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Goldman R., Krasauskas R. — Topics in algebraic geometry and geometric modeling
Goldman R., Krasauskas R. — Topics in algebraic geometry and geometric modeling

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Название: Topics in algebraic geometry and geometric modeling

Авторы: 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: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 366

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Delta$-monomial      220 245
$\mu$-basis      133
$\mu$-basis, special      149
$\Sigma_{\Delta}$-irreducible      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 $k\times l$-pie      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, $P^n_5$-patch      107
M-patch, $R_m^n$-patch      106
M-patch, $U^n_5$-patch      106
M-patch, $U^n_6$-patch      106
M-patch, $U^n_7$-patch      106
M-patch, $U^n_S$-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 $\mathbb{P}^1 \times \mathbb{P}^1$      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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