. It will also be useful to engineers and researchers working in computational geometry or other fields, like structural biology, 3-dimensional medical imaging, CAD/CAM, robotics, and graphics


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 360

Добавлена в каталог: 03.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha$-complex      238
$\alpha$-shape      238
$\varepsilon$-sample      202 248
$\varepsilon$-sample, weak $\varepsilon$-sample      203
Abstract Voronoi diagram      92 109
Additively weighted Voronoi diagram      88
Affine diagrams      80
Algebraic numbers      119
Ambient isotopy      184
Anisotropic Voronoi diagram      86
Apollonius diagram      38 88
Arithmetic      118
Bentley — Ottmann sweep      4 7
Betti numbers      285
Betti numbers, dependence on coefficient field      294
Betti numbers, incremental computation      290
Betti numbers, of a tree      286
Betti numbers, of the 2-sphere      286
Betti numbers, of the projective plane      293
Betti numbers, of the torus      287
Betti numbers, topological invariance      289
Bezout resultant      38
Boolean set-operation      55
Boundary operator      284
Boundary Representation      49
BRep      see “Boundary Representation”
CAD      see “Cylindrical algebraic decomposition”
Chain homotopy      292
Chain map      291
Chew’s algorithm for Delaunay mesh refinement      202
Closed ball property      see “Topological ball property”
Codimension      297
Collapse      292
Collapse, elementary      292
Collapse, simplicial      292
Complex, simplicial      280
Constructive solid geometry      49
contour      307
Contour tree      307
Contractible      282
Convergence of interval arithmetic      191
Core library      35
Correctness of meshing algorithms      183
Critical point      223 243 298
Critical point, in a direction      211
Critical point, index      244
Critical point, maximum      300
Critical point, minimum      300
Critical point, non-degenerate      300
Critical point, saddle      300
Critical value      223 298
Cylindrical algebraic decomposition      5 38 47 48
Davenport — Schinzel sequence      23
Delaunay refinement by Chew’s algorithm      202
Delaunay triangulation      74 235
Delaunay triangulation, restricted      201 238
Descartes method      38
Design pattern      25
Design pattern, observer      27
Design pattern, visitor      32
Differential      295
Distance function to sample points      243
Duality      74
Euler characteristic      280
Excursion set      see “Lower level set”
Fiber      185
Filters      121
filters, dynamic      122
filters, static      122
Floating point      119
Flow      244
functor      34
Gabriel simplex      237
General position      195 234
Generalized polygons      55
generic programming      25 31 314
Global parameterizability      191
Gradient vector field      303
Grazing intersections      195
Hausdorff distance      251
Height function      298
hessian      299
Homeomorphism      249 279
Homologous      285
Homology      282
Homology vector space      285
Homotopy      250 281
Homotopy equivalence      282
Hybrid motion-planning      58
IEEE 754 norm      119
Implicit function theorem      299
Implicit surface      182
Inclusion property      120
Index, Morse index      300
Integers      118
Interpolation, scattered data interpolation      182
Interval arithmetic      120 190
Isolating interval      19
isosurface      182
Isotopy      184 250 282
Jacobi curve      4 20 49
Johnson-Mehl diagrams      88
Join tree      308
Level set      223 301
Level set, lower level set      301
Lipschitz function      205
Local feature size      202 247
Lower envelope      70
Lower level set      301
Map (continuous function)      279
Marching Cubes      188
Maximum      300
Medial axis      110 244
Medial axis, medial axis transform      246
Minimum      300
Mobius diagram      81
Morse function      300
Morse function, genericity      302
Morse function, turning a function into a Morse function      223
Morse inequalities      302
Morse lemma      301
Morse number      300
Morse theory      223 295
Morse — Smale complex      306
Morse — Smale function      305
Multiplicatively weighted Voronoi diagram      82
Natural neighbor interpolation      182
Natural neighbors      241
Nef polyhedra      55
Numerical difficulty      208
observer design pattern      27
One-root number      12 14—16 20
Oriented simplex      280
Point location algorithm, landmarks      23 31 33
Point location algorithm, walk      23 31 40
Polarity      75
Pole (Voronoi center)      207 236
Power      79
Power diagram      79 241
Quadratic Voronoi diagram      87
Randomized Incremental Construction      53
Rational numbers      119
Rational univariate representation      47
Real numbers      118
Reeb graph      307
Regular triangulation      80 241
Regular value      298
Remeshing      213
Restricted Delaunay triangulation      201
Rounding mode      120
Saddle point      223 300
Sample, $\psi$-sample      202
Sample, $\varepsilon$-sample      202 248
Sample, weak $\psi$-sample      203
Sample, weak $\varepsilon$-sample      203
Scattered data interpolation      182
Seed triangle      206
Silhouette      210
simplex      279
Simplex, d-dimensional      279
Simplex, oriented      280
Simplicial collapse      292
Simplicial complex      280
Simplicial homology      282
Simplicial k-chain      283
Simplicial k-cycle      284
Simply connected      282
Sliver tetrahedron      235
Smooth surface      295
Snyder’s meshing algorithm      191—196
Space of spheres      75
Spherical diagrams      84
Split tree      309
Stable manifold      244 304
Sturm sequences      4 19 47
Subcomplex      280
Submanifold      297
Surface Delaunay ball      201
Surface extraction      182
Surface network      306
Surface, implicit      182
Surface, smooth      295
Sylvester matrix formulation      38
Systems of equations, zero-dimensional      213
Tangent space      297
Tangent vector      297
Topological ball property      209 228 241
Topological space      278
traits      25—28 30 32—34 40 314 315
Triangulation      280
Tubular neighborhood      185 202 247
Unstable manifold      304
Vertical decomposition      42
visitor design pattern      32
Voronoi diagram      72 235
Voronoi diagram, restricted      238
Voronoi hierarchy      106
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