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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
Convex polyhedra, reduced contact set for 242 Convex polyhedra, rigid bodies as 270 Convex polyhedra, separation of 324—325 Convex polyhedra, translation 429 Convex polyhedra, vertices 281 Convex programming, defined 420 Convex programming, problem 421 Convex programming, quadratic 264 423—426 Convex quadrilaterals 392 541 Convexity 421 ConvexPolygon class 286 295 ConvexPolyhedron class 298 Coordinate systems, affine 673—675 Coordinate systems, coordinate axis directions 16 Coordinate systems, illustrated 16 Coordinate systems, inertial 32 Coordinate systems, moving frame 16 21 Coordinate systems, noninertial 32 Coordinate systems, origin 16 CopyStateArrayToAllRigidBodies function 234 Critical points 667 Cross product 606—609 Cross product, anti-commutative 608 Cross product, defined 515 606 Cross product, illustrated 606 Cross product, not associative operation 613 Cross product, vector 515 Cubic polynomials 542 Culling with axis-aligned bounding boxes (AABBs) 354—360 Culling with bounding spheres 349—354 Culling with bounding spheres, against view frustum 349 Culling, algorithm 348 Culling, collision 334 348—360 Culling, defined 348 Culling, for performance enhancement 348 Culling, occlusion 278 Culling, system 350 Culling, time 348 Culling, view frustum 348 Curvature 20 21 Curve mass, as polyline 164 Curve mass, center of mass 55—56 see Curve mass, defined 14 Curve mass, equations of motion for 121—132 Curve mass, integration 15 CURVES 7 Curves, area under 463 Curves, B-spline 173—183 Curves, closed 181—183 Curves, Frenet — Serret equations for 22 Curves, motion on 102—104 Curves, NURBS 8 173 183—187 Curves, parametric 50 55 Curves, surfaces built from 190—197 Curves, torsion 22 Cusp 700 Cycling 413 Cylinder surfaces 192—193 see Cylinder surfaces, defined 192 Cylinder surfaces, generalized 193—194 Cylinder surfaces, illustrated 192 Cylinder surfaces, parametrization 193 Cylindrical coordinates, acceleration of points 23 Cylindrical coordinates, illustrated 23 Cylindrical coordinates, position of points 23 Cylindrical coordinates, spatial motion in 22—24 Cylindrical coordinates, velocity of points 23 Deep 364 Definite integrals, defined 703 Definite integrals, motivation 708 Deformable bodies 8 161—220 Deformable bodies, elasticity 161 Deformable bodies, first alternative models 163 Deformable bodies, fourth alternative models 164 Deformable bodies, mass-spring systems 164—173 Deformable bodies, parametric surface modeling 173 Deformable bodies, physics simulation of 163 Deformable bodies, second alternative models 163 Deformable bodies, strain 162 Deformable bodies, stress 162 163 Deformable bodies, third alternative models 163 Deformation, by vertex displacement 375—377 Deformation, control points 173—183 Deformation, free-form 197—203 Deformation, functions 205 Deformation, illustrated 205 Deformation, implicit surface 203—220 Deformation, model development 203 Deformation, time interval 218 Deformation, time-varying 206 Degeneracy 413 415 Degenerate feasible vector 403 Degrees of freedom, particle systems 112 119 Degrees of freedom, solid box (rough plane) 151 Degrees of freedom, unwanted 259 Delta functions in differential equations context 245 Delta functions, averaging property 254 Delta functions, Dirac 244 Delta functions, selection property 252 253 Dependent vectors 623 Derivative approximations 718—725 Derivative approximations, backward difference 719 720 Derivative approximations, bivariate functions 714—715 Derivative approximations, centered difference 719 720 Derivative approximations, defined 718 Derivative approximations, examples 721—723 Derivative approximations, forward difference 719 Derivative approximations, higher-order 719 Derivative approximations, multivariate functions 725 Derivative approximations, parameters 721 Derivative approximations, template 718 Derivative approximations, univariate functions 719—723 derivatives 700 701 Derivatives of bivariate functions 724—725 Derivatives, computing 701 Derivatives, directional 706—708 Derivatives, list of 700 Derivatives, of multivariate functions 725 Derivatives, of univariate functions 719—723 Derivatives, partial 705 Derivatives, total 114 Determinant functions 638—645 Determinant functions, defined 639 Determinant functions, formal construction of 638—645 Determinants 634—646 see Determinants of 2 x 2 matrix 634—636 Determinants of 3 x 3 matrix 636—638 Determinants of identity 645 Determinants of matrix, computing 643 Determinants of matrix, properties 644 Determinants of product 645 Determinants, computing formal expression for 642 Determinants, defined 634 Determinants, evaluation 644 Determinants, evaluation program 644 Determinants, geometric interpretation of 637 Determinants, of elementary row operations 644 Diagonal matrices 448 449 Diagonal matrices, defined 569 Diagonal matrices, identity 569 Diagonal matrices, power computation 448 Diagonal matrices, square 448 Dictionaries for basic variables 408 Dictionaries, balanced 409 416 Dictionaries, complementary variables 416 Dictionaries, entering 408 410 415 425 Dictionaries, feasible 409 410 411 Dictionaries, initial 409 411 414 416 Dictionaries, leaving 408 415 417 425 Dictionaries, modified, initial 425 Dictionaries, moving to 409 Dictionaries, moving variables from 413 Dictionaries, obtaining 408 Dictionaries, terminal 409 411 Difference equations 727—738 Difference equations, autonomous 728 Difference equations, constant-coefficient 734—736 Difference equations, implicit nth-order 727 Difference equations, linear 730—733 Difference equations, nth-order 727 Difference equations, systems of 736—738 Difference vectors 669 Differentiable functions 699 Differential calculus 691 Differential equation solver, implementation 275 Differential equation solver, multifunction evaluation 238 Differential equation solver, time step 343 Differential equations 2 437—455 Differential equations, characteristic polynomial for 444 Differential equations, equilibria 450—455 Differential equations, extrapolation methods application to 474—476 Differential equations, first-order 92 437—440 Differential equations, for motion 2 Differential equations, general-order 444—445 Differential equations, integration 580 Differential equations, linear 140 446—450 Differential equations, nonlinear 92 Differential equations, numerical methods 10—11 Differential equations, ridges and 3 Differential equations, second-order 91 140 442—444 Differential equations, solution computation 447 Differential equations, solutions 140 141 Differential equations, solving with Runge — Kutta method 275 Differential equations, stability 450—455 Differential equations, stiffness 503—506 Differential equations, system of 223 224 Differentiation, multivariate calculus 705—708 Differentiation, univariate calculus 698—701 Dirac delta function 244 Direct sum 655 656 Direct sum of eigenspaces 657 Direct sum of transformations 656 Direct sum, defined 656 Direction vectors 285 337 Directional derivatives 706—708 Directional derivatives, defined 707 Directional derivatives, example 707 Directional derivatives, independent variables form 707 DirectX 368 DirectX, pixel shader output 375 DirectX, vertex shader output 372—373 discontinuous functions 697—698 Discrete mass in one dimension 44—45 Discrete mass in three dimensions 52 Discrete mass in two dimensions 46—48 Discrete mass, balancing, in a plane 47 see Discrete mass, balancing, in a plane on a fulcrum 48 Discrete mass, balancing, on a line 44 Displacement 102 Displacement of force 102 Displacement of mass 102 Displacement, infinitesimal 102 Dissipative forces see also Forces Dissipative forces, examples with 139—152 Dissipative forces, flat board on rough plane 148—150 Dissipative forces, multiple particles on rough plane 145—146 Dissipative forces, one particle on rough plane 141—143 Dissipative forces, solid box on rough plane 150—152 Dissipative forces, thin rod on rough plane 147—148 Dissipative forces, two particles on rough plane 143—145 Dissipative forces, viscous 140 Distance, between convex polygons 431—434 Distance, between convex polyhedra 434—436 Distance, between point and convex polygon 427—429 Distance, between point and convex polyhedron 429—431 Distance, calculations 427—436 Divergence theorem 66 67 69 Diving board example 133—134 see Diving board example, board flexibility 133—134 Diving board example, defined 133 Diving board example, illustrated 133 Diving board example, Lagrangian equation of motion 134 Diving board example, potential energy 134 Division in back substitution 564 Division, avoiding 553—554 Division, computation expense 553 Dobkin — Kirpatrick hierarchy 301 303 Dobkin — Kirpatrick hierarchy, data structure for 303 Dobkin — Kirpatrick hierarchy, implementation of 303 DoCollisionDetection function 271 DoImpulsefunction 274—275 Domain vectors 624 DoMotion function 275 DoSimulation function 234 Dot product in terms of coordinates 602 Dot product, coordinate-dependent 608 Dot product, coordinate-free 608 683 685 Dot product, defined 515 601 Dot product, orthogonality and 601 Dot product, real-valued vector 515 Dotting equation 612 Double-pendulum problem 135—136 Double-pendulum problem with kinetic friction 141 Double-pendulum problem, defined 121 135 Double-pendulum problem, illustrated 121 Double-pendulum problem, kinetic energy 135 Double-pendulum problem, Lagrangian equations of motion 136 Double-pendulum problem, potential energy 135 Drag acceleration 30 Drag coefficient 481 Drag simulation 481 Dual MP problem 426 Dual problem 404—407 see Dual problem with vector notation 405 Dual problem, defined 404 405 Dual problem, feasible vector for 406 407 Dual problem, optimizing 407 Dual problem, primal problem relationships 405 Dual problem, strong duality principle 407 Dual problem, unboundedness property 406 Dual problem, vector of slack variables 407 Dual problem, work duality principle 405—406 Dual slack equation 423 Duality gap 426 Dynamic equivalence 125 Dynamics 7 Dynamics, defined 87 Dynamics, Lagrangian 7 14 87 100—152 Dynamics, Newtonian 87 88—100 d’Alembert’s equation 102 Ear-clipping-based mesh construction 215—220 Earth, orbit 90 Earth, particle attraction 93 Earth, rotation 92 93 Edge meshes, adjacent vertices removal from 216—217 Edge meshes, extracted 216 Edge meshes, for each voxel face 215 Edge meshes, precomputed table 215 Edge meshes, triangle removal 217 Edge(s) see also Intersections Edge(s), convex polygon 286 302 Edge(s), input 327 Edge(s), interactions 211 Edge(s), isosurface intersection 207 Edge(s), moments for 63—64 Edge(s), oriented bounding boxes (OBBs) 334 Edge(s), overlap 320 Edge(s), products of inertia for 63—64 Edge(s), projections 302 Edge(s), sign changes on 209
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