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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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Ðóáðèêà: Ôèçèêà /
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
Matrices, exponential of 663—664
Matrices, identity 569 572
Matrices, inverse 572—574
Matrices, juxtaposed 567
Matrices, lower echelon 570
Matrices, lower triangular 570
Matrices, LU decomposition 577—583
Matrices, nilpotent 655
Matrices, permutation 578 579
Matrices, power of 662
Matrices, projection 623 624
Matrices, skew-symmetric 569 570
Matrices, special 569—570
Matrices, symmetric 448 569 570 623
Matrices, tridiagonal 581
Matrices, upper echelon 577
Matrices, upper triangular 571
Matrices, zero 573
Matrix multiplication 569
Matrix of coefficients 567 612
Maximum independent set of vertices 301 302
Medical imaging 3
Mesh, consistency with isocurves 210
Mesh, ear-clipping-based construction 215—220
Mesh, edge, precomputed table 215
Mesh, extracted edge 216
Mesh, reduction algorithms 208
Mesh, table-based selection 214—215
Mesh, triangle 190 214 215
Mesh, vertex positions 202
Method of Lagrange see also Constrained optimization
Method of Lagrange, defined 715—716
Method of Lagrange, multipliers 715—716
Method of Lagrange, using 717
Method of separating axes 284—285
Method of separating axes, collision detection systems built on 343
Method of separating axes, defined 283
Method of separating axes, naive implementation of 288
Method of separating axes, use of 311
Middle index 290 291
Midpoint method 466 see
Midpoint method, defined 466
Midpoint method, modified 477—478
Minors 642
Mirtich’s formulas 75—76
Mirtich’s formulas, comparison to 75—76
Mirtich’s formulas, implementing 79
Modal equation, defined 491
Modal equation, explicit Euler’s method 499
Modal equation, implicit Euler’s method 500
Modal equation, leap frog method 502
Modal equation, Runge — Kutta fourth-order method 501
Modified Euler’s method 463 467
Modified midpoint method 477—478
Moments, about x-axis 47 49 50
Moments, about xy-plane 52 53 54 56
Moments, about xz-plane 52 53 54 55
Moments, about y-axis 47 49 50 51
Moments, about yz-plane 52 53 54 55
Moments, calculating 62 63 64
Moments, defined 41
Moments, for continuum of mass 60
Moments, for edges 63—64
Moments, for faces 64—65
Moments, for vertices 63
Moments, inertia about line 59
Moments, inertia about x-, y- and z-axes 59
Moments, inertia in one dimension 57
Moments, inertia in three dimensions 58—66
Moments, inertia in two dimensions 58
Moments, inertia with respect to center of mass 57 58
Moments, inertia with respect to origin 57 58
Moments, products of inertia and 57—66
Momentum 41—79
Momentum, angular 43—44 225 247 262
Momentum, linear 42 225 245 262
Motion, about fixed access 25—26
Motion, about moving axis 26—27
Motion, circle of 26
Motion, constrained 240—280
Motion, equations of 32 87 93 95 96 102—114
Motion, equations, for Foucault pendulum 95 96
Motion, equations, in Lagrangian dynamics 87
Motion, Euler’s equations of 61
Motion, on a curve 102—104
Motion, on a surface 104—112
Motion, path of 88
Motion, period, square of 91—92
Motion, plane, equal areas in 89—90
Motion, rigid 677
Motion, rigid body 87—160
Motion, unconstrained 222 223—239
Moving axis, motion about 26—27
Moving frames 16 21
Multidimensional integrals 709
Multilinear transformations, defined 638
Multilinear transformations, equality as consequence of 640
Multiple contact points 250—258
Multiple particles (rough plane) 145—146
Multiple particles (rough plane), defined 145
Multiple particles (rough plane), frictional forces 146
Multiple particles (rough plane), kinetic energy 146
Multiple particles (rough plane), Lagrangian equations of motion 146
Multiplication, as associative operation 513
Multiplication, complex numbers 547
Multiplication, matrix 569
Multiplication, number of cycles 552
Multiplication, quaternions 514—515
Multiplication, scalar 588 589
Multiplication, vector 587—588
Multiplicative identity 545 546 588 591
Multiplicative inverse 545 546
Multistep methods 470—472 see
Multistep methods, Adams — Bashforth m-step 471 490
Multistep methods, Adams — Moulton m-step 472 490
Multistep methods, defined 470
Multistep methods, derivable 470
Multistep methods, explicit 471
Multistep methods, formulation 490
Multistep methods, generalization 472
Multistep methods, implicit 70
Multistep methods, stability 490—491
Multistep methods, two-step 471
Multivariate calculus 704—710 see
Multivariate calculus, continuity 704—705
Multivariate calculus, defined 691
Multivariate calculus, differentiation 705—708
Multivariate calculus, integration 708—710
Multivariate calculus, limits 704—705
Museum principle 415—416
Museum principle, defined 415
Museum principle, path of visitation 416
Museum principle, satisfying 416
N-dimensional affine space 669
NetImmerse 4
Neville’s method 476
Newtonian dynamics 87 88—100 see
Newtonian dynamics, examples 91—100
Newtonian dynamics, for unconstrained motion 223
Newtonian dynamics, frictional forces and 87
Newton’s laws 31—32
Newton’s Second Law 100 223
Newton’s second law, equations of motion 224
Newton’s second law, for object motion control 221
Newton’s second law, Lagrangian formulation as extension of 118
Nipotent 655
NoIntersect function 317 318
Nonbasic variables 402 403
Nonconvex functions 420
Noninertial frame 32 101
Nonlinear complementarity problems (NCP) 362
Nonpenetration constraints 240
Nonuniform rational B-splines see NURBS
Normal equations 622
Normal form, constraints 397
Normal form, defined 397
Normal form, feasible basis vector for 402
Normal form, restricted 397
Normal form, solving 397
Nth-order difference equation 727
Nth-order differential equations see General-order differential equations
number systems 545—548
Number systems, complex numbers 546—547
Number systems, fields 547—548
Number systems, integers 545
Number systems, rational numbers 545—546
Number systems, real numbers 546
Numerical methods 10—11 457—506
Numerical methods, convergent 489
Numerical methods, Euler’s method 458—461
Numerical methods, explicit 463
Numerical methods, extrapolation methods 473—478
Numerical methods, Gear’s fifth-order predictor-corrector method 485—487
Numerical methods, higher-order Taylor methods 461—462
Numerical methods, implementing 10
Numerical methods, implicit 463 464
Numerical methods, leap frog method 481—483
Numerical methods, multistep methods 10 470—472
Numerical methods, predictor-corrector methods 472—473
Numerical methods, Runge — Kutta methods 465—470
Numerical methods, single-step 10
Numerical methods, stability 487—502
Numerical methods, stiffness 11
Numerical methods, Velocity Verlet method 483—485
Numerical methods, Verlet method 478—487
Numerical methods, via integral formulation 462—464
Numerical round-off errors 226
Numerical stability 487—502
Numerical stability, defined 489
Numerical stability, explicit Euler’s method 500
Numerical stability, implicit Euler’s method 500
Numerical stability, leap frog method 502
Numerical stability, multistep methods 490—491
Numerical stability, Runge — Kutta fourth-order method 501
Numerical stability, single-step methods 488—490
Numerical stability, stable step-size selection 491—502
Numerical stability, strongly stable 491
Numerical stability, unstable 491
Numerical stability, weakly stable 491
NURBS curves 8 173 183—187
NURBS curves, concept 183
NURBS curves, control points 183 185 186
NURBS curves, control weights 183 185
NURBS curves, defined 183
NURBS curves, encapsulation 184
NURBS curves, evaluator 184—185
NURBS curves, examples 183—187
NURBS curves, initial control points 185
NURBS curves, later control points 186
NURBS curves, split 187
NURBS surfaces 173
NURBS surfaces, defined 188
NURBS surfaces, encapsulation 190
NURBS surfaces, example 188—190
NURBS surfaces, flexibility 188
NURBSCurve class 184
NURBSSurf ace class 190
Objective function 398 418 419 427
Objective function, auxiliary 397 398 401
Objective function, defined 396
Objective function, MP and 418
Objective function, quadratic term 420
Objects, coherence 350
Objects, gravitational forces on 33 34
Objects, in equilibrium 40
Objects, moving, constant linear velocity 311—334
Objects, number of comparisons between 351
Objects, OBBs as 342
Objects, stationary 286—310
Objects, weight of 34
Occlusion culling 278
Odd permutation 639 686 687
One-dimensional array (masses) 164—166 see
One-dimensional array (masses), configurations 164
One-dimensional array (masses), defined 164
One-dimensional array (masses), equations of motion 165
One-dimensional array (masses), gravitational forces 165
One-dimensional array (masses), illustrated 167
One-dimensional array (masses), open linear chain 166
OpenGL, pixel shader output 374
OpenGL, shader support 368
OpenGL, vertex shader output 371—372
Optimal feasible vector 396
Optimization (calculus) 711—715
Optimization (calculus), constrained 692 710
Optimization (calculus), defined 692
Optimization (calculus), multivariate functions 713—715
Optimization (calculus), univariate functions 711—713
Organization, this book 6—11
Orientation matrix 225
Orientation matrix, angular velocity relationship 225
Orientation matrix, computing 227
Orientation, modification 248
Orientation, quaternions 233 236
Orientation, values 249
Oriented bounding boxes (OBBs) 4 334—342
Oriented bounding boxes (OBBs), as objects 342
Oriented bounding boxes (OBBs), axes 343
Oriented bounding boxes (OBBs), axes at time zero 347
Oriented bounding boxes (OBBs), center point 334 335
Oriented bounding boxes (OBBs), coordinate axis directions 335
Oriented bounding boxes (OBBs), defined 334
Oriented bounding boxes (OBBs), edges 334
Oriented bounding boxes (OBBs), extents 335
Oriented bounding boxes (OBBs), face normals 338
Oriented bounding boxes (OBBs), faces 334
Oriented bounding boxes (OBBs), illustrated 335
Oriented bounding boxes (OBBs), intervals computation 343
Oriented bounding boxes (OBBs), potential separating axis tests 335
Oriented bounding boxes (OBBs), potential separating directions 338
Oriented bounding boxes (OBBs), projecting 335
Oriented bounding boxes (OBBs), projection intervals 336
Oriented bounding boxes (OBBs), symmetry 335
Oriented bounding boxes (OBBs), test-intersection query 344
Oriented bounding boxes (OBBs), testing 334
Oriented bounding boxes (OBBs), trees 363
Oriented bounding boxes (OBBs), use of 334
Oriented bounding boxes (OBBs), vertices 334
Oriented bounding boxes (OBBs), with constant angular velocity 346—348
Oriented bounding boxes (OBBs), with constant linear velocity 343—346
Orthogonal set of vectors 6
Orthogonal subspaces 613—615 620
Orthogonal subspaces, complement 614
Orthogonal subspaces, defined 613
Orthogonal subspaces, illustrated 614
Orthogonal vectors, defined 601
Orthogonal vectors, illustrated 602
Orthonormal set of vectors 508 510 604
Orthonormal set of vectors, already constructed 606
Orthonormal set of vectors, constructing 604
Orthonormal set of vectors, defined 604
Orthonormal set of vectors, right-handed 509
Orthonormalization for rotation matrices 227
Orthonormalization, application 226
Orthonormalization, Gram-Schmidt 226 227 604 615
Output states 231 234
Pairwise intersections 394—396
Parabolas, area bounded by 702
Parabolas, continuous mass bounded by 49
Parallelogram law, defined 670
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