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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
Kinetic energy, thin rod (rough plane)      147
Kinetic energy, time-varying frames      115
Kinetic energy, two particles (rough plane)      144
Kinetic energy, two-body problem      137
Kinetic norm      362
Kink      700
Knot vectors      175—176 see
Knot vectors, control point modification and      183
Knot vectors, nonuniform      175
Knot vectors, open, nonuniform      176
Knot vectors, open, uniform      175
Knot vectors, periodic      175
Knot vectors, rows of      177
Lagrange multipliers      692
Lagrange multipliers, defined      716
Lagrange multipliers, method of      715—716 717
Lagrangian dynamics      7 100—152 see
Lagrangian dynamics, constrained motion      278—280
Lagrangian dynamics, defined      87 101
Lagrangian dynamics, frictional forces and      87 222
Lagrangian dynamics, kinetic energy and      14
Lagrangian equations of motion      87 101 see
Lagrangian equations of motion for constraint variable      133
Lagrangian equations of motion for constraints of interest      118
Lagrangian equations of motion for continuum of mass      121—132
Lagrangian equations of motion, ball at top of frictionless hill example      109
Lagrangian equations of motion, ball constrained on frictionless table example      107
Lagrangian equations of motion, bent pipe physical system example      131
Lagrangian equations of motion, conservative force      133
Lagrangian equations of motion, constraining force      103
Lagrangian equations of motion, diving board example      134
Lagrangian equations of motion, double—pendulum problem      136
Lagrangian equations of motion, external force      103
Lagrangian equations of motion, flat board (rough plane)      150
Lagrangian equations of motion, for particle constrained on a surface      106
Lagrangian equations of motion, for particle constrained to a curve      103
Lagrangian equations of motion, for particle systems      118—121
Lagrangian equations of motion, frictionless metal chute example      111
Lagrangian equations of motion, interpretation of      117—118
Lagrangian equations of motion, masses aligned vertically example      120
Lagrangian equations of motion, multiple particles (rough plane)      146
Lagrangian equations of motion, pulley and mass system example      127
Lagrangian equations of motion, simple pendulum friction example      140
Lagrangian equations of motion, simple pendulum problem      104
Lagrangian equations of motion, single particle on rough plane      143
Lagrangian equations of motion, thin rod (rough plane)      148
Lagrangian equations of motion, triangle pendulum      125
Lagrangian equations of motion, two particles (rough plane)      145
Lagrangian equations of motion, two-body problem      138
Lagrangian function      133 426
Lamina      14
Law of Cosines      602
LCP applications      427—436 see
LCP applications, contact forces      436
LCP applications, distance calculations      427—436
LDU decomposition method      578 582 583
Leap frog method      481—483
Leap frog method, advantages      483
Leap frog method, application to modal equation      502
Leap frog method, applied to simple pendulum problem      499
Leap frog method, characteristic polynomial      502
Leap frog method, defined      481
Leap frog method, first position approximation      482
Leap frog method, implicit assumption      482
Leap frog method, iterate generation pseudocode      498
Leap frog method, region of stability      502
Leap frog method, velocity      482 484
Least-squares problem      621
Left inverse      622—623
Lemke — Howson algorithm      391 408—413
Lemke — Howson algorithm, complementary variable cannot leave dictionary      418
Lemke — Howson algorithm, defined      408
Lemke — Howson algorithm, example      409—413
Lemke — Howson algorithm, first phase      408 416
Lemke — Howson algorithm, numerical implementation of      415
Lemke — Howson algorithm, problems of zero constants      412
Lemke — Howson algorithm, second phase      408 416
Level set extraction      206—208
Levi—Civita permutation tensor      686
Limit notation      694
Limits      694—696 see
Limits, approach of      694 696
Limits, continuous variables and      696
Limits, defined      691
Limits, multivariate calculus      704—705
Limits, of a sequence      696—697
Limits, univariate calculus      694—696
Line integrals, computation by reduction to      68—73
Line integrals, planar integral conversion to      69
Line segments, as function of y      683
Line segments, contact sets as      254 316
Line segments, end points      683
Line segments, length of      681—682
Line segments, vector-valued function      254
Linear algebra      545—668
Linear algebra, advanced topics      634—668
Linear algebra, applications      661—668
Linear algebra, determinants      634—646
Linear algebra, eigendecomposition      652—655
Linear algebra, eigenvalues and eigenvectors      646—651
Linear algebra, fundamental theorem of      616—620
Linear algebra, matrices      566—583
Linear algebra, number systems      545—548
Linear algebra, S + N decomposition      655—661
Linear algebra, systems of linear equations      548—566
Linear algebra, vector spaces      583—633
Linear combinations      593—594
Linear combinations, defined      593
Linear combinations, example      593
Linear combinations, finite      593
Linear complementarity problem (LCP)      10 264 269 407—418
Linear complementarity problem (LCP), complementary variables and      416—418
Linear complementarity problem (LCP), conversion to      409 411
Linear complementarity problem (LCP), defined      391 407
Linear complementarity problem (LCP), formulation      392
Linear complementarity problem (LCP), Lemke — Howson algorithm and      391 408—413
Linear complementarity problem (LCP), online summary      408
Linear complementarity problem (LCP), overview      391—392
Linear complementarity problem (LCP), quantities in      407—408
Linear complementarity problem (LCP), simplex method solution      408
Linear complementarity problem (LCP), software requirement      265
Linear complementarity problem (LCP), solution      410
Linear complementarity problem (LCP), solver      264
Linear complementarity problem (LCP), variations      362
Linear complementarity problem (LCP), zero constant terms and      413—416
Linear difference equations      730—733 see
Linear difference equations, defined      730
Linear difference equations, first-order      730—731
Linear difference equations, homogeneous      730
Linear difference equations, second-order      731—733
Linear differential equations      446—450
Linear differential equations, nth-order homogeneous      446
Linear differential equations, solution      450
Linear differential equations, systems of      446—150
Linear equations, defined      548
Linear equations, nonhomogeneous      730
Linear equations, nonsquare systems of      558—559
Linear equations, re-creating      567
Linear equations, systems of      548—566
Linear independence      595—601
Linear inequality constraints      392
Linear interpolation, over a tetrahedron      680
Linear interpolation, over a triangle      679
Linear momentum      42 225
Linear momentum, change in      246
Linear momentum, conservation of      42
Linear momentum, continuum of mass      42
Linear momentum, defined      42
Linear momentum, discontinuity in      245
Linear momentum, simultaneous updates      262
Linear programming (LP)      10 392—407
Linear programming (LP), defined      392
Linear programming (LP), dual problem      404—407
Linear programming (LP), general problem      396—104
Linear programming (LP), problems      2
Linear programming (LP), solution by pairwise intersections      394—396
Linear programming (LP), two-dimensional example      392—394
Linear systems      548—566
Linear systems, geometry      559—562
Linear systems, iterative methods for solving      565—566
Linear systems, nonsquare      558—559
Linear systems, sparse      565
Linear transformations      525—526 624—633
Linear transformations of sum of vectors      624
Linear transformations, applied to basis vectors      629
Linear transformations, bilinear      525 608
Linear transformations, composition of      633
Linear transformations, defined      526 624
Linear transformations, examples      625—626
Linear transformations, expansion      628 631
Linear transformations, matrix notation and      538
Linear transformations, on weighted sums      526
Linear transformations, with respect to chosen bases      629
Linear transformations, with respect to two different bases      631
Linear velocity      26
Linear velocity, constant      311—334 343—346
Linear velocity, convex polygons      311
Linear velocity, impulse equation      260
Linear velocity, instantaneous update      264
Linear velocity, postimpulse      246 249
Linear velocity, preimpulse      246
Linear velocity, update      254 255
Linearity      525—526
Linearity, weighted sums mutation and      535
Linearity, “distributed law”      526
Linearly dependent sets      see also Vectors
Linearly dependent sets, cardinality      599
Linearly dependent sets, defined      506
Linearly dependent sets, example      596
Linearly dependent sets, inserting vectors into      598—601
Linearly dependent sets, removing vectors from      598 600
Linearly independent sets      see also Vectors
Linearly independent sets, cardinality      599
Linearly independent sets, defined      596
Linearly independent sets, examples      597
Linearly independent sets, obtaining      598
Linearly independent sets, retaining      598—601
Lines, coincident      559
Lines, horizontal parallel      695
Lines, nonparallel      559
Lines, parallel      559
Lines, secant      698
Lines, tangent      698 708
Local control      175 181
Local minimum      421
Local truncation error      488
Lower echelon matrices      570
Lower triangular matrices      571
LU decomposition      577 577—583
LU decomposition, approximate solution      581—583
LU decomposition, defined      577
LU decomposition, exact solution      580—581
LU decomposition, LDU      578 582 583
L’Hopital’s Rule      701
Magnitude of forces, product of      79—80
Magnitude, computing      247
Magnitude, impulsive forces      251 264
Magnitude, normal component      259
Magnitude, vectors      583
Magnitude, velocity      258 263
Marching Cubes algorithm      206—208
Marching Cubes algorithm, 2D images and      209
Marching Cubes algorithm, defined      206
Marching Cubes algorithm, sign analysis      207
Marching Cubes algorithm, sign combinations      207
Marching Cubes algorithm, table lookup      208
Marching Cubes algorithm, triangle mesh      215
Marching Cubes algorithm, undesirable consequences      207
Marching Cubes algorithm, voxel analysis      206
Marching Squares      209
Mass matrix      59
Mass(es), ball      106 107
Mass(es), bead      104
Mass(es), center of      41 44—56
Mass(es), constrained      116
Mass(es), continuous      42
Mass(es), continuous, in one dimension      45—46
Mass(es), continuous, in three dimensions      52—56
Mass(es), continuous, in two dimensions      48—51
Mass(es), continuum of      14 42 60
Mass(es), curve      14 15 55—56
Mass(es), defined      31
Mass(es), density      121 125
Mass(es), discrete, in one dimension      44—45
Mass(es), discrete, in three dimensions      52
Mass(es), discrete, in two dimensions      46—48
Mass(es), displacement      102
Mass(es), infinitesimal      45 48 50 121
Mass(es), integral computation      53
Mass(es), inverse      249
Mass(es), measurement      31
Mass(es), motion, over time      100
Mass(es), one-dimensional array of      164—166
Mass(es), particle      93
Mass(es), pendulum      100
Mass(es), projectile      80
Mass(es), solid polyhedron      66—79
Mass(es), surface      14 15 53—55
Mass(es), three-dimensional array of      170—171
Mass(es), torque      44—45
Mass(es), total, of body      122 224
Mass(es), total, of system      46 47 53 54
Mass(es), total, of wire      50 55
Mass(es), two-dimensional array of      166—170
Mass(es), volume      14 15 52—53
Mass-spring systems      164—173
Mass-spring systems, arbitrary configurations      171—173
Mass-spring systems, one-dimensional array of masses      164—166
Mass-spring systems, three-dimensional array of masses      170—171
Mass-spring systems, two-dimensional array of masses      166—169
Mass-spring systems, volume mass representation      170
Masses aligned vertically example      119—121
Masses aligned vertically example, defined      119
Masses aligned vertically example, force      119
Masses aligned vertically example, illustrated      119
Masses aligned vertically example, kinetic energy      120
Masses aligned vertically example, Lagrangian equations of motion      120
Mathematica      74 76
Mathematical Programming (MP)      10 418—427
Mathematical programming (MP), convex      420
Mathematical programming (MP), defined      392 418
Mathematical programming (MP), dual problem      426
Mathematical programming (MP), goal      418
Mathematical programming (MP), notation      419
Mathematical programming (MP), objective function      418
Mathematical programming (MP), primal problem      426
Mathematical programming (MP), problem categories      420
Mathematical programming (MP), quadratic      420
Matrices      566—583
Matrices of cofactors      642
Matrices of minors      642
Matrices, augmented      555 557 563 566
Matrices, block      619 675
Matrices, change of basis      631 633
Matrices, column      555
Matrices, concept      566—567
Matrices, decomposition of      662
Matrices, diagonal      448 449 569
Matrices, diagonal entries      569
Matrices, elementary row      570—572
1 2 3 4 5 6 7 8 9 10 11
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