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Elberly D.H., Shoemake K. — Game Physics
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Íàçâàíèå: Game Physics
Àâòîðû: Elberly D.H., Shoemake K.
Àííîòàöèÿ: Game Physics is an introduction to the ideas and techniques needed to create physically realistic 3D graphic environments. As a companion volume to Dave Eberly's industry standard 3D Game Engine Design, Game Physics shares a similar practical approach and format. Dave includes simulations to introduce the key problems involved and then gradually reveals the mathematical and physical concepts needed to solve them. He then describes all the algorithmic foundations and uses code examples and working source code to show how they are implemented, culminating in a large collection of physical simulations. This book tackles the complex, challenging issues that other books avoid, including Lagrangian dynamics, rigid body dynamics, impulse methods, resting contact, linear complementarity problems, deformable bodies, mass-spring systems, friction, numerical solution of differential equations, numerical stability and its relationship to physical stability, and Verlet integration methods. Dave even describes when real physics isn't necessary—and hacked physics will do.
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Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö
ed2k: ed2k stats
Ãîä èçäàíèÿ: 2004
Êîëè÷åñòâî ñòðàíèö: 776
Äîáàâëåíà â êàòàëîã: 19.03.2006
Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
Functions (calculus), global minimum 711—712 714 715
Functions (calculus), local maximum 711
Functions (calculus), local minimum 711
Functions (calculus), multivariate 691
Functions (calculus), multivariate, derivatives 725
Functions (calculus), multivariate, local extrema 664—668
Functions (calculus), multivariate, optimization 713—715
Functions (calculus), range 691
Functions (calculus), recursive descent 713—714
Functions (calculus), univariate, derivatives 719—723
Functions (calculus), univariate, optimization 711—713
Functions (calculus), value change 694
Fundamental theorem of algebra 445 547 616—620 647 656
Fundamental theorem of calculus 703
Gamma 363
Gaussian elimination 554—558
Gaussian elimination, defined 554
Gaussian elimination, elementary row operations and 554—558
Gaussian elimination, total cost 558
Gauss’s principle of least constraints 362
Gear’s fifth-order predictor-corrector method 485—487
Gear’s fifth-order predictor-corrector method, energy conservation 487
Gear’s fifth-order predictor-corrector method, matrix prediction step 486
Gear’s fifth-order predictor-corrector method, reversibility and 487
Gear’s fifth-order predictor-corrector method, Taylor’s Theorem basis 485
Gear’s fifth-order predictor-corrector method, Velocity Verlet method vs. 486 487
Gelatinous cube 172 174
General autonomous systems, defined 453
General autonomous systems, stability analysis 453—454
General autonomous systems, stability of 453—455
General duality theory 426—127
General-order differential equations 444—145 see
General-order differential equations, characteristic polynomial for 444 447
General-order differential equations, constant coefficients 444
General-order differential equations, converting 445
General-order differential equations, defined 444
General-order differential equations, homogeneous linear 446
General-order differential equations, initial-value problem 444
Generalized cylinder surfaces 193—194 see
Generalized cylinder surfaces, defined 193
Generalized cylinder surfaces, normal vectors 193
Generalized cylinder surfaces, skirt model 194
Generalized eigenspaces 657 658
Generalized forces 118
Generalized forces of rigid bodies 124
Generalized forces, bent pipe physical system example 131
Generalized forces, constraint force determination and 113
Generalized forces, defined 103
Generalized forces, flat board (rough plane) 150
Generalized forces, multiple particles (rough plane) 146
Generalized forces, pulley and mass system example 127
Generalized forces, single particle (rough plane) 142
Generalized forces, thin rod (rough plane) 147—148
Generalized forces, total 118
Generalized forces, two particles (rough plane) 144—145
Generalized function 244
Geodesic curves 3
Get Intersection function 283
GetESegment function 334
GetFPolygon function 334
GetKey function 180
GetMaximumlndependentSet function 302
Gill’s method 470
Global extremum 711—712
Global state arrays 231 238
GNU Image Manipulation Program (GIMP) 379
Gouraud shading 367
Gram — Schmidt orthonormalization 226 227 615
Gram — Schmidt orthonormalization applied to three vectors in space 605
Gram — Schmidt orthonormalization applied to two vectors in the plane 604
Gram — Schmidt orthonormalization, defined 604
Gram — Schmidt orthonormalization, illustrated 604 605
Graphics processing units (GPUs) 4
Graphs, cusp 700
Graphs, illustrated 699
Graphs, kink 700
Graphs, nonconvex functions 420
Graphs, secant line of 698
Graphs, tangent line of 698 708
Gravitational forces 32—34
Gravitational forces, conservative 82
Gravitational forces, constraint force balance 114
Gravitational forces, infinitesimal 45
Gravitational forces, on objects by Earth 33
Gravitational forces, on objects located near Earth’s surface 34
Gravitational forces, one-dimensional array (masses) 165
Gravitational forces, single particle on rough plane 142
Gravitational forces, two-body problem 137
Gravitational forces, universal constant 32
Green’s Theorem 67 69
Half angles 517—518 528
Hessian matrix 465
Heun’s method 467
High Level Shading Language 368
Higher-order Taylor methods 461—462
Higher-order Taylor methods, defined 461
Higher-order Taylor methods, example 461
Hollerith cards 1
Hooke’s law 34 106 173
Householder reduction 655
Hypervolume of simplex 682 686—689
Hypervolume, defined 682
Hypervolume, notation 683 685
Hypervolume, recursive formula 686
Hypervolume, signed 689
Hypervolume, summations in 689
I-COLLIDE 363—364
I-COLLIDE, defined 363
I-COLLIDE, variations 364
Identity matrices 569 572 574
impact 364
Implicit Euler’s method 463 464 see
Implicit Euler’s method, application to modal equation 500
Implicit Euler’s method, applied to simple pendulum problem 496
Implicit Euler’s method, characteristic polynomial 500
Implicit Euler’s method, iterate generation pseudocode 495
Implicit Euler’s method, numerical method 495
Implicit Euler’s method, time between zeros 496
Implicit nth-order difference equation 727
Implicit surface deformation 203—220
Implicit surface deformation, example 217—220
Implicit surface deformation, functions 205
Implicit surface deformation, illustrated 205
Implicit surface deformation, isocurve extraction 208—212
Implicit surface deformation, isosurface extraction 212—220
Implicit surface deformation, level set extraction 206—208
Implicit surface deformation, time-varying 206
Impulse functions 258
Impulse-based approach 221
Impulses 243—245
Impulses at spatial points 253
Impulses, angular velocity after 247 249
Impulses, angular velocity before 247
Impulses, imparted by force 245
Impulses, simultaneous 257
Impulses, velocity after 245
Impulses, velocity before 245 246
Impulsive forces 240
Impulsive forces, change of angular velocity 246
Impulsive forces, change of velocity 246
Impulsive forces, computing 254
Impulsive forces, defined 245
Impulsive forces, magnitude 251 264
Impulsive forces, opposite direction 247
Impulsive forces, postulating 246 259
Impulsive forces, variation 362
Impulsive torque 246
Incidence angles 383
Independent vectors 624
Index of refraction 384
Inequality 459 460
Inequality constraints 394 692
Inequality constraints, four 392
Inequality constraints, linear 392 398
Inequality constraints, lines 395
Inequality constraints, redundant 395
Inequality constraints, six 394
Inertia tensor 225—226
Inertia tensor for single particle 60
Inertia tensor for solid triangle 61
Inertia tensor in body coordinates 226 236
Inertia tensor, computing 66 225—226
Inertia tensor, coordinate system construction 225
Inertia tensor, defined 59
Inertia tensor, inverse 249
Inertia tensor, measurement 225
Inertia tensor, solid polyhedron 66—79
Inertia, defined 31
Inertia, moment, about line 59
Inertia, moment, in one dimension 57
Inertia, moment, in three dimensions 58—66
Inertia, moment, in two dimensions 58
Inertia, moments, about õ-, y- and z-axes 59
Inertia, products of 57—66
Inertial coordinates 32 101
Inertial frame 32 101
Infinitesimal area 702
Infinitesimal displacement 102
Infinitesimal forces 123
Infinitesimal mass 45 48 121
Infinitesimal mass for parametric curves 50 55
Infinitesimal mass, distribution 45
Infinitesimal quantities 691
Infinitesimal volume 708
Initial value problem, defined 437
Initial value problem, first-order differential equations 438 445
Initial value problem, general-order differential equations 444
Initial value problem, positional condition 479
Initial value problem, second-order differential equations 442 479
Initial value problem, solution 443
Initial value problem, velocity condition 479
InitializeBodyState function 229 230
Input states 231 234
Insertion sort 357
Instantaneous speed 693 699
Integers 545
Integral calculus 691 701—704
Integral formulation 462—464
integrand 703
integration, defined 703
Integration, iterated 709 710
Integration, multivariate calculus 708—710
Integration, univariate calculus 701—704
Interpolation, bilinear 541
Interpolation, linear, over a tetrahedron 680
Interpolation, linear, over a triangle 679
Interpolation, polynomial 476—477
Interpolation, quadrangle 541 542
Interpolation, quaternions 539—542
Interpolation, spherical linear 539—541
Interpolation, spherical quadrangle 541—542
Intersecting boxes 360
Intersecting intervals 354—359
Intersecting intervals, active 355
Intersecting intervals, determining 354
Intersecting intervals, moved 358
Intersecting intervals, nonoverlapping 358 360
Intersecting intervals, sorted end points 355
Intersecting intervals, sweep algorithm 354—355
Intersecting rectangles 359—360
Intersection calculators, features 333
Intersection calculators, possible outputs 333
Intersection calculators, pseudocode 322—324 331—333
Intersection set 282
Intersections of polytopes 283
Intersections, convex polygons 312
Intersections, convex polygons, testing pseudocode 312—314
Intersections, detection 281
Intersections, edge-edge 242 266 270
Intersections, edge-face 241 242
Intersections, face-face 241 242
Intersections, pairwise 394—396
Intersections, prediction 312 315
Intersections, testing pseudocode 291—292
Intersections, vertex-face 241 242 270
Intersections, vertex-vertex 315
Intervals, active 355 356
Intervals, average speed calculation on 693
Intervals, intersecting 354—359
Intervals, OBB computation 343
Intervals, projection 317 318 336 344 346
Intervals, time 343
Inverse matrices 572—574
Inverse matrices, computing 226
Inverse matrices, defined 572
Inverse matrices, examples 572—573 574
Inverses, computing 576
Inverses, construction of 575—577
Inverses, defined 574
Inverses, left 574 622—623
Inverses, properties 574—575
Invertible matrix 449
Iridescence 388—389
Iridescence, defined 388
Iridescence, shader application 388
Iridescence, shader application screen shots 389
Isocurves in entire plane 210—211
Isocurves, extraction 208—212
Isocurves, form 208
Isocurves, hyperbolic, configurations 211
Isocurves, intersection 209
Isocurves, mesh consistency with 210
Isosurfaces, extraction 212—220
Isosurfaces, form 212—213
Isosurfaces, interior edge point intersection 214
Iterated integration see also Calculus Integration
Iterated integration, defined 709
Iterated integration, dimensions 710
Karush — Kuhn — Tucker (KKT) points, conditions 423 see
Karush — Kuhn — Tucker (KKT) points, critical points analogy 422
Karush — Kuhn — Tucker (KKT) points, defined 422
Karush — Kuhn — Tucker (KKT) points, first condition 423
Karush — Kuhn — Tucker (KKT) points, reformulated conditions 424
Karush — Kuhn — Tucker (KKT) points, second condition 423
Karush — Kuhn — Tucker (KKT) points, third condition 423
Kepler’s laws, defined 88
Kepler’s laws, first law 89—90
Kepler’s laws, second law 90—91
Kinematics 15—31
Kinematics, continuous materials 28—31
Kinematics, defined 13 15
Kinematics, particle systems 28—31
Kinematics, single particle 15—27
kinetic energy 14 108
Kinetic energy of system 81
Kinetic energy, additive nature 81
Kinetic energy, bent pipe physical system example 130—131
Kinetic energy, constraining forces 113
Kinetic energy, defined 81
Kinetic energy, double-pendulum problem 135
Kinetic energy, flat board (rough plane) 149
Kinetic energy, Lagrangian dynamics and 14
Kinetic energy, masses aligned vertically example 120
Kinetic energy, maximum 245
Kinetic energy, measurement 81
Kinetic energy, multiple particles (rough plane) 146
Kinetic energy, pulley and mass system example 126
Kinetic energy, simple pendulum friction example 140
Kinetic energy, single particle (rough plane) 142
Kinetic energy, solid box (rough plane) 151 152
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