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Elberly D.H., Shoemake K. — Game Physics
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.


ßçûê: en

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
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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
1 2 3 4 5 6 7 8 9 10 11
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