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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
Parallelogram law, illustrated 671 Parallelograms, area of 634 Parallelograms, obtained by transforming cube 638 Parallelograms, obtained by transforming square 635 Parametric curves 50 55 Parametric surfaces, control points 163 Parametric surfaces, for deformable body modeling 173 Parametrization, arc length 254 Parametrization, cylinder surfaces 193 Parametrization, revolution surfaces 195 Parametrization, triangle faces 74 Partial derivatives 705 see Partial derivatives, defined 705 Partial derivatives, first 665 Partial derivatives, rates of change measurement 706 707 Partial derivatives, second 665 Partial derivatives, vector of 707 Particle systems, defined 14 Particle systems, degrees of freedom 112 119 Particle systems, equations of motion for 118—121 Particle systems, external forces 40 Particle systems, kinematics 28—31 Particle systems, total torque for 41 Particles, acceleration of 16 19 Particles, defined 14 Particles, discrete set of 58 Particles, equations of motion for 102—114 Particles, inertia tensor for 60 Particles, kinematics 15—27 Particles, kinetic energy of 81 Particles, mass 93 Particles, motion about fixed axis 25—26 Particles, motion about moving axis 26—27 Particles, multiple, on rough plane 145—146 Particles, path of 80 Particles, planar motion in Cartesian coordinates 15—18 Particles, planar motion in polar coordinates 18—19 Particles, position of 15—16 19 Particles, single, on rough plane 141—143 Particles, spatial motion in Cartesian coordinates 19—22 Particles, spatial motion in cylindrical coordinates 22—24 Particles, spatial motion in spherical coordinates 24—25 Particles, speed of 16 19 Particles, total torque 41 Particles, two, on rough plane 143—145 Particles, velocity equation 243 Particles, velocity of 16 19 Path(s) of motion 88 Path(s), Foucault pendulum tip 97 Path(s), work independence of 82 Permutation matrix 579 Permutation matrix, defined 578 Permutation matrix, factorization of 639 Permutations, defined 638 Permutations, even 639 686 687 Permutations, multi-index as 641 Permutations, odd 639 686 687 Permutations, summation over 641 Permutations, tensor 688 Permutations, transposition 638 Perp function 429 Perp vectors, defined 683 Perp vectors, length 684 Physical stability of equilibrium solution 488 Physical stability, defined 487 Physics engines 8 221—365 Physics engines, constrained motion 240—280 Physics engines, defined 4 Physics engines, performance 278 Physics engines, unconstrained motion 223—239 Physics in real time 5 Physics, concepts 6 13—85 Physics, shader programs and 367—389 Pixel shaders 367 see Pixel shaders, basic 374 Pixel shaders, defined 369 Pixel shaders, DirectX output 375 Pixel shaders, OpenGL output 374 Pixel shaders, rendering with 376 Pixel shaders, rippling ocean waves 381 Pixels, ambiguous, resolutions for 210 Pixels, sign configurations 209 Pixels, vertex-edge configurations 213 Planar lamina 14 Planar motion in Cartesian coordinates 15—18 Planar motion in polar coordinates 18—19 Planes, coincident 561 562 Planes, disjoint 561 Planes, nonparallel 561 Planes, tangent 708 Points, affine coordinates 673 Points, body 242 Points, collision 240—242 251 252 Points, contact 248—258 270 281 Points, continuum of 46 Points, control 173—197 202—203 Points, defined 669 Points, extreme 302—303 Points, feasible 418 Points, separating 243 Points, spatial 253 Points, tetrahedron 679 Points, vectors vs. 671 Polar coordinates, equations of motion in 91 Polar coordinates, frame at point on curve 18 Polar coordinates, planar motion in 18—19 Polarization 386 Polygonal faces, area 70 Polygonal faces, projection 71 POLYGONS see also Convex polygons Polygons, clockwise ordering 320 Polygons, overlapping 324 Polygons, projection intervals 317 Polyhedra see also Convex polyhedra Polyhedra, boundary of 67 Polyhedra, faces 67 Polyhedra, inertia tensor 66—79 Polyhedra, mass 66—79 Polyhedra, mass pseudocode 76—78 Polyhedra, rigid bodies 229 Polyhedra, triangle faces 73 74—75 Polynomial coefficients 630 Polynomial interpolation 476—477 Polynomial interpolation, extrapolation and 476 Polynomial interpolation, rational 476—477 Polynomials, Bernstein 189 Polynomials, characteristic 444 447 659—660 Polynomials, generation by vector fields 68 Polynomials, interpolation 476—477 Polynomials, quartic 190 Polynomials, Taylor 458 465 Polytope see Convex polyhedra Portal systems 278 Position of particles 15—16 19 Position of points 23 24 Position, total derivative of 114 Position, vector 26 Postimpulse velocities 259 Postimpulse velocities as reflection of preimpulse velocity 260 Postimpulse velocities, angular 247 249 Postimpulse velocities, linear 246 249 Postimpulse velocities, magnitude 251 Postimpulse velocities, nonnegative 260 Postimpulse velocities, rectangle intersecting two objects 257 Postimpulse velocities, relative 247 Postimpulse velocities, sequential processing 265 Postimpulse velocities, simultaneous processing 265 Postimpulse velocities, world 259 260 potential energy 83—85 92 Potential energy, defined 83 Potential energy, dependency 83—84 Potential energy, diving board example 134 Potential energy, double-pendulum problem 135 Potential energy, infinitesimal quantities 84 Potential energy, quantity 83 Potential separating axes 311 315 Potential separating axes, for sphere 349 Potential separating axes, separating equation 348 Potential separating axes, tests 335 Power series 663 664 Powers of a matrix 662 Predictor-corrector methods 472—473 Preimpulse velocities 246 264 Preimpulse velocities, angular 247 Preimpulse velocities, as reflection to postimpulse velocity 260 Preimpulse velocities, computing 273 Preimpulse velocities, linear 246 Preimpulse velocities, replacing by postimpulse vectors 274 Preimpulse velocities, world 259 260 Pressure 162 Primal MP problem 426 Primal problem see also Linear programming Primal problem, defined 404 Primal problem, dual problem relationships 405 Primal problem, feasible vector for 405 407 Primal problem, optimizing 407 Primal problem, vector of slack variables 407 Primal problem, with vector notation 405 Product rule 700 Products of inertia 57—66 see Moments Products of inertia, calculation 62 63 64 Products of inertia, defined 59 Products of inertia, for continuum of mass 60 Products of inertia, for edges 63—64 Products of inertia, for faces 64—65 Products of inertia, for vertices 63 Projection integrals 71—73 Projection intervals of two OBBs 336 Projection intervals, intersection 318 Projection intervals, one stationary, one moving 346 Projection intervals, order 317 Projection intervals, overlapping 336 Projection intervals, polygons 317 Projection intervals, relative position 344 Projection intervals, separated 336 Projection intervals, sum of the radii 336 Projection intervals, values computation 344 Projection matrix 623 624 Projection of vectors 602 603 621—624 see Projection of vectors, equation 621 Projection of vectors, onto range 622 Projection of vectors, onto subspace 621 Pulley, spring, and mass system example 125—128 Pulley, spring, and mass system example, defined 125 Pulley, spring, and mass system example, generalized forces 127 Pulley, spring, and mass system example, gravitational force 125 Pulley, spring, and mass system example, illustrated 126 128 Pulley, spring, and mass system example, kinetic energy 126 Pulley, spring, and mass system example, Lagrangian equations of motion 127 Pulley, spring, and mass system example, mass position 127 Pulley, spring, and mass system example, principle moment 126 Pulley, spring, and mass system example, pulley 128 Pulley, spring, and mass system example, spring 128 Pulleys, springs, and mass system example 129 Pythagorean Theorem 601 Q-COLLIDE 364 Quadrangle interpolation 541 542 Quadratic programming see also Mathematical programming Quadratic programming, convex 423—426 Quadratic programming, defined 420 Quadratic programming, problem 421 423 436 Quadratic programming, quantities of interest 425 Quaternions 11 507—544 Quaternions, addition 512 Quaternions, algebraic operations 512—515 Quaternions, classical approach 512—516 Quaternions, conversion to rotation matrix 537 Quaternions, defined 507 512 Quaternions, geometric understanding 517 Quaternions, interpolation of 539—542 Quaternions, linear algebraic approach 517—522 Quaternions, multiplication 513—515 Quaternions, notation 538 Quaternions, orientation 233 236 Quaternions, product of 515 Quaternions, representation as coordinate-free description 514 Quaternions, rotation matrix 516 537 Quaternions, rotations relationship 515—516 Quaternions, scalar multiplication 513 Quaternions, specification 512 Quaternions, square function of 542 Quaternions, subtraction 513 Quaternions, time-varying, derivatives of 543—544 Quaternions, unit constraint 534 Quaternions, unit-length 512 517 543 Queries, AABB computation 354 Queries, external 326 Queries, find-intersection 316 325 Queries, quotient rule 700 Queries, test-intersection 222 344 349 350 R-Plus 4 Range of the function 624 RAPID 363 Rational numbers 545—546 Rational numbers, addition 546 Rational numbers, defined 546 Ray tracking 4 Reactive forces 101 Real numbers 546 588 Rectangles, approximation of area by 463 Rectangles, axis-aligned 359 Rectangles, height 702 Rectangles, infinitesimal area 702 Rectangles, infinitesimal width 702 Rectangles, intersecting 359—360 Rectangles, overlapping 360 Rectangles, two-object intersection 256—257 Rectangular surface patch 187 Recursive descent in dimension 713 Reduced contact set 241 see Reduced contact set for convex polyhedra 242 Reduced contact set, processing 242 Redundant constraints 395 Reference system 83 Reflection 383 Reflection, angles 383 384 Reflection, effects 384 Reflection, Fresnel 386—388 Reflection, illustrated 383 Reflection, light direction 383 Reflection, refraction with 384 Refraction 383—386 Refraction, angle 384 Refraction, application 386 Refraction, application screen shots 385 Refraction, defined 383 Refraction, illustrated 383 Refraction, index of 384 Refraction, light direction 384 Refraction, observation 384 Refraction, reflection with 384 Relative acceleration 266 Relative velocity 243 245 Relative velocity at resting contact 266 Relative velocity, between points on path 258 Relative velocity, equation 262 Relative velocity, formula 258 Relative velocity, normal component 265 Relative velocity, postimpulse 247 Resolution of forces 268
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