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Goldman R., Krasauskas R. — Topics in algebraic geometry and geometric modeling
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Название: Topics in algebraic geometry and geometric modelingАвторы: Goldman R., Krasauskas R. Аннотация: Surveys, tutorials, and research papers from a summer 2002 workshop examine a range of topics in algebraic geometry and geometric modeling. Papers are divided into sections on modeling curves and surfaces, multisided patches, implicitization and parametrization, topic varieties, and mixed volume and resultants, and papers from both disciplines are included in each section. Some specific topics include polar forms, interference analysis of conics and quadrics, rational M-patches and tensor-border patches, and toric ideals, real toric varieties, and the moment map. A translation of an 1841 paper which foreshadows the modern application of mixed volumes in algebraic geometry is also included.
Язык: Рубрика: Математика /Алгебра /Алгебраическая геометрия /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2003Количество страниц: 366Добавлена в каталог: 12.03.2005Операции: Положить на полку |
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220 245 133 149 248 1-parameter subgroup 205 Adjoints 191 Affine space 203 Approximate implicitization 169 Approximate implicitization, accuracy 177 Approximate implicitization, convergence rate 176 Approximate implicitization, weak form 180 Automobile design 56 Barycentric coordinates 11 12 14 93 174 Barycentric coordinates, facial behavior 95 Barycentric coordinates, linear precision 94 Barycentric coordinates, non-negative 93 Barycentric coordinates, uniqueness 96 Base point 103 135 140 230 Base point, conditions imposed by 144 Base point, degree of 141 164 Base point, differential conditions for 167 Base point, multiplicity of 141 164 Base point, rectangular 155 162 Base point, triangular k-ple 155 162 Bernstein basis 4 7 22 170 Bernstein basis, bivariate 12 Bernstein coefficients 4—7 13 20 22 Bernstein polynomial for lattice polygon 71 72 Bernstein polynomial, depth of 80 Bernstein polynomial, properties of 71 Bernstein — Bezier form 41 Bernstein's theorem 14—16 293 310 311 313 315 317 318 Bernstein, D.N. 308 317 Bezier control points 4 6 7 11 12 Bezier curve 4 6—8 10 11 226 231 Bezier patch 226 231 Bezier patch, rectangular 80 Bezier patch, tensor product 14 80 Bezier patch, toric 73 Bezier patch, triangular 11 12 Bezier surface 10 13 Bezout's formula 194 Bezout's theorem 294 310 313 Bezoutian 329 Bicubic patch 157 Binomial system 296—299 316 BKK bound 355 BKK bound, affine case 360 BKK bound, genericity assumptions 361 Blending 44 Blending functions 40 42 152 Blossom 3 4—14 16 20-24 Blossom, affine blossom 9 Blossom, homogeneous blossom 9 13 14 16 Blossoming 3—14 Blossoming of toric Bezier patch 84 Blossoming, blossoming axioms 4 10 14 Blow-up of the origin 215 Blowing-up 103 Blowing-up, T-equivariant 270 Castelnuovo's criterion 190 Categorical quotient 214 217 Cayley trick 305 cell 358 Cell, mixed 359 Cell, unmixed 359 CHARACTER 204 Characteristic polynomial 26 30 Collision detection for conies 26 27 Collision detection for quadrics 28 Combinatorial coefficient 344 Cone, dimension of 206 Cone, dual of 207 Cone, edge of 206 Cone, face of 206 Cone, facet of 206 Cone, maximal 212 Cone, rational polyhedral 206 Cone, simplicial 212 Cone, smooth 212 Cone, strongly convex 206 Control point 40 43 102 229 231 Convergence rate, approximate implicitization 176 Convex polytope 93 Coordinate ring 209 Corner cutting 157 de Casteljau algorithm 5 de Casteljau algorithm for mixed volume 21 de Casteljau algorithm for toric Bezier patches 77 de Casteljau algorithm, blossomed version 6 20 21 de Casteljau algorithm, differentiation 10 de Casteljau algorithm, evaluation 5—7 de Casteljau algorithm, homogenized 9 de Casteljau algorithm, pyramid 13 22 de Casteljau algorithm, subdivision 7 de Casteljau algorithm, tetrahedral 11 14 Deficiency values 154 164 Del Pezzo surface 189 Depth of polygonal array 75 Derivative ideal 153 162 166 Differential surface 39 Directional derivative 40 46 Discriminant 304 305 Dual cone 207 Dual functional property 6 13 Dual polytope 219 Ehrhart polynomial 221 Euler's formula 162 Facet of a cone 206 Facet of a polytope 217 Facet variable 219 244 Fan 211 225 244 Fan, normal 217 Fan, normal, of a polytope 226 236 Fan, support of 212 Fat point 162 Genericity 294 296 299 302 313 Genus 190 Genus, arithmetic 190 Genus, formula 194 Genus, geometric 190 Genus, plurigenus 190 Geometric continuity 37 Geometric quotient 214 Geometric smoothness 56 Geometrically continuous function 38 40 49 51 Geometrically continuous octahedron 38 Geometrically continuous rational function 44 Geometrically continuous spline 41 Geometrically continuous surface complex 38 50 Gordan's lemma 207 Groebner basis 153 Groups generated by real structures 275 Hilbert polynomial 133 Hilbert syzygy theorem 133 Implicit degree 154 164 Implicitization 90 131 151 Implicitization approximate 169 Implicitization bezoutian 335 Implicitization surface 330 Implicitizationsyzygy 332 334 Implicitizationtoric patch 336 Incidence variety 323 INDEX function 30 Intersection 339 Intersection algorithm 8 Intrinsic parametric degree 194 Inverse image 337 Irregularity 190 Itenberg, I. 317 Key function 105 Khetan, A. 306 317 Khovanskii, A.G. 317 Kodaira dimension 190 Koszul complex 137 Koszul syzygy 137 140 Kushnirenko's theorem 299 302 307 308 310 315 Kushnirenko, A.G. 299 Lattice point 207 Lattice polygon 70 Lattice polytope 217 Laurent monomial 204 Laurent polynomial 204 Linear precision 239 Local complete intersection 140 162 M-patch 68 104 M-patch, 107 M-patch, 106 M-patch, 106 M-patch, 106 M-patch, 106 M-patch, 106 Mass-point 67 74 Minding's formula 353 355 Minding, F. 311 351 Minkowski sum 15 21 22 75 Minkowski sum decomposition 87 Mixed area 313 314 355 Mixed area, compute via a mixed subdivision 357 Mixed area, compute via inclusion-exclusion 357 Mixed area, compute via recursion 357 Mixed area, definition of 357 Mixed cell 312 314 315 Mixed subdivision 312—314 316 358 Mixed volume 14—23 311 313 317 Mixed volume, axioms 15 Moment map 238 Moving line 132 Moving plane 135 152 Moving quadric 135 152 332 Moving surface 152 Multi-sided hole 56 68 Multi-sided patch 56 68 101 Multi-sided patch, M-patch 68 Multi-sided patch, S-patch 68 109 Multi-sided patch, Sabin's patch 68 124 Multi-sided patch, toric Bezier patch 68 Multiaffine 4 11 Multiplicative equivalence 276 Multiplicity 95 Nested polygon net 105 Newton polygon 70 156 355 Newton polytope 15 16 294 295 Newton, I. 355 Non-degenerate configurations of conies 32 33 Non-degenerate configurations of quadrics 34 Normal fan 217 244 Normal vector, inward pointing 206 217 357 Normal vector, outward pointing 357 Parametrization 186 330 Parametrization, problem 186 Parametrization, proper 186 Parametrization, quantitative theory 193 Parametrization, rational 246 Parametrization, universal rational 241 249 258 Pencil 187 Polar form 3 14 Polar polytope 219 Polynomial bases 170 Polynomial bases, Bernstein basis 170 Primitive element 206 Primitive set of edge generators 213 Principal orbit coordinates 270 Projective space 67 204 Puiseux series 355 Puiseux series with decreasing exponents 353 356 357 Pure degree surface 152 Quadratic form 29 189 Quadratic form, index of 30 Quadratic map 29 Quadratic map, classification 30 Quadratic map, non-degenerate 29 Quadric moving 152 Rational map to smooth toric variety 259 Rational mapping 102 Rational motion 26 Rational parametrization 246 Rational parametrization, universal 241 249 258 Rational variety 229 231 Rationality 186 Real part 267 Real structure 267 Real structure, canonical real structure 267 Real structure, toric real structure 268 271 Real structure, toric real structure, multiplicative part 272 Real structure, toric real structure, multiplicative real structure 272 Real variety 267 Regularity 134 139 145 Regularity for 139 148 165 Rendering algorithm 8 Reparametrization 114 Residue at a vertex 346 Resultant 149 305 322 355 Resultant, anisotropic 326 Resultant, bezoutian 329 Resultant, projective 325 Resultant, residual 327 Resultant, sparse 14 15 90 Resultant, toric 15 327 S-patch 68 109 Sabin's patch 68 124 Saturation 143 163 165 Self-intersections 178 Semigroup algebra 209 Separation conditions for conies 26 Separation conditions for quadrics 27 28 Shub, M. 310 simplex 299 302 310 simplification 186 Singularity 339 Spline surface 55 Steiner surface 242 Subdivision 4 5 8 13 Subdivision Surface 58 Support 295 Surface, artifact 58 Surface, Bezier 10 13 Surface, curvature 56 Surface, Del Pezzo 189 Surface, fairness 56 Surface, implicitization 330 Surface, moving 152 Surface, spline 55 Surface, Steiner 242 Surface, subdivision 58 Surface, toric 194 Syzygy 132 334 Syzygy module 132 Syzygy vanishes at basepoints 141 T-equivariant 269 T-equivariant, T-equivariant blowing-up 270 Tangent space 46 49 Tensor product surface 135 152 tensor Tensor-border net 114 Tensor-border patch 68 114 Toric automorphism 271 Toric automorphism, elementary toric automorphism 270 Toric automorphism, multiplicative automorphism 270 Toric Bezier patch 68 73 Toric Bezier patch, blossoming of 84
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