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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
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
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