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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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Предметный указатель
Center of mass, computing 51 Center of mass, construction 41 Center of mass, continuous mass in one dimension 45—46 Center of mass, continuous mass in three dimensions 52—56 Center of mass, continuous mass in two dimensions 48—51 Center of mass, defined 44 45 Center of mass, discrete mass in one dimension 44—45 Center of mass, discrete mass in three dimensions 52 Center of mass, discrete mass in two dimensions 46—48 Center of mass, formula 45 Center of mass, location determination 224—225 Center of mass, modification 248 Center of mass, moment of inertia with respect to 57 58 Center of mass, polyhedron rotation about 354 Center of mass, resolution of forces at 268 Center of mass, two-body problem 137 Center of mass, values 249 Center of mass, velocity 130 243 Center of mass, world velocity 123 Center of mass, y-value 51 Center of mass, z-value 55 Centered difference approximation 720 see Centered difference approximation, defined 719 Centered difference approximation, example 722 723 Centered difference approximation, occurrence 721 Centered difference approximation, parameters 721 Centered difference approximation, with fourth-order error 720 centripetal acceleration 17 26 Cg, CgConverter tool 370 Cg, compiler 369 Cg, installation 370 Cg, Toolkit 369 370 Chain rule 114 704 705—706 Chain rule, applied to velocity 105 Chain rule, defined 705 Chain rule, use of 706 Change of basis matrix, computing 633 Change of basis matrix, defined 631 Change of velocity 243 245—250 Change of velocity, discontinuous 245 Change of velocity, impulsive force 246 Change of velocity, of center of mass 246 Characteristic equations 647 Characteristic polynomials 444 447 659 660 Characteristic polynomials of matrix representation 657 Characteristic polynomials, explicit Euler’s method 499 Characteristic polynomials, general-order differential equations 444 447 Characteristic polynomials, implicit Euler’s method 500 Characteristic polynomials, leap frog method 502 Characteristic polynomials, Runge — Kutta fourth-order method 501 Characteristic polynomials, second-order differential equations 452 Classes, AxisAlignedBox 352 Classes, BasisFunction 180 Classes, BoundingVolumeTree 363 Classes, BSplineSurface 188 Classes, BSplineVolume 200 Classes, BSPNode 307 Classes, CollisionGroup 363 Classes, CollisionRecord 363 Classes, ConvexPolygon 286 295 Classes, ConvexPolyhedron 298 Classes, NURBSCurve 184 Classes, NURBSSurface 190 Classes, RigidBody 275—276 279 classes, Sphere 352 Clifford algebras 522 538 Closed B-spline curves 181—183 see Closed B-spline curves with open knot vector 181 Closed B-spline curves with periodic knot vector 181 Closed formulas 440 Coefficient vectors 628 Coefficients of restitution 245 Cofactors, defined 642 Cofactors, expansion 643 Cofactors, matrix of 642 Coherence 350 Coherence, spatial 350 Coherence, temporal 350 358 Collection of functions 691 Colliding contact 242—265 243 258 see Resting Colliding contact, change of velocity at 245 Colliding contact, change to resting contact 245 Colliding contact, collision response for 242—265 Colliding contact, defined 240 Colliding contact, illustrated 241 Colliding contact, operation order 270 Colliding contact, physical simulation at point of 245 Colliding contact, processing point of 248 Collision culling see Culling Collision detection 221—222 Collision detection for constrained motion 222 Collision detection systems 4—5 280 281 324 Collision detection systems, intersection detection 281 Collision detection systems, not reporting collisions 281 Collision detection systems, on method of separating axes 343 Collision detection systems, outline 360 Collision detection systems, performance 348 Collision detection, contact set 222 316—324 325—334 Collision detection, contact time 222 Collision detection, defined 221 Collision detection, enabling 251 Collision detection, of convex polyhedra 9 223 280—348 Collision detection, with nonpenetration constraint 324 Collision points 240—242 Collision points, object movement at 240 Collision points, processing 251 252 Collision response for colliding contact 242—265 Collision response for resting contact 265—270 Collision response, function 271 Collision response, system 277 278 CollisionGroup class 363 CollisionRecord class 363 Column matrices 555 Column swap 564 Complementary slackness 407 423 Complementary variables 407 410 412 Complementary variables, dictionary 416 Complementary variables, nonbasic 416 Complementary variables, not leaving dictionary 416—418 complex numbers 546—547 Complex numbers, addition 547 Complex numbers, defined 547 Complex numbers, imaginary part 514 Complex numbers, multiplication 547 Complex numbers, real part 514 Complex structures 538 ComputeLCPMatrix function 272—273 Computelnterval function 301 310 314 317 ComputePrelmpulseVelocity function 273 ComputeRestingContactVector function 273—274 Conjugate gradient method 566 Conservative forces 82—83 see Conservative forces, applied in general system 83 Conservative forces, consequences 85 Conservative forces, defined 82 Conservative forces, exactness conditions and 85 Conservative forces, examples 82—83 133—139 Conservative forces, gravitational 82 Conservative forces, Lagrangian equation of motion for 133 Consistency 488 constant angular velocity 346—348 see Constant angular velocity, distance quantity 347 Constant angular velocity, moving bodies formulation 347 Constant angular velocity, rotation matrices 347 Constant angular velocity, separating equation 348 Constant linear velocity 311—334 Constant linear velocity, analysis basis 346 Constant linear velocity, boxes moving with 343—346 see Constant linear velocity, contact set for convex polygons 316—324 Constant linear velocity, contact set for convex polyhedra 325—334 Constant linear velocity, separation of convex polygons 311—316 Constant linear velocity, separation of convex polyhedra 324—325 Constant linear velocity, time-varying distance between centers 346 Constant-coefficient difference equations 734—736 Constrained local minimum 421 Constrained motion 240—280 Constrained motion, change of velocity computation 245—250 Constrained motion, collision points 240—242 Constrained motion, collision response for resting contact 265—270 Constrained motion, illustrative implementation 270—278 Constrained motion, impulses 243—245 Constrained motion, Lagrangian dynamics 278—280 Constrained motion, multiple contact points 250—258 Constrained motion, simultaneous processing of contact points 258—265 Constrained optimization 692 715—718 see Constrained optimization, defined 710 715 Constrained optimization, method of Lagrange multipliers 715—716 717 Constraining forces, balancing 114 see Constraining forces, defined 101 Constraining forces, determining 112—114 Constraining forces, equations of motion 113 Constraining forces, generalized forces and 113 Constraining forces, kinetic energy 113 Constraining functions 418 419 Contact colliding 240 241 242—265 Contact forces, acceleration computation and 269 see Contact forces, at resting contact 267 Contact forces, choosing 269 Contact forces, computing 240 Contact forces, derivation of 436 Contact forces, exerting 267 Contact forces, zero 269 Contact points of colliding contact 248—250 Contact points, computing 281 Contact points, edge-to-edge intersection 270 Contact points, finite set of 256 281 Contact points, four rigid bodies 261 Contact points, magnitude of velocity at 258 Contact points, multiple 250—258 Contact points, processing 251 Contact points, simultaneous processing of 258—265 Contact points, vertex-face intersection 270 Contact sets as line segments 254 316 Contact sets for convex polygons 316—324 Contact sets, calculation 316 317 see Contact sets, convex polyhedra 325—334 Contact sets, defined 222 Contact sets, determining 222 Contact sets, reduced 241 242 Contact space formulation 362 Contact time 246 Contact time, defined 222 Contact time, determining 222 Contact time, last 283 Contact, at instant of 258 Contact, convex polyhedra 325—326 Contact, edge-to-edge 320 Contact, last time of 283 Contact, line segment of 256 Contact, resolution 362 Contact, resting 5 240 241 Continuity, multivariate calculus 704—705 Continuity, univariate calculus 697—698 Continuous dependence 442 Continuous functions, multivariate calculus 704 Continuous functions, univariate calculus 697 Continuous mass in one dimension 45—46 Continuous mass in shape of hemicircle 51 Continuous mass in three dimensions 52—56 Continuous mass in two dimensions 48—51 Continuous mass, balancing, on a line 46 see Continuous mass, bounded by parabola and line 49 Continuous mass, moments for 60 Continuous mass, products of inertia for 60 Continuous materials, defined 14 Continuous materials, kinematics 28—31 Continuous variables 696 Continuum of mass, defined 14 Continuum of mass, equations of motion 121—132 Continuum of mass, linear momentum 42 Continuum of points 46 Control points for parametric surface 163 Control points, B-spline curves 173 Control points, deformation 173—197 Control points, in free-form deformation 204 Control points, knot vectors and 183 Control points, lattice of 200 Control points, management 190 Control points, mesh vertex positions 202 Control points, modified 202 Control points, NURBS curves 183 185 186 Control points, perturbations 202—203 Control points, symmetric 189 Control points, vertices 163 Control theory 441 Control weights 183 185 Control weights, definition 189 Control weights, management 190 Control weights, symmetric 189 Convergent methods 489 Conversion to rotation matrix 537 Conversion, planar integral 69 Conversion, primary state to secondary state 238 Conversion, restricted normal form 398 Conversion, to LCP 409 411 CONVERT function 238 239 Convex functions of two variables 421 Convex functions, defined 420 Convex functions, graph of 420 421 convex polygons 286—298 Convex polygons, bisection formula 291 Convex polygons, Boolean operations on 316 Convex polygons, contact set 316—324 Convex polygons, counterclockwise-ordered vertices 427 Convex polygons, distance between 431—434 Convex polygons, distance between point and 427—429 Convex polygons, edge-edge contact 287 Convex polygons, edges 286 302 Convex polygons, find-intersection query for 316 Convex polygons, illustrated 293 Convex polygons, intersecting 287 312 Convex polygons, intersection testing pseudocode 312—314 Convex polygons, linear velocities 311 Convex polygons, lines between 288 Convex polygons, nonintersecting 287 Convex polygons, number of edges 304 Convex polygons, planar 298 Convex polygons, separation of 299 311—316 Convex polygons, spherical 304 Convex polygons, two-dimensional intersector 326 Convex polygons, vertex-edge contact 287 Convex polygons, vertex-vertex contact 287 Convex polyhedra 223 298—310 Convex polyhedra, colliding, intersection points for 256 Convex polyhedra, collision detection of 223 280—348 Convex polyhedra, computing points of contact between 280 Convex polyhedra, contact set for 325—334 Convex polyhedra, contact type 326 Convex polyhedra, defined 284 Convex polyhedra, distance between 434—436 Convex polyhedra, distance between points and 429—431 Convex polyhedra, finite set of direction vectors and 299 Convex polyhedra, interfaces 307 Convex polyhedra, intersection calculator for 283 Convex polyhedra, intersection testing cost 349 Convex polyhedra, intersections 283 329 Convex polyhedra, moving 282 329 Convex polyhedra, moving with constant linear velocity 324—325 Convex polyhedra, nonconvex polyhedra decomposition into 363—364 Convex polyhedra, penetration of 280
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