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Elberly D.H., Shoemake K. — Game Physics
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Название: Game Physics
Авторы: Elberly D.H., Shoemake K.
Аннотация: 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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Рубрика: Физика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2004
Количество страниц: 776
Добавлена в каталог: 19.03.2006
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Предметный указатель
matrix determinant 634—636
matrix determinant 636—638 see
matrix determinant, butterfly rule 636—637
matrix determinant, defined 636
matrix determinant, inverse 637
2D images, continuous representation 208
2D images, definition 208
2D images, isocurve extraction in 208—212
2D images, Marching Cubes to 209
2D rotations 523—525
3D images, algebra 531—534
3D images, base 531
3D images, definition 212
3D images, fixed x-axis 526
3D images, fixed y-axis 526
3D images, fixed z-axis 526
3D images, geometry 526—528
3D images, illustrated 527
3D images, isosurface extraction in 212—220
3D images, matrix 529
3D rotations 522 see
4D rotation matrices 518 529 534—537
4D rotation matrices for xy-plane 529
4D rotation matrices, 3D rotation correspondence 518 535
4D rotations 517 521 529—531
A-stable method 506
Acceleration of particles 16 19
Acceleration, angular 25
Acceleration, centripetal 17 26
Acceleration, drag 30
Acceleration, equation for 30
Acceleration, Foucault pendulum 95
Acceleration, normal 17
Acceleration, of points 23 24—25
Acceleration, polar coordinate form 91
Acceleration, polar frame representation 19
Acceleration, relative 266
Acceleration, tangential 17 26
Acceleration, Taylor expansion for 483
Acceleration, world 30
Acid solutions example 548—549
Active intervals see also Intersecting intervals
Active intervals, defined 355
Active intervals, not reported 356
Active intervals, reported 356
Adams — Bashforth m-step method 471 490
Adams — Moulton m—step method 472 490
Addition, complex numbers 547
Addition, number of cycles 552
Addition, quaternions 512
Addition, vector 584 588
Additive identity 585 588
Additive identity, complex numbers 547
Additive identity, integer 545
Additive identity, rational numbers 546
Additive identity, real numbers 546
Additive identity, zero polynomial 590
Additive inverse 545 546 590
Adjacent indices 171
Affine algebra 669—689
Affine algebra, barycentric coordinates 677—689
Affine algebra, consequences 670
Affine algebra, coordinate systems 673—675
Affine algebra, essence 669
Affine algebra, introduction 669—673
Affine algebra, parallelogram law 670 671
Affine algebra, points and vectors 669 671
Affine algebra, subspaces 675—676
Affine algebra, transformations 676—677
Affine constraints 421
Affine coordinate systems 673—675
Affine coordinate systems, defined 673
Affine coordinate systems, illustrated 674
Affine coordinate systems, relationship between 674
Affine coordinates 673
Affine space, n-dimensional 669
Affine transformations 676—677 see
Affine transformations, as functions 676
Affine transformations, as pure rotation 677
Affine transformations, as translations 677
Affine transformations, condition 1 of definition of 676
Affine transformations, defined 676
Algebra, affine 669—689
Algebra, linear 545—668
Analytic functions 438
Angular acceleration 25
Angular momentum, angular velocity relationship 225
Angular momentum, change in 247
Angular momentum, conservation of 43
Angular momentum, defined 43
Angular momentum, simultaneous updates 262
Angular speed 25 98 see
Angular speed, defined 25
Angular speed, freely spinning top example 155
Angular velocity 25 27
Angular velocity in body coordinates 154
Angular velocity in fixed frame 94
Angular velocity of body 29
Angular velocity of body, about center of mass 243
Angular velocity of rigid body 153
Angular velocity, angular momentum relationship 225
Angular velocity, change in 246
Angular velocity, clockwise rotation correspondence 250
Angular velocity, constant 346—348
Angular velocity, determination 227
Angular velocity, edge rotation due to 266
Angular velocity, freely spinning top example 155
Angular velocity, impulse equation 260
Angular velocity, instantaneous update 264
Angular velocity, orientation matrix relationship 225
Angular velocity, postimpulse 247 249
Angular velocity, preimpulse 247
Angular velocity, solid box (rough plane) 151
Angular velocity, update 255
Angular velocity, world 123 130 154
Anti-commutative cross product 608
Antiderivative 703—704
Applications (calculus) 710—725
Applications (calculus), constrained optimization 715—718
Applications (calculus), derivative approximations by finite differences 718—725
Applications (calculus), optimization 711—715
Applications (linear algebra) 661—668
Applications (linear algebra), exponential of a matrix 663—664
Applications (linear algebra), local extrema of multivariate functions 664—668
Applications (linear algebra), power of a matrix 662
Arbitrary mass-spring system 171—173 see
Arbitrary mass-spring system, defined 171
Arbitrary mass-spring system, differential equation solver 173
Arbitrary mass-spring system, equations of motion 171
Arbitrary mass-spring system, illustrated 174
Artificial variables, defined 397
Artificial variables, need for 402
Artificial variables, restricted normal form conversion and 398
Augmented matrix 563 564
Augmented matrix, after forward elimination 557
Augmented matrix, defined 555 566
Augmented matrix, elementary row operations to 570
Augmented matrix, row-reducing 563
Augmented matrix, searching entries in 563
Augmented matrix, swapping columns of 564
Autonomous systems of equations 451
Autonomous systems, general, stability for 453—455
Auxiliary objective function 398 see
Auxiliary objective function, defined 397
Auxiliary objective function, increase 401
Auxiliary variables 409 411 414 416
Averaging property 254
Axis-aligned bounding boxes (AABBs) 354
Axis-aligned bounding boxes (AABBs), computation queries 354
Axis-aligned bounding boxes (AABBs), culling with 354—360
Axis-aligned bounding boxes (AABBs), generating 360
Axis-aligned bounding boxes (AABBs), intersecting intervals 354—359
Axis-aligned bounding boxes (AABBs), intersection determination 360
Axis-aligned bounding boxes (AABBs), intersection with 354
Axis-aligned bounding boxes (AABBs), polyhedra pairs 354
Axis-aligned bounding boxes (AABBs), update 354
Axis-aligned box, collision example 253—254
Axis-aligned box, postimpulse angular velocity 251
Axis-aligned box, sloped plane collision 250
Axis-aligned ellipse 418
Axis-ligned rectangles 359
AxisAlignedBox class 352
B-spline curves 173—183
B-spline curves, basis functions 175
B-spline curves, closed 181—183
B-spline curves, computation pseudocode 179
B-spline curves, control points 173
B-spline curves, defined 175
B-spline curves, evaluation 176—181
B-spline curves, knot vectors 175—176
B-spline curves, local control 175 181
B-spline curves, open, nonuniform 182
B-spline curves, open, uniform 182
B-spline curves, periodic 182
B-spline curves, recursive dependencies 177
B-spline curves, six pairs of 182
B-spline surfaces 187—188
B-spline surfaces, defined 187
B-spline surfaces, encapsulation 188
B-spline volume 200
Back elimination 564
Back substitution 572
Back substitution, applying 550—551
Back substitution, cost computation 557
Back substitution, defined 548
Back substitution, divisions in 564
Backward difference approximation see also Derivative approximations
Backward difference approximation, defined 719
Backward difference approximation, occurrence 721
Backward difference approximation, parameters 721
Backward difference approximation, with second-order error 720
Backward elimination 645
Balanced dictionary 409
Barycentric combinations 679 680
Barycentric combinations of two points 678
Barycentric combinations, defined 677
Barycentric coordinates 677—689 see
Barycentric coordinates, defined 677—678
Barycentric coordinates, simplices 680—681
Barycentric coordinates, tetrahedra 679—680
Barycentric coordinates, triangles 678—679
Bases see also Vector spaces
Bases, change of 630
Bases, choices 629
Bases, defined 598
Bases, linear transformations 629
Bases, linear transformations (two different) 631
Bases, standard Euclidean 601 629
Bases, vector representation relative to 599
BasicShader application 370
BasicShader application, rendering with pixel shader 376
BasicShader application, rendering with vertex and pixel shader 376
BasisFunction class 180
Bent pipe physical system example 129—132
Bent pipe physical system example, center of mass velocity 130
Bent pipe physical system example, defined 129
Bent pipe physical system example, generalized forces 131
Bent pipe physical system example, illustrated 130
Bent pipe physical system example, kinetic energy 130—131
Bent pipe physical system example, Lagrangian equations of motion 131
Bent pipe physical system example, world angular velocity 130
Bernstein polynomials 189
Bezier curve 542
Bilinear interpolation 541
Bilinear transformations 608
Binary space partitioning (BSP) tree 293
Binary space partitioning (BSP) tree for children of root 306
Binary space partitioning (BSP) tree of spherical polygons 304
Binary space partitioning (BSP) tree, balanced 310
Binary space partitioning (BSP) tree, code 303
Binary space partitioning (BSP) tree, construction 306
Binary space partitioning (BSP) tree, construction pseudocode 307—310
Binary space partitioning (BSP) tree, interior nodes 295
Binary space partitioning (BSP) tree, recursive splitting construction 294
Binary space partitioning (BSP) tree, root 305
Binary space partitioning (BSP) tree, vertice/edge access 295
Binning 353
Binormal vectors, defined 21
Binormal vectors, derivative 22
Binormal vectors, unit length 21
Bisection, algorithm 291
Bisection, alternative 311
Bisection, intersection testing pseudocode 291—292
Bisection, performance issues 343
Bisection, problem 292
Bivariate approximation 724—725
Block matrix 619 675
Body axes 28
Body coordinates, angular velocity in 154
Body coordinates, defined 28
Body coordinates, illustrated 29
Body coordinates, of rigid body 153
Body coordinates, time variance 28
Body observer, body coordinate system by 29
Body observer, defined 28
Body observer, location of points by 28
Body origin, defined 28
Body origin, world velocity 29
Body points 242
bouncing ball example 217—220 see
Bouncing ball example, defined 217
Bouncing ball example, deformed ball 220
Bouncing ball example, floor 217
Bouncing ball example, illustrated 219
Bouncing ball example, level surface extractor 218
Bouncing ball example, spherical body definition 217
Bouncing ball example, time interval 218
Bounding spheres 348
Bounding spheres, center choice 354
Bounding spheres, culling 349—354
Bounding spheres, culling, against view frustum 349
Bounding spheres, update 353
BoundingVolumeTree class 363
Brick wall application 342—343
BSplineSurface class 188
BSplineVolume class 200
BSPNode class 307
Bulirsch — Stoer method 478
bulk modulus 162 163
Butterfly rule 636—637
Butterfly rule, defined 636
Butterfly rule, illustrated 637
Calculus 691—725
Calculus, applications 710—725
Calculus, differential 691
Calculus, infinitesimal quantities 691
Calculus, integral 691 701—704
Calculus, limits 691
Calculus, multivariate 691
Calculus, processing functions 691
Calculus, univariate 691
Cartesian coordinates, acceleration of particle 16 19
Cartesian coordinates, planar motion in 15—18
Cartesian coordinates, position of particle 15—16 19
Cartesian coordinates, spatial motion in 19—22
Cartesian coordinates, speed of particle 16 19
Cartesian coordinates, velocity of particle 16 19
Cayley — Hamilton theorem 447
Center of mass 41 44—56 see
Center of mass, change of velocity 246
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