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Bergh J., Teillaud M. (Ed) — Effective Computational Geometry for Curves and Surfaces
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Название: Effective Computational Geometry for Curves and SurfacesАвторы: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2007Количество страниц: 360Добавлена в каталог: 03.06.2008Операции: Положить на полку |
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238 238 202 248 203 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, 202 Sample, 202 248 Sample, weak 203 Sample, weak 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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