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Gallier J. — Geometric Methods and Applications: For Computer Science and Engineering
Gallier J. — Geometric Methods and Applications: For Computer Science and Engineering

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Название: Geometric Methods and Applications: For Computer Science and Engineering

Автор: Gallier J.

Аннотация:

As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics, which sometimes do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine geometry, projective geometry, Euclidean geometry, basics of differential geometry and Lie groups, and a glimpse of computational geometry (convex sets, Voronoi diagrams and Delaunay triangulations) and explores many of the practical applications of geometry. Some of these applications include computer vision (camera calibration) efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 587

Добавлена в каталог: 13.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^p$-continuous function      417 467
$C^\infty$-function      417
$G^n$-continuity      453
(n,s)-set      141
3-sphere $S^3$      249
Absolute points definition      133
Absolute quadric      137
Absolute quadric, use of      137
Absolute value      532
Acceleration vector $f''(t)$      423
action      12
Adjoint map      174 295
Adjoint of a matrix      300
Adjoint of f      174 175 194 296
Adjoint representation of G      404
Affine bijections      39 88
Affine combination      16
Affine combination definition      18
Affine combination of points      7
Affine curvature      454
Affine dependence      29
Affine dilatation      38
Affine form      44
Affine form definition      44
Affine frame      7 27 78
Affine frame with origin $a_0$, definition first version      28
Affine frame with origin $a_0$, definition second version      28
Affine geometry      vii viii 3 7
Affine geometry, a glimpse      40
Affine group      56
Affine group definition      38
Affine Hermitian space      297
Affine hyperplane      7 44
Affine hyperplane definition      25
Affine independence      7 26
Affine independence definition      27
Affine isometry      217
Affine isometry definition      217
Affine map      6 7 31 118 182
Affine map definition      31
Affine map representation in terms of a matrix      36
Affine normal      454
Affine patch definition      113
Affine space      6 11
Affine space definition      12
Affine space example, a line      14
Affine space example, a paraboloid of revolution      15
Affine space example, a plane      15
Affine structure, canonical      14
Affine structure, natural      14
Affine subspace      7
Affine subspace definition      20
Affine subspace, flat      21
Affinely dependent families      29
Affinely independent families      27
Algebraic arc length      425
Algebraic curvature      437 461
Algebraic curve      92
Algebraic geometry      87 93 103 105 114
Algebraic plane curves      105
Algebraic radius of curvature      438
Algebraic surface      92 105
Algebraic variety      92
Altitude of a point      136
angle      130
Angle of complex lines      136
Angle of lines      132 133
Angle of unit vectors      132
Angle of unit vectors definition      233
Antipodal map      255
Antipodal points      94
Applications of curves      452
Applications of Delaunay triangulations      283
Applications of Euclidean geometry      188 264
Applications of Lie groups      405
Applications of projective geometry      137
Applications of surfaces      518
Applications of Voronoi diagrams      283
Applications to robotics      61
Arbitrary field      72
Arc length      424
Artin, Emil      202
Associative algebra      250
Astroid      459
Asymptotic directions      502 521
Asymptotic directions definition      491
Asymptotic line      510 511
Asymptotic line definition      510
Axis of a projectivity      151
Axis of rotation      209 242
B-splines      452
Barycenter      3 7 16 72 77
Barycenter definition      18
Barycenter of a family of weighted points      18
Barycentric combination definition      18
Barycentric coordinates      276
Barycentric coordinates of x w.r.t. an affine frame definition      28
Base points of a pencil      159
Basis      8 78
Basis associated with a projective frame      98
Basis of $\vec{E}$      28
Basis, projective      98
Basis, vector space      27
Beltrami      336
Beltrami's pseudosphere      491
Berger      71
Berger and Gostiaux      415 466 467
Bertrand      464
Bertrand curves      462
Bezier sites      76
Bidual space      126
Bijection between E and its dual E*      172
Bijective affine maps      38
Bijective linear maps      38
Binormal vector      441
Birapport      121
Biregular point      423
Bisector hyperplane      270
Bisector line      268
Bisector plane      268 269
Block diagonalization of a normal linear map      316
Block diagonalization of a normal matrix      325
Block diagonalization of a skew self-adjoint linear map      320
Block diagonalization of a skew symmetric matrix      326
Block diagonalization of an orthogonal linear map      321
Block diagonalization of an orthogonal matrix      326
Boldface notation of vectors      14
Bolyai      2
Bonnet      483 503 523
Bonnet's formula      508
Bonnet's theorem      506
Boundary face of a simplex      275
Boundary of a simplex      275
Boy surface      114
Brianchon's theorem      155
Calabi      x 454 465 480
Camera calibration and Cayley's formula      136
Camera calibration problem      139
Camera calibration projective geometry      137
Camera extrinsic parameters      138
Camera intrinsic parameters      138
Camera position and orientation      138
Camera projection matrix      139
Camera reference frame      138
Canonical frame of $\mathbb{P}^1_\mathrm{K}$      100
Canonical isomorphism      173
Canonical projection      91
Caratheodory's theorem      29 64
Cardioid      436 460 462
Cartan      446
Cartan — Dieudonne Theorem      ix 197 198 212 228 246 294
Cartan — Dieudonne theorem affine isometries      229
Cartan — Dieudonne theorem Euclidean case      202
Cartan — Dieudonne theorem sharper version      323
Cartan, Elie      202
Catenary      456 476
Catenoid      475 521
Cauchy — Schwarz inequality      165 291
Caustics      462 527
Cayley      2 3 130
Cayley's formula      135 140
Cayley's representation of rotations      331
Center      138
Center of a circle      157
Center of curvature      428 447
Center of mass      19
Central dilatation      7
Central dilatation definition      38
Central projection      88 89
Centroid      53
Ceva's theorem      51
Change of basis      10
Change of frame      10
Chart      393
Chasles      130 198 223
Chasles's identity      16
Chevalley      368
Christoffel symbols      483 485 524
Christoffel symbols of the first kind      484
Christoffel symbols of the second kind      484
circle      87 135 240
Circle of curvature      431
Circulant matrix      303
Circular convolution rule      304
Circular helix      448 460 464
Circular points      104 132
Circular points definition      133
Circular shift matrix      303
Cissoid of Diocles      456
Clairaut's relation      524
Classical groups      310
Classical Lie groups      376
Closed curve of class $C^p$      419
Closed half-space definition      63
Closed half-space, associated with f      63
Closed half-space, associated with H      63
Closed subgroup of GL(n,R)      391
Closed under affine combinations      20
Closed under linear combinations      20
Closed unit ball      95
Clothoids      461
Cocyclic      149
Codazzi      503
Codazzi — Mainardi equations      506
Codimension one      25
Cofactor      238
Collinear      149
Collinear points      25
Collineation      110
Column vectors      14
Complete quadrilaterals      124
COMPLEX      276
Complex Lie group      383
Complex logarithm      135
Complexification of a linear map, definition      131
Complexification of a vector space      311
Complexification of a vector space, definition      131
Complexification of an inner product      312
Complexification of P(E)      131
Computational geometry      viii ix 188 267
Computer graphics      vii 4 140 264 364
Computer science      vii
Computer vision      vii 4 136 137 189 264 364
Condition number      217
conic      52 87 132 135 190
Conic, nondegenerate      52
Conic, projective      152
Conjugate of a complex number      249 287
Conjugate of a matrix      299
Conjugate of a quaternion      250
Conjugate of a vector      131
Conjugate vectors      193 305
Constant affine map      35
Constrained minimization problems      359
Constrained optimization problems      454
Constraint      359
Control points      20 458
Convex combination      30
Convex hull      30 62 270
Convex hull and Delaunay triangulation      282
Convex hull and Voronoi diagram      283
Convex hull definition      62
Convex polygon      270
Convex polyhedron      270
Convex set      viii 30 62 270
Convexity      7
Convolution $f \star g$      304
Coordinate curves      468
Coordinate system      7
Coordinates in affine space      28
Coordinates of x w.r.t. an affine frame definition      28
Coplanar points      25
Cornu spirals      461
Courant — Fischer formula      332
Coxeter      1
Cross product      240
Cross product definition      237
Cross-product      401
Cross-ratio      108 121 132 133 149
Cross-ratio definition      121
Cross-ratio of hyperplanes      129
Cryptography      140 141
Curvature      415 426 440 447
Curvature $\kappa$      430
Curvature definition      428
Curve      395
Curve continuously differentiable      416
Curve in SO(3)      264
Curve nowhere differentiable      416
Curve of class $C^p$      418
CURVES      7 415
Curves $C^p$-equivalent      420
Curves global properties      415
Curves local properties      415
Curves on a surface      473
Curves, parametrized      415
Curvilinear coordinate systems      394
Cusp      435 455
Cusp of the second kind      455
Cusp of the third kind      455
Cuspidal cubic      459
Darboux      161 446 467 481 505
Darboux frame      507
Darboux vector      443 447
Data compression      348
de Casteljau's algorithm      125
Definite Hermitian form      306
Definite symmetric bilinear form      194
Degenerate conic      153
Delaunay triangulation      viii ix 188 267 274
Delaunay triangulation, definition      279
Derivative of f at p      402
Desargues's theorem      7 160 161
Desargues's theorem affine version      43
Desargues's theorem improved affine version      52
Desargues's theorem projective version      111 120
Desargues's theorem, dual      150
Determinant of a linear map      185
Determining orbits of asteroids      352
Developable ruled surface      526
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