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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 
                  
                
                    
                        634—636 636—638 see 636—637 636 637 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, 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 Center of mass, change of velocity 246 
                            
                     
                  
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