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Elberly D.H., Shoemake K. — Game Physics
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Название: Game PhysicsАвторы: 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: Рубрика: Физика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 776Добавлена в каталог: 19.03.2006Операции: Положить на полку |
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Stability, asymptotic 453 454 Stability, explicit Euler’s method 500 Stability, for constant-coefficient linear systems 451—453 Stability, for general autonomous systems 453—455 Stability, for single-step methods 488—490 Stability, implicit Euler’s method 500 Stability, leap frog method 502 Stability, numerical 487—502 Stability, physical 487 Stability, results 451 Stability, Runge — Kutta fourth-order method 501 Stability, solution 450 Stack variables 238 Standard Euclidean basis 601 State arrays, copying data from 238 State arrays, copying of data and 234 State arrays, design 236 State arrays, global 231 238 State arrays, size 235 State variables, copying 230 State variables, initialization 229 State variables, projection of 223 State variables, rigid body 239 State vectors of entire system 227 State vectors, as list of pairs 224 State vectors, defined 223 State vectors, n blocks of values 227 State vectors, updating 223 Static friction 36 Stationary objects 286—310 Stationary objects, convex polygons 286—298 Stationary objects, convex polyhedra 298—310 Steiner points 208 Stiff equations 503—506 Stokes’s theorem 15 strain 162 Stress, defined 162 Stress, ratio to strain 162 Stress, volume 163 Strong duality principle 407 426 Subsets, span of 618 Subspaces, affine 675—676 Subspaces, analysis 613 Subspaces, defined 595 Subspaces, four fundamental 620 Subspaces, one-dimensional 621 Subspaces, orthogonal 613—615 620 Subspaces, parallel 675 Subspaces, projection 621 Subspaces, span of subsets as 618 Subspaces, subsets as 595 Subspaces, two-dimensional 621 675 Subtraction 545 Subtraction, quaternions 513 Subtraction, vector 585 Superscript asterisk 514 Surface integrals, decomposition 67—68 Surface integrals, volume integral conversion to 67 Surface mass 14 15 53—55 see Surface mass, center of mass 53—55 Surface mass, defined 14 Surface mass, equations of motion for 121—132 Surface mass, in space 15 Surface mass, integration 15 Surface(s), B-spline 187—188 Surface(s), built from curves 190—197 Surface(s), closed 192 Surface(s), cylinder 192—193 Surface(s), generalized cylinder 193—194 Surface(s), motion on 104—112 Surface(s), NURBS 188—190 Surface(s), parametric 163 173 Surface(s), revolution 195—196 Surface(s), tube 197 198 199 Swapping 688 Sweep algorithm 354—355 Sweep algorithm, defined 354 Sweep algorithm, illustrated 355 SWIFT 364 Symmetric matrices 448 570 623 Symmetric matrices, defined 569 Symmetric matrices, eigendecomposition for 652—655 Symmetric matrices, eigenvalues of 655 Symmetric matrices, example 569 Symmetric matrices, real-valued 652 Systems of difference equations 736—738 Systems of difference equations, defined 737 Systems of difference equations, homogeneous solution 738 Systems of difference equations, uses 737 Table-based mesh selection 214—215 Tableau of coefficients and constants 399 Tableau, defined 399 Tableau, rows 402 Tableau, updated 400 401 Tangent line 708 Tangent line, defined 698 Tangent line, direction 708 Tangent plane 708 Tangential acceleration 17 26 Taylor expansions, for acceleration 483 Taylor expansions, for velocity 483 Taylor polynomials 458 465 664 665 Taylor series 720 Taylor series, approach 438 Taylor series, for exponential function 446 Taylor’s Theorem 454 458 467 478 481 Taylor’s Theorem, application of 466 Taylor’s Theorem, extension to bivariate functions 465 Taylor’s Theorem, with second-degree polynomial 461 Temporal coherence 350 358 Terminal dictionary 409 411 Test-intersection queries 344 see Test-intersection queries, defined 222 Test-intersection queries, total cost 349 350 Testlntersection function 289 291—292 298 316 326 328—329 339—341 344—346 Tetrahedrons, barycentric coordinates 679—680 Tetrahedrons, edges 305 Tetrahedrons, illustrated 304 Tetrahedrons, spherical dual of 304 Tetrahedrons, triangle base 685 Tetrahedrons, triangle slices 684 685 Tetrahedrons, vertices 304 Tetrahedrons, volume of 684—685 688 Thin rod (rough plane) 147—148 Thin rod (rough plane), defined 147 Thin rod (rough plane), frictional force 147 Thin rod (rough plane), generalized force 147—148 Thin rod (rough plane), kinetic energy 147 Thin rod (rough plane), Lagrangian equations of motion 148 Third-order Runge — Kutta methods 468 Three-dimensional array (masses) 170—171 Three-dimensional array (masses), defined 170 Three-dimensional array (masses), equation of motion 170—171 Three-dimensional array (masses), illustrated 170 Three-dimensional Perlin noise 375 Time, as continuous variable 281 Time, coherence 284 Time, collision, predicting 283 Time, culling 348 Time, intervals, constancy over 343 Time, last, of contact 283 Time, object at 282 Time, step 343 Time-varying frames 114—116 Time-varying frames, equations of motion 115 Time-varying frames, generalized force 116 Time-varying frames, kinetic energy 115 Time-varying frames, relevant derivatives 116 Time-varying frames, total time derivative 115 Time-varying quaternions, derivatives 543—544 Topics, this book 6—11 torque 37—39 see Torque, applied 227 228 Torque, computing 238 Torque, defined 37 Torque, driving 225 Torque, due to internal forces 38 Torque, equation 60 Torque, evaluation 276 Torque, external 267 Torque, impulsive 246 Torque, infinitesimal 49 Torque, mass 44—45 Torque, nonzero vector 40 Torque, quantity 37 Torque, resolution 268 Torque, total 39 41 Torsion 22 Total derivatives 114 Transfer of axes 66 transpositions 638 639 Trapezoids, approximation of area by 462—463 Triangle faces 73 74—75 Triangle faces, counterclockwise ordered 74 Triangle faces, parametrization of 74 Triangle pendulum 124—125 Triangle pendulum, defined 124 Triangle pendulum, illustrated 124 Triangle pendulum, Lagrangian equation of motion 125 Triangle pendulum, mass density 125 Triangle slices 684 685 Triangles, area of 682—684 687 Triangles, barycentric coordinates 678—679 Triangles, base length 682 Triangles, direct parametrization of 74—75 Triangles, extraction 208 Triangles, generation 215 Triangles, height 682 Triangles, large number issue 208 Triangles, linear interpolation over 679 Triangles, mesh 190 214 215 Triangles, moving, edge-to-edge contact 321 Triangles, removal in edge mesh 217 Tridiagonal matrices 581 Triple pendulum problem 137 Triple scalar product 609—610 Triple scalar product, defined 609 Triple scalar product, signed volume 609 610 Triple vector product 610—613 Triple vector product, defined 610 Triple vector product, illustrated 611 Tube surfaces 197 see Tube surfaces, closed 198 Tube surfaces, construction 197 Tube surfaces, defined 197 Tube surfaces, wriggling snake modeled as 199 Two particles (rough plane) 143—145 Two particles (rough plane), defined 143 Two particles (rough plane), generalized force 144—145 Two particles (rough plane), illustrated 143 Two particles (rough plane), kinetic energy 144 Two particles (rough plane), Lagrangian equations of motion 145 Two-body problem 137—139 see Two-body problem, center of mass 137 Two-body problem, defined 137 Two-body problem, gravitational force 137 Two-body problem, kinetic energy 137 Two-body problem, Lagrangian equations of motion 138 Two-dimensional array (masses) 166—169 see Two-dimensional array (masses), equations of motion 168 Two-dimensional array (masses), illustrated 169 Two-dimensional array (masses), mass location 166 Two-dimensional array (masses), surface mass representation 168 Two-dimensional example (linear programming) 392—394 Umbrella parents 302 Unboundedness property 406 Unconstrained motion 9 222 223—239 Unconstrained motion, equations of motion 228 Unconstrained motion, illustrative implementation 228—233 Unconstrained motion, Newtonian dynamics for 223 Unconstrained motion, practical implementation 234—239 Unique representation 597 Unique solution 441 Uniqueness question 441 Unit-area square 635 Unit-length quaternions 512 517 543 Unit-volume cube 638 Univariate calculus 692—704 see Univariate calculus, continuity 697—698 Univariate calculus, defined 691 Univariate calculus, differentiation 698—701 Univariate calculus, functions 691 Univariate calculus, integration 701—704 Univariate calculus, limits 694—696 Univariate calculus, limits of a sequence 696—697 Univariate calculus, l’Hopital’s rule 701 Universal gravitational constant 32 Update function 238 239 Upper echelon matrices 577 Upper triangular matrices 571 V-Collide 364 Vector addition 584 588 Vector addition, associative 584 Vector addition, commutative 585 Vector addition, defining 589—590 591 Vector addition, scalar multiplication distributive over 595 vector class 671 Vector equality 588 589 Vector multiplication 587 Vector spaces 583—633 see Vector spaces, axiom consequences 591 Vector spaces, axiom verification 589 594 Vector spaces, bases 598—601 Vector spaces, cross product 606—609 Vector spaces, defined 583 Vector spaces, definition of 588—593 Vector spaces, dot product 601 602 Vector spaces, finite dimensional 599 625 Vector spaces, linear combinations 593—594 Vector spaces, linear independence 595—601 Vector spaces, linear transformations 624—633 Vector spaces, orthogonal subspaces 613—615 Vector spaces, over real numbers 588 Vector spaces, projections 621—624 Vector spaces, properties 599 Vector spaces, spans 593—594 Vector spaces, subspaces 595 Vector spaces, triple products 609—613 Vector subtraction 79 585 Vector sum 586 Vector sum, distributing across 587 588 Vector sum, linear transformation of 624 Vectors, acceleration 17 21 Vectors, additive identity 585 Vectors, basis 152 Vectors, binormal 21 Vectors, coefficient 628 Vectors, degenerate feasible 403 Vectors, dependent 623 Vectors, difference 586 669 Vectors, direction 285 337 583 Vectors, domain 624 Vectors, feasible 396 402 Vectors, feasible basis 396 402 Vectors, frame 23 Vectors, independent 624 Vectors, knot 175—176 Vectors, linear combination of 593—594 Vectors, linearly dependent 596 Vectors, linearly independent 596 600 610
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