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272 Index

Heaviside function, 14, 64, 68, 141,
domain of dependence, 44, 66
227
dynamic implicit surfaces, 7
dynamic surface extension, 93
ideal gas, 164
image deblurring, 98
edge detector, 119, 120, 124
image denoising, 98
eigensystem, 161, 162, 164, 165
Index image processing, 95
elliptic di¬erential equations, 147
image restoration, 97
ENO (essentially nonoscillatory),
image segmentation, 95
31“39, 49, 53, 54, 68, 69, 104,
immersed boundary method, 227, 228
155“160, 162, 166, 210, 211
implicit surfaces, 1, 25, 64, 140“142
entropy condition, 46, 48, 104, 191
incomplete Choleski preconditioner,
entropy ¬x, 105, 153, 159
213, 238, 250, 253
equation of state, 147, 167, 169, 174,
incompressible ¬‚ow, 67, 79, 147, 209,
175, 181, 183, 184, 192
210, 217, 223, 224, 227“230, 232,
Euler equations, 48, 163“165, 174,
238, 240
176, 189
interpolation, 11, 31“34, 65, 69, 73,
Eulerian formulation, 23
74, 93, 151, 155“158, 183, 184, 186,
expansion shocks, 48, 52, 159
203“206, 214, 224
extrapolation, 75, 76, 174, 189, 206,
isobaric ¬x, 173“175, 177“179
253, 254

Jacobian matrix, 161, 165
fast marching method, 69, 73, 76
active contours, 95, 127 consistent ¬nite di¬erence
¬nite di¬erence, 11, 30, 100, 103, 142,
kink, 49
approximation, 30
arbitrary Lagrangian-Eulerian, 202
154“156, 175, 202
constrained minimization, 101
arti¬cial viscosity, 31, 46, 53, 58, 174,
¬‚ame front, 26, 59, 190, 239, 242
Lagrange multiplier, 71, 101
201, 205 constructive solid geometry (CSG), 9
¬‚ames, 59, 239
Lagrangian formulation, 23, 26, 28
contact discontinuities, 48, 150, 155,
¬‚ux, 31, 48, 149, 152“155, 157“159,
Lax-Friedrichs schemes, 50
171, 197
backward Euler, 45, 251
161“163, 170“172, 174, 240
Lax-Wendro¬ theorem, 171
convection, 23, 26, 45, 51, 104, 120,
Boolean operations, 9
forward Euler method, 29, 37
level set equation, 23, 26, 42, 43, 47,
142, 150“153, 156, 160, 163, 249
bounding box, 142
free surface ¬‚ows, 147
55, 59, 89, 167, 174, 217
convection-di¬usion equations, 45
Burgers™ equation, 48, 152, 153
front tracking methods, 26
level set methods, 23, 26, 37, 46, 64,
convergent, 30
79, 82, 87, 172, 205, 218, 219, 228
crossing times, 65
cell averages, 154, 155
gamma law gas, 167 limiters, 201
curvature, 12, 28, 41“44, 47, 59, 79,
CFL condition, 30, 31, 44, 50, 59,
Gaussian, 97, 106, 113, 120 Liouville equation, 90
88“90, 103“105, 120, 124, 142, 218,
213, 223
geometric optics, 90 liquid-gas interactions, 223
224, 228, 240
Chapman-Jouguet detonation, 195
G-equation, 26, 59, 190, 191, 195 local Lax-Friedrichs scheme, 52
characteristic function, 13
ghost ¬‚uid method, 76, 126, 172, local level set, 64, 90, 92
de¬‚agration, 147, 189“191, 195,
chemical reactions, 150, 163, 164, 191
178“182, 190, 191, 193“195
197“200
codimension-two, 87, 90
Godunov™s scheme, 54 MAC grid, 210, 233
Delaunay triangulations, 139
compressible, 48, 149, 163, 167, 169,
gradient descent, 69, 101, 102, 125, marching cubes algorithm, 16
delta function, 14, 49, 68, 123, 228
171, 173, 223“225, 240
127, 144 mass conservation, 82
detonation, 147, 195“197
computational ¬‚uid dynamics (CFD),
gradient projection method, 69 mean curvature, 23
di¬usion, 104, 150, 151, 163
46, 48, 223, 271
minimization procedure, 101, 125
Dijkstra™s method, 71
computational physics, 147
Hamilton-Jacobi equations, 23, 31, monotone numerical methods, 49
computer graphics, 147, 214, 242 dimension by dimension, 49, 156
47, 49, 52, 65 monotone schemes, 49, 50
computer-aided design (CAD), 9 discrete conservation form, 154
harmonic map, 144 morphological, 104, 105, 141
conservation form, 152, 154, 170, 171 distance function, 17, 28, 36, 43“46,
heat equation, 43, 44, 97“99, 104, motion by mean curvature, 23
conservation laws, 31, 48, 49, 54, 98, 51, 55, 56, 60, 61, 63, 64, 66, 69, 70,
106, 249, 251, 256 multicomponent ¬‚ow, 147
99, 149, 150, 155, 160, 165 77, 123, 140, 142, 205, 206, 253
Index 273

multiphase ¬‚ow, 76 stable, 30, 38, 51, 124, 142, 214
multiple junctions, 125, 127 Stefan problems, 147, 253, 254
Mumford-Shah segmentation, 120 surface tension, 141, 142, 224, 227,
228, 256, 258
Navier-Stokes equations, 28, 48, 173, systems of conservation laws, 160
178, 209, 210, 217, 227, 231
normal to a surface, 9 Tait equation of state, 169
numerical ¬‚ux, 154 textures, 100
NURBS, 139 total variation-based image
restoration, 99
open curves and surfaces, 90 transformation to characteristic
overheating e¬ect, 173, 175 variables, 160
trapezoidal rule, 45
particle level set method, 79, 82, 84, TVD (total variation diminishing),
219, 221, 222 37, 38, 50, 100, 154, 160
phase-space-based level set TVD RK (total variation diminishing
framework, 90 Runge-Kutta), 37“39, 46
Poisson equation, 213, 228, 251, 252
preconditioned conjugate gradients, unorganized data points, 139
213 upwind di¬erencing, 29, 30, 32, 54,
projection method, 210, 212 57, 75, 151

radial basis functions, 140 vanishing viscosity solutions, 46
Rankine-Hugoniot jump conditions, variational level set formulation, 120,
169, 170, 172, 174, 175, 178, 183, 121
189, 192, 224, 240, 255 velocity extension, 27
rarefaction waves, 48, 52 velocity extrapolation, 76
ray tracing, 90, 92 viscosity solutions, 19, 46, 79, 82
reconstruction of surfaces, 139 volume conservation, 82
reinitialization, 64, 66, 67, 73, 82, volume of ¬‚uid methods, 147
102, 123 Voronoi diagrams, 139, 140
reinitialization equation, 66 vorticity con¬nement, 214
Riemann problem, 54, 172, 178, 190,
193, 195 waves, 30, 48, 93, 150, 151, 160,
Roe-¬x scheme, 52 162, 167, 173, 174, 185, 189, 195,
Runge-Kutta method, 31, 67, 160 197“199, 213, 223
weak solution, 46, 172
scale space, 98 weighted minimal surface model, 140
semi-Lagrangian method, 214 WENO (weighted essentially
shape o¬sets, 65 nonoscillatory), 33“35, 37“39, 50,
shock waves, 48, 150, 167, 173, 174, 52“54, 66, 68, 69, 104
185, 189, 190, 223
signed distance, 1, 28, 36, 43“46, 51,
55, 56, 60, 61, 63“67, 69, 70, 73,
75“77, 205, 206, 253
smoke, 214, 215
snakes, 95, 119, 120, 124
solid/¬‚uid problems, 147
sonic point, 53, 57, 159

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