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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
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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