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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
Edge(s), tetrahedrons      305
Edge(s), umbrella parents      302
Edge(s), vertex configurations      213
Edge-edge contact      287 321
Edge-to-edge intersections      242 270 315
Edge-to-face intersections      241 242
Eigendecomposition      652—655
Eigenspaces, dimension of      649
Eigenspaces, direct sum of      657
Eigenspaces, finding      647—648
Eigenspaces, generalized      657 658
Eigenvalues      60 455 632 646—651 667—668
Eigenvalues as roots      647 648
Eigenvalues of negative real parts      487
Eigenvalues of symmetric matrix      655
Eigenvalues, defined      646
Eigenvalues, diagonal entries      654
Eigenvalues, example      646
Eigenvalues, finding      647 647—648
Eigenvalues, method of construction      646
Eigenvalues, negative      504
Eigenvalues, of first-derivative matrix      505
Eigenvalues, real-valued      60—61 649
Eigenvectors      455 632 646—651
Eigenvectors, characterizing, for realvalued symmetric matrices      653
Eigenvectors, corresponding      647
Eigenvectors, defined      646
Eigenvectors, example      646
Eigenvectors, linearly independent      650
Eigenvectors, method of construction      646
Eigenvectors, unit-length      653
Elastic collision      249
Elasticity      161
Elementary row matrices      570—572
Elementary row matrices, defined      570
Elementary row matrices, examples      570—572
Elementary row matrices, inverses      573
Elementary row matrices, last row operation      578
Elementary row matrices, listing      572
Elementary row matrices, nonzero determinants      645
Elementary row matrices, product of      572
Elementary row operations, determinants of      644
Elementary row operations, order of      572
Elementary row operations, representation      570
Ellipse, area      91 418—419
Ellipse, axis-aligned      418
Ellipse, path of motion      107 108
Ellipse, points contained in      419
Energy      79—85
Energy, kinetic      14 79—81
Energy, potential      83—85 92
Energy, time derivative      85
Energy, total      85
Equality constraints      692
Equations of motion      32 93 165 224 227 228 343
Equations of motion for time-varying frames      115
Equations of motion, arbitrary mass-spring system      171
Equations of motion, constraining forces      113
Equations of motion, for continuum of mass      121—132
Equations of motion, for Foucault pendulum      95 96
Equations of motion, for particle systems      118—121
Equations of motion, for particles      102—114
Equations of motion, interpretation of      117—118
Equations of motion, Lagrangian      87 101 103
Equations of motion, motion on a curve      102—104
Equations of motion, motion on a surface      104—112
Equations of motion, Newton’s second law      224
Equations of motion, simple pendulum      492
Equations of motion, three-dimensional array (masses)      170—171
Equations of motion, two-dimensional array (masses)      168
Equations of motion, unconstrained motion      228
Equilibrium      39—41 450—455
Equilibrium, defined      40 450
Equilibrium, equations for      41
Equilibrium, objects in      40
Equilibrium, physical stability      488
Equilibrium, solution      450 451
Equilibrium, stability properties and      487
Equilibrium, unstable      487
Equilibrium, zero      487
Euler’s equations of motion      7 61 152—160
Euler’s method      234 277 see
Euler’s method, consistency      488
Euler’s method, defined      458
Euler’s method, explicit      463 493—494 499—500
Euler’s method, implicit      464 495—496 500—501
Euler’s method, local truncation error      488
Euler’s method, modified      463 467
Euler’s method, numerical solver using      233 343
Euler’s method, obtaining      458
Even permutation      639 686 687
Exactness test, defined      84
Exactness test, satisfaction      85
Examples/exercises, this book      11
Existence question      440
Explicit Euler’s methods      463 493—494 see
Explicit Euler’s methods, application to modal equation      499
Explicit Euler’s methods, applied to simple pendulum problem      494
Explicit Euler’s methods, characteristic polynomial      499
Explicit Euler’s methods, iterate generation pseudocode      493—494
Explicit Euler’s methods, numerical method      493
Explicit Euler’s methods, region of stability      500
Exponent matrices      448 663—664
Extended free-form deformation (EFFD)      203
External forces      31 267 see
External forces, applied to rigid bodies      123
External forces, motion of objects undergoing      41
External forces, particle reaction to      88
External forces, particle system      40
External torque      267
Extraction, isocurve, in 2D images      208—212
Extraction, isosurface, in 3D images      212—220
Extraction, level set      206—208
Extraction, triangle      208
Extrapolation methods      473—478 see
Extrapolation methods, application to differential equations      474—476
Extrapolation methods, Bulirsch — Stoer      478
Extrapolation methods, modified midpoint      477—478
Extrapolation methods, Neville’s      476
Extrapolation methods, polynomial interpolation and      476
Extrapolation methods, rational polynomial interpolation and      476—477
Extrapolation methods, Richardson extrapolation      473—474
Extreme point      302—303
Extreme point, search for      302
Extreme point, unique      304
Face(s)      see also Intersections
Face(s), moments for      64—65
Face(s), oriented bounding boxes (OBBs)      334
Face(s), polygonal, area      70
Face(s), polygonal, projection      71
Face(s), polyhedron      67
Face(s), products of inertia for      64—65
Face(s), spherical      305 306
Face(s), triangle      73 74—75
Face-to-face intersection      241 242
Feasible basis vectors for normal form      402
Feasible basis vectors, defined      396
Feasible dictionary      409 410 411
Feasible points      418
Feasible vectors for dual problem      406 407
Feasible vectors for primal problem      405 407
Feasible vectors in constraints      402
Feasible vectors, choosing      406
Feasible vectors, defined      396
Feasible vectors, degenerate      403
Feasible vectors, optimal      396
Fields      547—548
Fields, finite      588
Fields, vector      68
Find-intersection queries      see also Queries
Find-intersection queries, defined      222
Find-intersection queries, for convex polygons      316
Find-intersection queries, for convex polyhedra      325
FindIntersection function      329—331
Finite dimensional vector spaces      599 625
Finite fields      588
First-derivative matrix      492 493
First-order differential equations      437—440 see
First-order differential equations with initial time      439
First-order differential equations, closed form solution      439
First-order differential equations, initial conditions      457
First-order differential equations, initial value problem      438 445
First-order differential equations, linear      439
First-order differential equations, numerical solvers      445
First-order differential equations, separable      439
First-order linear difference equations      730—731
Fixed axis, motion about      25—26
Flat board (rough plane)      148—150
Flat board (rough plane), defined      148
Flat board (rough plane), frictional forces      150
Flat board (rough plane), generalized force      150
Flat board (rough plane), illustrated      149
Flat board (rough plane), kinetic energy      149
Flat board (rough plane), Lagrangian equations of motion      150
Flat board (rough plane), velocity      148
Forces      32—41
Forces with velocity component      480—481
Forces without velocity component      479—480
Forces, applied      227 228
Forces, computing      238
Forces, concurrent      39
Forces, conservative      82
Forces, constraining      101 112—114
Forces, contact      240 267
Forces, couple      38
Forces, defined      31
Forces, displacement      102
Forces, dissipative      139—152
Forces, equilibrium      39—41
Forces, evaluation      276
Forces, external      31 267
Forces, frictional      35—36
Forces, generalized      103
Forces, gravitational      32—34
Forces, impulsive      240 245 246
Forces, infinitesimal      123
Forces, moment of      37—39
Forces, nonconcurrent      39
Forces, nonconservative      83
Forces, product of magnitude of      79—80
Forces, reactive      101
Forces, resolution, at center of mass      268
Forces, spring      34—35
Forces, torque      37—39
Forces, viscous      36—37
Forward difference approximation      see also Derivative approximations
Forward difference approximation, defined      719
Forward difference approximation, example      721—723
Forward difference approximation, occurrence      721
Forward difference approximation, parameters      721
Forward difference approximation, with second-order error      719
Forward elimination      563 564
Forward elimination, augmented matrix      557
Forward elimination, defined      548
Forward elimination, design      558
Forward elimination, elementary row operations and      555
Forward elimination, first step      556
Forward elimination, snags      549—550
Forward elimination, two equations in two unknowns      551—554
Foucault pendulum      94—97
Foucault pendulum, acceleration      95
Foucault pendulum, defined      94
Foucault pendulum, equation of motion      95 96
Foucault pendulum, illustrated      94 97
Foucault pendulum, tip path      97
Foucault pendulum, velocity      95
Four rigid bodies contact points example      261—263
Four rigid bodies contact points example, defined      261
Four rigid bodies contact points example, illustrated      261
Four rigid bodies contact points example, impulsive contact forces      261
Four rigid bodies contact points example, relative velocity equation      262
Four rigid bodies contact points example, simultaneous updates of angular momenta      262
Four rigid bodies contact points example, simultaneous updates of linear momenta      262
Fourth-order Runge — Kutta methods      469—470 see
Fourth-order Runge — Kutta methods, defined      469
Fourth-order Runge — Kutta methods, Gill’s      470
Fourth-order Runge — Kutta methods, RK4a      469—470
Free-form deformation (FFD)      197—203
Free-form deformation (FFD) with B-spline volume function      200—201 203
Free-form deformation (FFD), algorithm      200
Free-form deformation (FFD), control points      204
Free-form deformation (FFD), defined      200
Free-form deformation (FFD), extended (EFFD)      203
Free-form deformation (FFD), illustrated      204
Freely spinning top example      155—156
Freely spinning top example, angular speed      155
Freely spinning top example, defined      155
Freely spinning top example, Euler equations      155
Freely spinning top example, illustrated      155
Freely spinning top example, top angular velocity      155
Freely spinning top example, world coordinate axes      155
Freely spinning top modification      156—158
Freely spinning top modification, angular momentum      157
Freely spinning top modification, defined      156
Freely spinning top modification, differential equations      157—158
Freely spinning top modification, Euler’s equations      156
Freely spinning top modification, snapshots      159
Freely spinning top modification, torque      156
Frenet — Serret equations      22
Fresnel effect      386
Fresnel factor in refraction application      388
Fresnel factor, defined      386
Fresnel factor, per pixel      388
Fresnel reflectance      386—388
Fresnel reflectance, defined      386
Fresnel reflectance, reflection effects produced by      384
Fresnel shader application      386—388
Fresnel shader application, design      386
Fresnel shader application, illustrated      387
Friction      35—36 see
Friction on flat surfaces      141
Friction, coefficient of      140
Friction, defined      35
Friction, flat board on rough plane      148—150
Friction, kinetic, coefficient of      36
Friction, Lagrangian dynamics and      87
Friction, magnitude      35
Friction, multiple particles on rough plane      145—146
Friction, Newtonian dynamics and      87
Friction, one particle on rough plane      141—143
Friction, simple pendulum friction example      140
Friction, solid box on rough plane      150—152
Friction, static      36
Friction, static, coefficient of      36
Friction, thin rod on rough plane      147—148
Friction, two particles on rough plane      143—145
Friction, velocity computation and      480
Frictionless metal chute example      111—112
Frustum, object outside      348
Full pivoting      565
Functions (calculus) as indeterminate form      701
Functions (calculus), bivariate, derivatives      724—725
Functions (calculus), collection of      691
Functions (calculus), continuous      697 704
Functions (calculus), defined      691
Functions (calculus), derivatives      698 700 701
Functions (calculus), differentiable      699
Functions (calculus), discontinuous      697—698
Functions (calculus), domain      691
Functions (calculus), global maximum      712
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