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Index 1013
repeated, 598
bilinear, 594
linear, 578–581
rotation invariant, 539
trilinear, 166
intersection testing, 725–792
k-DOP/k-DOP, 765–767
k-DOP/ray, 744
AABB/AABB, 765
box/plane, 755–757
box/ray, 741–746
ray slope, 746
slabs method, 742–744
BV/BV, 762–771
convex polyhedron/ray, 744
crossings test, 752–755
dimension reduction, 737
dynamic, 783–791, 797–802
dynamic separating axis test, see
intersection testing, separating
axis test
dynamic sphere/plane, 784–785
dynamic sphere/polygon, 787–791
dynamic sphere/sphere, 785–786
frustum, 771–778
frustum/box, 777–778
frustum/ray, 744
frustum/sphere, 774–777
hardware-accelerated, 726–727
interval overlap method, 757–760
line/line, 780–782
OBB/OBB, 767–771
SAT lite, 808
octant test, 776, 778
picking, 725–726
plane/ray, 751
polygon/ray, 750–755
rejection test, 731
rules of thumb, 737–738
separating axis, 731
separating axis test, 731, 744, 757,
760, 761, 766, 767, 777
dynamic, 791
lite, 808
shaft/box, 778–780
sphere/box, 763–765
sphere/ray, 738–741
sphere/sphere, 763
static, 783
three planes, 782–783
triangle/box, 760–762
triangle/ray, 746–750
triangle/triangle, 757–760
interval arithmetic, 858
interval overlap method, see intersection
testing
intrinsic functions, 33
inverse displacement mapping, see
texturing, relief
irradiance, 102, 203, 314, 409
map, see environment mapping
volume, 423
irregular vertex, 614
isocube, 306
isosurface, 502, 606, 607
isotropic scaling, see transform, scaling,
uniform
jaggies, see aliasing, 117
Java ME, 877
jittering, 60, see antialiasing, 389
joint, 578, 585, 587, 590
Jordan curve theorem, 752
joule, 203
k-ary tree, see tree
k-d tree, see spatial data structure
k-DOP, 675, 730, 731, 744, 762, 765, 783,
807
collision detection, 807
creation, 732
key, 479
Killzone 2, 280, 493
Kochanek-Bartels curves, see curves
LAB, 216
Lafortune model, see BRDF
Lambert’s law, 110
Lambertian shading, see BRDF,
Lambertian
N
ehale
m, 883
latency, 1, 704, 717, 719–721, 835, 842,
847, 853–854, 861
occlusion query, 674
latitude, 300, 728
law of cosines, see trigonometry
law of sines, see trigonometry
law of tangents, see trigonometry
layered depth image, see impostor
layered distance map, 392
lazy creation, 804
LCD, 134, 830–831
LDI, see impostor, layered depth image
least-crossed criterion, 653
left-handed, see coordinate system
basis, see handedness
lens flare, 482
lenticular display, 837
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1014 Index
level of detail, 576, 680–693, 718, 720
alpha, 684–686
benefit function, 687, 692
bias, 166, see also texturing
blend, 684
continuous, 562, 569, 571, 573, 630,
686
cost function, 691
discrete geometry, 683
fractional tessellation, 631
generation, 681
geomorph, 686–691
hysteresis, 690–691
N-patch, 603
popping, 567, 683, 684, 685
projected area-based, 688–690
range-based, 688
selection, 681, 687–691
simplification, 567
subdivision surface, 611
switching, 681, 683–687
time-critical, 680, 691–693
LIC, see line, integral convolution
LIDAR, 533
light
absorption, 393
adaptation, 475, 478
attenuation mask, 340
back, 324
baking on, 714
bidirectional, 324
bleeding, 369
field, 208
fill, 324
key, 324
leak, 352–353, 369, 370
mapping, see texturing
meter, 103, 204, 210
probe, 301
rim, 324
source, 100–104, 713
area, 289–295, 331, 337
directional, 100
point, 206
spot, 220
spotlight, 418
volume, 331
three-point, 324
vector, 100
light-field rendering, 444
lighting equation, 146, see also BRDF
Phong, 201
Lightspeed Memory Architecture, 857
limit
curve, 608, 610
surface, 615
tangent, 618
Lindstrom, 569
line, 19, 527–530, 906–908, see also edge
drawing, 11
edge highlighting, 527
haloing, 528, 530
hidden-line rendering, 528–529
integral convolution, 492
polygon edge rendering, 527–528
three-dimensional, 908
explicit, 908
implicit, 908
two-dimensional, 906–908
explicit, 906
implicit, 906
line/line intersection, see intersection
testing
linear algebra, 889–911
linear independence, 892–893
linear interpolation, see interpolation
linear speedup, 721
LiSPSM, see shadow, map, light space
perspective
LittleBigPlanet, 425, 886
LMA, 857
load balance, 846
load balancing, 861
local frame, 258
local lighting model, see lighting model
LOD, see levels of detail
log, 8
longitude, 300, 728
look-up table, 474, 689
loop, see silhouette, see polygon
Loop subdivision, see surfaces,
subdivision
loop unrolling, 707
loose octree, see spatial data structure
lossy compression, see texturing,
compression
Lost Planet, 495, 504
LSPSM, se
e sh
adow, map, light space
perspective
LU decomposition, see matrix, inverse
Lumigraph, 444
luminaire, 217
luminance, 212, 215
luminescence, see light, emission
LUT, see look-up table
LUV, 216
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Index 1015
M3G, 877
M¨obius strips, 543
Macbeth ColorChecker, see Munsell
ColorChecker
Mach banding, 832, 832
MacLaurin series, see trigonometry
macroscale, 107, 184, 271
magnification, see texturing
mailboxing, 651
main axes, 7
manifold, 352, 545
map
caustic, 400
marching cubes, 607
marching tetrahedra, 607
mask, 614
masking
perceptual, 217
shader, 31
material, 104–107
matrix, 897–905, see also transform
addition, 898
adjoint, 901–902
change of base, 904–905
column-major, 61n, 890
definition, 897
determinant, 59, 900–901
eigenvalue, 903–904
eigenvector, 734, 903–904
homogeneous form, 905
identity, 897, 903, 904
multiplication, 899
orthogonal, 65, 68, 76, 904
rotation, 57, 66
row-major, 61n, 92
scalar multiplication, 898
subdeterminant, 901
trace, 57, 76, 898
transpose, 59, 898
notation, 7
matte, 139
MB subdivision, see surfaces, subdivision,
modified butterfly
MBX/SGX, see hardware
mean width, 736
memory
allocation, 705
architecture, 849–850
bandwidth, see bandwidth
bank, 853
dynamic random access, 703
optimization, see optimization
tiled, 868
UMA, 849
unified, see unified memory
architecture
memory hierarchy, 703
mental mill, 36
merging
pixel, 23–25
merging stage, 23–24, 44–45
mesh, see polygon
mesh parameterization, 153
mesoscale, 107, 183–184, 271
message-passing architecture, see
multiprocessing
metaball, 42, 533, 606
metal, 235
metamers, 212
microfacets, 246–249
microgeometry, 241–246
masking, 244
shadowing, 243
micropatch, 372
micropolygon, 26
microscale, 107, 184, 241, 271
minification, see texturing
Minkowski sum, 787, 789, 791, 798, 819
mipmap chain, 163
mipmapping, see texturing, minification
mirror transform, see transform, reflection
model space, 16, 842
modeler, 532–533, 535, 547
solid, 532–533
surface, 533
m
odi
fied butterfly subdivision, see
surfaces, subdivision
modulate, see texturing, blending
operations
Mollweide’s formula, see trigonometry
monitor, 141, 830–831
gamut, 216
Moore’s Law, 880
morph targets, see transform
morphing, see transform
Morton sequence, 849
mosaicing, see texturing, tiling
motion blur, 126, 490–496
motion parallax, 837
MRT, 44
MSAA, see antialiasing, multisampling
multi-view rendering, 836–837
multicore, 717
multipass lighting, 278
multipass rendering, 857
multiple angle relations, see trigonometry
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1016 Index
multiprocessing, 716–722, 846
dynamic assignment, 721
message-passing, 716
parallel, 720–722
pipeline, 717–720
shared memory multiprocessor, 716
static assignment, 721
symmetric, 717
multisampling, see antialiasing
multitexturing, see texturing
multum in parvo, 163
Munsell ColorChecker, 145
N-patch, see surfaces
nailboard, see impostor, depth sprite
NDF, see normal, distribution function
near plane, 90, 96, 688, 771
nearest neighbor, see texturing and
filtering
negatively oriented, see handedness,
left-handed basis
Nehalem, 883
Newell’s formula, 535
Newton’s formula, see trigonometry
node, 648–649
internal, 648
leaf, 648
root, 648
noise function, see texturing
non-photorealistic rendering, 507–526
stylistic rendering, 507
noncommutativity, 61, 72, 899
norm of vector, see vector
normal
cone, 664
distribution function, 246, 273
map, 258
incidence, 232
map, see bump mapping
transform, see transform
normal-patches, see surfaces, N-patch
normalize vector, see vector
normalized device coordinates, 19,90
north bridge, 859, 860
NPR, see non-photorealistic rendering
N-rooks sampling, 131
NTSC, 217
phosphors, 216
NURBS, see surfaces
Nusselt analog, 410
NV
depth clamp, 344
NvTriStrip, 552, 573
Nyquist limit, see sampling
OBB, 729–730, 731, 762, 807
collision detection, 807–809
plane/box intersection, 757
ray/box intersection, 742–744
OBB/OBB intersection, see intersection
testing
OBB/plane intersection, see intersection
testing
OBB/ray intersection, see intersection
testing
OBBTree, see collision detection
obscurance, 378, 379, 381, 383, 426
occluder, 673
shrinking, 679
virtual, 680
occluding power, 673
occlusion
culling, see culling
horizons, see culling
reflection, 430
octant test, see intersection testing
octree, see spatial data structure
octree texture, 171
Okami, 508, 509, 881
omni light, 218
opacity
spectral, 141
OpenEXR format, 481
OpenGL ARB, 37
OpenGL ES, 176, 870, 873, 877
OpenRT, 646
OpenSG, 552, 573
optimal placement, see simplification
optimization
application stage, 703–707
code, 703–707
geometry stage, 713–714
lighting, 713–714
memory, 704–707
pipeline, 697–723
pixel shader, 711, 716, 857
rasterizer stage, 714
vertex shader, 711
ordinary vertex, 614
Oren and Nayar model, see BRDF
orientation, 56, 65, see polygon
oriented bounding box, see OBB
orthogonal
decomposition, 895
vectors, 891
outline, see polygon, with multiple
outlines
over operator, 136–140, 393, 684
overblurring, 166
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Index 1017
overclock, 701
overdraw, 851
oversampling, see supersampling
packed pixel format, 832
padding, 705
page flipping, 834
painter’s algorithm, 654
painterly rendering, 508
parabola, 579
parabolic mapping, see environment
mapping
paraboloid mapping, see environment
mapping
parallax, 443, 460, 460
barrier display, 837
mapping, 191–193
occlusion mapping, see texturing,
relief
parallel
close proximity, see collision
detection
graphics, 723, 842
processing, see multiprocessing
projection, see projection,
orthographic
parallelism, 720
spatial, 717
temporal, 717
parameter space values, see texturing
parametric
curves, see curves
surfaces, see surfaces
particle, 39n
soft, 452–454
system, 455–456
patch, 593
path planning, 818
PCF, see percentage-closer filtering
PCI Express, 712, 849, 850, 883
PCIe, 850
PCU, see culling,programmable, 876
PDI, 422
Peano curve, 556
pen and ink, 508
pending buffer, see buffer
penetration depth, 818
penumbra, see shadow
penumbra map, see shadow, map,
penumbra method
penumbra wedge, 348
per-polygon operations, see per-vertex
operations
per-vertex operations, 15
percentage-closer filtering, 361–366
performance measurement, 702
perp dot product, 6, 780, 781
perspective projection, see projection
perspective-correct interpolation, see
interpolation
Peter Panning, 352
Phong lighting equation, see lighting
equation and BRDF
Phong lobe, 257
Phong shading, see shading
phosphor, 214–216
phosphorescence, see light, emission
photogrammetry, 532, 533
photometric curve, 209
, 212, 216
photom
etr
y, 209–210
photon mapping, 399, 416
photons, 202
photorealistic rendering, 440, 507
pick window, see intersection testing
picking, 725–726, 728, 740
piecewise
B´ezier curves, see curves
smooth subdivision, see surfaces,
subdivision
ping-pong buffers, 472, 483
pipeline, 11–27, 697–723
application stage, 12, 14–15, 697
conceptual stages, 12
fixed-function, 26, 201, 220, 467,
496, 701
lighting, 219
flush, 711, 854
functional stages, 13
geometry stage, 12, 15–20, 697
rasterizer stage, 12, 21–25, 697
software, 718
speedup, 12
stage, 12–14, 841–842
Pirates of the Caribbean, 381
pitch, 66,68
pixel, 21n, 125n
overdraw, 716
processor, see pixel, shader
shader, 29, 42–44, 137
depth sprite, 464
PLAYSTATION
R
3, 866–868
Pixel-Planes, see hardware
pixelation, 158
PixelFlow, see hardware
pixels per second, 702
Planck’s constant, 202
plane, 6, 908–909
axis-aligned, 7
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