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| Ïîèñê ïî óêàçàòåëÿì |
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| Glassner A.S. — Graphics gems (Vol. 1) |
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| Ïðåäìåòíûé óêàçàòåëü |
RGB triples, mapping onto four bits, hexagonal construction 238
RGB triples, mapping onto four bits, nolid 238
RGB triples, mapping onto four bits, proximity testing 237—239
RGB triples, mapping onto four bits, related methods 239—240
RGB triples, mapping onto four bits, rhombic dodecahedron 236
RGB triples, mapping onto four bits, three versus four bits 243—244
RGB, transform from HSL 448—449
Rhombic dodecahedron 236
Root finding 403
Root finding, Bezier curve-based see Bezier curve-based root-finder
Root finding, cubic 404—407
Root finding, quartic 406—407
Root-finding algorithm 412—413
Rotation matrix 180
Rotation matrix methods 455
Rotation matrix methods, fast matrix multiplication 460—461
Rotation matrix methods, matrix inversion 470—471
Rotation matrix methods, matrix orthogonalization 464
Rotation matrix methods, rotation tools 465—469
Rotation matrix methods, transforming axes 456—459
Rotation matrix methods, virtual trackball 462—463
Rotation minimizing frames 569
Rotation tools 465—469
Rotation tools, converting between matrix and axis-amount representations 466—467
Rotation tools, iteration 468
Rotation tools, nesting 467—468
Rotation tools, transformation inverses 468
Rotation, 3D space see also Orthonormal base
Rotation, about general line, orthonormal bases 520—521
Rotation, bit patterns for encoding angles 442
Rotation, fast 2D-3D 440—441
Rotation, geometrical representation 503—504
Rotation, quaternions 503—506
Rotation, transformation matrices 474
Sampled data, defining surfaces from 552—557
Sampled signals 147
Sampling theorem 147
Sanson — Flamsteed sinusoidal projection 312—314
Sawtooth transform function 203 207—209
Scaling, transformation matrices 474—475
Scan conversion 75
Scan conversion, algorithm, polygon 77—82
Scan conversion, arbitrary polygons 92—97
Scan conversion, concave polygon 87—91
Scan conversion, generic polygon and clipping 84—86
Scanline depth gradient, Z-buffered triangle 361—363
Seed fill algorithm 275—277
Shading, fast dot products 348—360
shadows 278
Shadows, attenuation for ray tracing transparent objects 397—399
Shadows, filling 280—281
Shape construction 551
Shared chord 44
Shear matrices 181
Shearing, algorithm 188
Shearing, raster rotation through 181—183
Shearing, scan-line 187—190
Shuffle generator 66
Sinc function 156—157
Sinc function, Lanczos-windowed 156—158
Sinc function, Lanczos2, decimation by 160—161
Sinc function, Lanczos2, interpolation by factor of two 158—159
Sine, in exponentials 15
Smoothing algorithm, monochrome enlargements 166—170
Snell’s law, refraction 353—354
Software, scrambling integers in 223
Solid objects, box-sphere intersection testing 335—337
Space curve, reference frame calculation 567—571
span 278
Special effects, contrast enhancement 197—198 201—202 270—271 274
Special effects, dissolve see Digital dissolve effect
Special effects, photo-inversion 196 198 270—271
Sphere 326
Sphere, box-sphere intersection testing 335—339
Sphere, intersection with ray 388—389
Spheres-to-voxels conversion 327—334
Spherical coordinate transformation 317—318
Splines 585—586
Square root, high speed, low-precision 424—426
Stereographic map 316
Stirling’s numbers 597
Storage-free swapping 436—437
Sturm sequences 416—422
Sturm sequences, characteristics 420
Sturm sequences, counting sign changes 419
Sturm sequences, driving algorithm 418—419
Sturm sequences, example 417—418
Sturm sequences, method of bisection 420—421
Sturm sequences, pseudo-division of polynomials 419
Sturm’s Theorem 416—417
Subpixel coordinates 77—78
Subtabulation 601
Surface normals 3D models
Surface-normal transformations 539—547
Surface-normal transformations, affine modeling transformations 539—542
Surface-normal transformations, backface culling 544—545
Surface-normal transformations, composition 543
Surface-normal transformations, isotropic transformations 542
Surface-normal transformations, orthogonal transformations 542—543
Surface-normal transformations, shading 545—547
Surface-normal transformations, transformations of metric properties 543—545
Surfaces, defining, from contour data 558—561
Surfaces, defining, from sampled data 552—557
Surfaces, defining, from sampled data, assumptions 552—553
Surfaces, defining, from sampled data, methods 553—557
Swapping, storage-free 436—437
Swept contours 562—564
Symmetric double step line algorithm 101—104
Symmetric double step line algorithm, double speed Bresenham’s 101—102
Symmetric double step line algorithm, line drawing 101
Symmetric double step line algorithm, using symmetry 102—104
Temporal refinement, progressive, recording animation in binary order 265—269
Tensor, modern view 533—535
Tensor, product, matrix 473
Tent filter 149—150
Texture cell 366—367
Texture cell, types 371—372
Texture map indices, interpretation 366—376
Texture map indices, interpretation, algorithm 373—375
Texture map indices, interpretation, decision tree 369—371
Texture map indices, interpretation, replicating cells to create larger texture 369
Texture map indices, interpretation, rigid transformation of square cell 374—375
Texture map indices, interpretation, texture space as two-torus 367—368
Texture-space images, polygons 366—367
Textured cylinder 366—367
Three-dimensional geometry, 297—300 see also Digital cartography
| Three-dimensional geometry, 3D grid hashing function 343—345
Three-dimensional geometry, backface culling 346—347
Three-dimensional geometry, boxes 326
Three-dimensional geometry, intersection of three planes 305
Three-dimensional geometry, intersection of two lines 304
Three-dimensional geometry, mapping 306
Three-dimensional geometry, spheres 326
Three-dimensional geometry, spheres-to-voxels conversion 327—334
Three-dimensional grid, defining surfaces from sampled data 552—557
Three-dimensional models, surface normals 562—566
Tick marks 61—63
Tilings, periodic, plane on raster grid 129—139
Trackball, virtual 462—463
Transformation identities 485—493
Transformation identities, anisotropic scaling following rotation 490
Transformation identities, commuting, rotation and anisotropic scaling 490
Transformation identities, commuting, rotation and isotropic scaling 488
Transformation identities, commuting, skewing and isotropic scaling 489
Transformation identities, exchanging order, of skews 491
Transformation identities, exchanging order, of translation and rotation, rules 487
Transformation identities, matrix representations of primitive transformations 492—493
Transformation identities, reversing order, skewing and anisotropic scaling 489
Transformation identities, reversing order, translation and scaling 487
Transformation identities, reversing order, translation and skewing 488
Transformation identities, rotation expressed as combination of skews and scales 489
Transformation identities, rotation expressed as three skews 489
Transformation identities, skew expressed as two rotations and a scale 491
Transformation inverses 468
Transformation matrix 472—475
Transformation matrix, DDA coefficient conversion between step sizes 602
Transformation matrix, mirror image 473
Transformation matrix, notation 472 485—486
Transformation matrix, observations 472
Transformation matrix, post-concatenation 476—481
Transformation matrix, post-concatenation, computational cost comparison 479—481
Transformation matrix, post-concatenation, direct 478—479
Transformation matrix, post-concatenation, implementation 476—477
Transformation matrix, post-concatenation, primitive transformations 492—493
Transformation matrix, post-concatenation, projection 474
Transformation matrix, post-concatenation, rotation 473
Transformation matrix, post-concatenation, scaling 473—474
Transformation matrix, post-concatenation, translation 472
Transformation, 3D, coding see Quaternions
Transformation, axis-aligned bounding boxes 548—550
Transforming axes 456—459
Transition table 93—95
Translation, transformation matrices 473
Transparent objects, ray tracing, shadow attenuation 397—399
Transpose of the inverse 541
Triangles 20—23
Triangles in center 20—21
Triangles in radius 20—21
Triangles, area 20
Triangles, center of gravity 20—21
Triangles, circumcenter 20—23
Triangles, circumradius 20—23
Triangles, generating random points 24—28
Triangles, hypotenuse 57—59
Triangles, intersection, of altitudes 22
Triangles, intersection, of perpendicular bisectors 22—23
Triangles, intersection, with ray 393
Triangles, perimeter 20
Triangles, prime pythagorean 58
Triangular interpolants 535—538
Trigonometry, angle sum and difference relations 16
Trigonometry, DeMoivre’s Theorem 15
Trigonometry, double-angle relations 17
Trigonometry, fixed-point, CORDIC 494—497
Trigonometry, functions 18—19
Trigonometry, half-angle relations 16
Trigonometry, inverse functions 14
Trigonometry, Law of Cosines 13
Trigonometry, Law of Sines 13
Trigonometry, Law of Tangents 13
Trigonometry, Mollweide’s Formula 13
Trigonometry, multiple-angle relations 17
Trigonometry, Newton’s Formula 14
Trigonometry, power relations 15
Trigonometry, product relations 16
Trigonometry, sines and cosines in exponentials 15
Trigonometry, sums and differences 14
Two-dimensional array, randomly traversing, digital dissolve effect 221—222
Two-dimensional clipping 121—128
Two-dimensional clipping, algorithm 124—126
Two-dimensional clipping, approximation error 186
Two-dimensional clipping, basic considerations 123—124
Two-dimensional clipping, implementation 126—127
Two-dimensional clipping, integers and vectors 121—122
Two-dimensional geometry 3—11 see
Two-dimensional geometry, circles 4—5
Two-dimensional geometry, cosine of angle between lines 11
Two-dimensional geometry, distance from point to line 10
Two-dimensional geometry, intersection of circle and line 5—6
Two-dimensional geometry, line structures 3—4
Two-dimensional geometry, lines tangent, to circle and perpendicular to line 8—9
Two-dimensional geometry, lines tangent, to two circles 7—8
Two-dimensional geometry, point of intersection between lines 11
Two-dimensional geometry, point-on-line test 49—50
Two-dimensional geometry, triangles 20—23
Two-dimensional rendering, circles of integral radius on integer lattices 57—60
types of cells 371—372
Uniform grid, line-edge intersections 29—36
Uniform quantization 288
Unimodular transforms 135
Unit quaternions, set, properties 502—503
UVN coordinate system 518—519
Vector rotation, CORDIC 494—497
Vectors, 3D 522—523 526
Vectors, differences with forms 533—535
Vectors, normal see Normal vectors
Vectors, triangular interpolants 535—538
Vertex normal, computing 563—565
Vertical distance, point to line 47—48
Viewing transformation, pseudo-code 521
Viewing, 3D see Orthonormal base
Virtual trackball 462—463
Visibility algorithm 30—31
Voxel subdivision, 3D grid hashing function 343
Wallpaper groups, tiling in raster grids 133—139
Wide line bevel joints, algorithm for filling in 107—113
Winding number transitions 94—95
Write-only write mask, reading 219—220
X-transition table 93—95
Y extrema, polygon fast scan conversion 95—96
Z-buffered triangle, scanline depth gradient 361—363
Zero-phase filters, frequency response, decimation by two 162
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