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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
Resting contact 5 243 see Contact
Resting contact, colliding contact change to 245
Resting contact, collision response for 265—270
Resting contact, contact force at 267
Resting contact, defined 240
Resting contact, distance 266
Resting contact, illustrated 241
Resting contact, relative velocity 266
Resting contact, support 277
Restricted normal form, conversion 398
Restricted normal form, defined 397
Restricted normal form, solving 497
Revolution surfaces 195—196 see
Revolution surfaces, defined 195
Revolution surfaces, example 195—196
Revolution surfaces, illustrated 195
Revolution surfaces, parameterization 195
Richardson extrapolation 473—474 see
Richardson extrapolation, approximation combination 474
Richardson extrapolation, approximation form 473
Richardson extrapolation, defined 473
Richardson extrapolation, variation 474
Ridges 3
Right-hand rule 607
Rigid bodies, angular velocity 153
Rigid bodies, as convex polyhedral solids 270
Rigid bodies, as not single points 224
Rigid bodies, basis vectors 152
Rigid bodies, body coordinates 153
Rigid bodies, characterization 14
Rigid bodies, classification 13 14—15
Rigid bodies, continuous material 14 28—31
Rigid bodies, continuum of mass 14
Rigid bodies, curve mass 14 15
Rigid bodies, derived quantities of 229—230
Rigid bodies, external forces applied to 123
Rigid bodies, generalized force for 124
Rigid bodies, global array of 229
Rigid bodies, initialization 276
Rigid bodies, integration 14—15
Rigid bodies, kinematics 15—31
Rigid bodies, lamina 14
Rigid bodies, motion 87—160
Rigid bodies, orientation determination 225
Rigid bodies, output state calculation 231
Rigid bodies, particle systems 28—31
Rigid bodies, planar lamina 14
Rigid bodies, polyhedra 229
Rigid bodies, preimpulse state 247
Rigid bodies, single particle 15—27
Rigid bodies, spatial coherence of 223
Rigid bodies, state variables 239
Rigid bodies, surface mass 14 15
Rigid bodies, temporal coherence of 223
Rigid bodies, values 235
Rigid bodies, volume mass 14 15
Rigid bodies, world coordinates 153
Rigid frictionless rod example 116—117
Rigid motion 677
RigidBody class 275—276 279
RigidBody function 276
Rippling ocean waves 379—382
Rippling ocean waves, diffuse color calculation 381
Rippling ocean waves, GIMP 379
Rippling ocean waves, pixel shader 381
Rippling ocean waves, screen shots 382
Rippling ocean waves, tweaks 381
Rippling ocean waves, vertex shader 379 381
Rippling ocean waves, water color calculation 381
RK3a method 468
RK3b method 468
RK4a method 469—470
Rotation (s), 2D 523—525
Rotation (s), 3D 522 526—528 531—534
Rotation (s), 4D 517 521 529—531
Rotation (s), about z-axis 519
Rotation (s), by angle 517
Rotation (s), composite 516
Rotation (s), composition of 516
Rotation (s), counterclockwise 515
Rotation (s), direction 508
Rotation (s), fixed point 526
Rotation (s), half-angle 518
Rotation (s), in xy-plane 507 518
Rotation (s), quaternions relationship 515—516
Rotation (s), vector 508 649
Rotation matrices 26 27 343 507—512
Rotation matrices, 3D 518 521 522
Rotation matrices, 4D 518 529 534—537
Rotation matrices, angular velocities 347
Rotation matrices, application of 512
Rotation matrices, defined 26
Rotation matrices, direction vector and 27
Rotation matrices, equation 512
Rotation matrices, for half angles 517—518
Rotation matrices, homogeneous 532
Rotation matrices, quaternions 516
Rough planes, flat board on 148—150
Rough planes, multiple particles on 145—146
Rough planes, one particle on 141—143
Rough planes, solid box on 150—152
Rough planes, solid disk rolling on 132
Rough planes, thin rod on 147—148
Rough planes, two particles on 143—145
Round-off errors 226 460
Row swapping 579 580
Runge — Kutta fourth-order solver 233 238 275
Runge — Kutta methods 465—470 496—498 see
Runge — Kutta methods, applied to model equation 501
Runge — Kutta methods, applied to simple pendulum problem 497
Runge — Kutta methods, characteristic polynomial 501
Runge — Kutta methods, design 465
Runge — Kutta methods, fourth-order 469—470
Runge — Kutta methods, Gill’s 470
Runge — Kutta methods, Heun’s 467
Runge — Kutta methods, iterate generation pseudocode 496—497
Runge — Kutta methods, midpoint 466
Runge — Kutta methods, numerical method 496
Runge — Kutta methods, output plot 497
Runge — Kutta methods, region of stability 501
Runge — Kutta methods, RK3a 468
Runge — Kutta methods, RK3b 468
Runge — Kutta methods, RK4a 469—470
Runge — Kutta methods, second-order 466—467
Runge — Kutta methods, third-order 468
S + N decomposition 655—661
S + N decomposition, defined 449 655
S + N decomposition, direct sum 655—656
S + N decomposition, examples 656—657 659—661
Scalar multiplication 588 see
Scalar multiplication, associativity 595
Scalar multiplication, defining 589 590 591
Scalar multiplication, distributive over real addition 594
Scalar multiplication, distributive over vector addition 595
Scalar multiplication, on left 590
Scalar multiplication, on right 590
Secant lines 698
Second Derivative Test 666 668
Second-order differential equations 442—444
Second-order differential equations, characteristic polynomial 452
Second-order differential equations, defined 442
Second-order differential equations, initial value problem 442 479
Second-order differential equations, linear 442
Second-order linear difference equations 731—733
Second-order linear difference equations, coefficient sequences 731
Second-order linear difference equations, defined 731
Second-order linear difference equations, homogeneous solution 732
Second-order linear difference equations, variation of parameters and 733
Second-order Runge — Kutta methods 466—467
Semisimple 655
Semisimple matrices 449
Separable equation 439
Separating axes, defined 284
Separating axes, direction vector 285
Separating axes, method of 283 284—285
Separating axes, potential 311 315
Separating axes, potential tests 335
Separating axes, potential, for sphere 349
Separating axes, potential, separating equation 348
Separating axes, results 333
Separating axes, terminology 285
Separating axes, translation of 284
Separating direction, defined 285
Separating direction, potential 288
Separating direction, potential, for OBBs 338
Separating equations 348
Separating points 243
SetState function 238
Shader programs 9 367—389
Shader programs, abilities 369
Shader programs, categories 367
Shader programs, custom build step 370
Shader programs, defined 367
Shader programs, directly in projects 370
Shader programs, Fresnel reflectance 386—388
Shader programs, introduction 367—369
Shader programs, iridescence 388—389
Shader programs, OpenGL support 368
Shader programs, physical effects with 367
Shader programs, pixel 367 369—375
Shader programs, refraction 383—386
Shader programs, rippling ocean waves 379—382
Shader programs, sequentially executed statements 368
Shader programs, skinning 378—379
Shader programs, vertex 367 369—375
Shading 367
shear modulus 162 163
Signed area 636
Signed hypervolume 689
Signed volume 609 610
Similarity relationship 632
Similarity transform 532
Simple pendulum friction example 139—141
Simple pendulum friction example, defined 139
Simple pendulum friction example, differential equation solutions 140 141
Simple pendulum friction example, frictional force 140
Simple pendulum friction example, kinetic energy 140
Simple pendulum friction example, Lagrangian equation of motion 140
Simple pendulum friction example, velocity 139—140
Simple pendulum problem 98—100
Simple pendulum problem, equations of motion 492
Simple pendulum problem, explicit Euler’s method applied to 494
Simple pendulum problem, illustrated 101
Simple pendulum problem, implicit Euler’s method applied to 496
Simple pendulum problem, integral equation 99
Simple pendulum problem, Lagrangian equations of motion 104
Simple pendulum problem, leap frog method applied to 499
Simple pendulum problem, modification 121
Simple pendulum problem, motion constraint 101
Simple pendulum problem, obtaining 98
Simple pendulum problem, Runge — Kutta method applied to 497
Simple pendulum problem, swinging assumption 99
Simplex method 396 404
Simplex method, defined 396
Simplex method, for solving LCP 408
Simplices, barycentric coordinates 680—681
Simplices, defined 680
Simplices, formation 680 681
Simplices, hypervolume of 686—689
Single particle (rough plane) 141—143
Single particle (rough plane), defined 141
Single particle (rough plane), frictional force 142
Single particle (rough plane), generalized forces 142
Single particle (rough plane), gravitational force 142
Single particle (rough plane), kinetic energy 142
Single particle (rough plane), Lagrangian equations of motion 143
Single particles see Particles
Skew-symmetric matrices 569—570 see
Skew-symmetric matrices, defined 569
Skew-symmetric matrices, diagonal entries 570
Skinning animation 378—379 see
Skinning animation, defined 378
Skinning animation, illustrated 378
Skinning animation, screen shots 380
Skinning animation, skin 378
Skinning animation, vertex shader 379
Slack variables 403
Slack variables, defined 396
Slack variables, positive 402
Slack variables, vector of 407
Slack variables, zero 403
Slerp. see Spherical linear interpolation
Snell’s law 384
SoftImage 5
Solid 3 5
Solid box (rough plane) 150—152
Solid box (rough plane), angular velocity 151
Solid box (rough plane), defined 150—151
Solid box (rough plane), degrees of freedom 151
Solid box (rough plane), frictional forces 152
Solid box (rough plane), illustrated 151
Solid box (rough plane), kinetic energy 151 152
Sort and sweep, algorithm 358
Sort and sweep, pseudocode 356—357
spans 593—594 see
Spans, defined 593
Spans, subset 618
Sparse linear systems 565
Spatial coherence 350
Spatial motion in Cartesian coordinates 19—22
Spatial motion in cylindrical coordinates 22—24
Spatial motion in spherical coordinates 24—25
Spatial points 253
Spatial variables 253 254
Speed 243
Speed of particles 16 19
Speed, angular 25 98
Speed, average calculation on intervals 693
Speed, instantaneous 693 699
Sphere class 352
Sphere trees 363
Sphere-based culling 350 see
Sphere-based culling with binning, cost 353
Sphere-based culling, cost 351
Sphere-based culling, modification 350
Spheres, candidate intersection boxes 353
Spheres, comparison cost 351
Spheres, intersecting, number of 351
Spheres, number, in each bin 351
Spherical coordinates, acceleration of points 24—25
Spherical coordinates, illustrated 24
Spherical coordinates, position of points 24
Spherical coordinates, spatial motion in 24—25
Spherical coordinates, velocity of points 24
Spherical linear interpolation 539—541
Spherical linear interpolation, defined 539
Spherical linear interpolation, derivative 540
Spherical linear interpolation, illustrated 539
Spherical quadrangle interpolation 541—542
Spin groups 522 538
Splitting 565—566
Splitting, defined 565
Splitting, method 565
Spring forces 34—35 see
Spring forces, compression 35
Spring forces, spring constant 34
Spring forces, stretch 34 35
Squared area 636
Squared height 635
Stability 450—455
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