Agoston M.K. Computer Graphics and Geometric Modelling: Implementation and Algorithms
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868 Index
AR, 687
Arc
in medial axis, 184
Arc length, 633, 638
C
k
continuity, 455
computation of, 635
for Bézier curves, 637
Arc-length parametrization, 634, 637, 638,
652
Arctic region, 667
Area
of parallelogram, 249
of set in picture, 25
of polygon, 250
of subtended region, 251
of triangle, 250
Area sampling, 265
Artificial intelligence, 688
Artzy’s algorithm
for volume rendering, 362
Aspect ratio, 120
hardware, 120
Assembly features, 194
Assignment
of points on trimlines, 680
Asymptotic curve, 526
Attractor
of iterated function system, 810
Augmented reality, 687
Axis-parallel box, 697
Axonometric projection, 133
Axonometric view, 133
B
Back clipping plane, 5
Back edge, 266
Back face, 267
removal of, 267
Background
of set in picture, 25
Balanced binary search tree, 698, 718
Band-limited function, 44, 788
Barnhill-Kersey algorithm, 561, 569, 573
comparison with others, 566
data structures for, 565
hunting phase for, 561
relaxing points in, 562
sorting phase for, 566
tolerances in, 562, 563, 565
tracing phase for, 563
Barycentric coordinate property
of affine maps, 418
Barycentric coordinate test, 233
Base frame, 142
Base surface, 679
Basic fill algorithm, 29
Basin of attraction, 220, 579, 800
Basis function, 375
Basis functions, 385, 455, 751
Haar wavelet, 793
properties of, 387
wavelet, 792
Beam tracing, 343
Bernstein polynomial, 398, 507, 549
Bessel end condition, 388
Beta constraint, 454
Beta-spline, 455
Beveling, 222
Bézier basis function, 399
Bézier clipping, 547
Bézier coefficients, 397, 501
Bézier control net, 508
Bézier curve, 398, 403, 432, 466
2
nd
derivative of, 402
advantages of, 403
affinely invariant, 403
as B-spline curve, 418
blossom of, 422, 469
convex hull property of, 399
cubic, 398
degree elevation of, 452
derivative of, 402, 459
derivatives of, 424
differences with B-spline curve, 466
disadvantages of, 403
invariant under affine parameter
transformations, 403
numerical stability of, 467
piecewise, 404
properties of, 399, 402, 403
rational, 432
similarities with B-spline curve, 466
subdivision, 451
use of, 403
variation diminishing property of, 466
Bézier matrix, 397
Bézier patches
geometric continuity of, 522
Bézier point, 399, 422
Bézier polygon, 399