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Elberly D.H., Shoemake K. — Game Physics
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.


Язык: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$2\times 2$ matrix determinant      634—636
$3\times 3$ matrix determinant      636—638 see
$3\times 3$ matrix determinant, butterfly rule      636—637
$3\times 3$ matrix determinant, defined      636
$3\times 3$ 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      43—44 225
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
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