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Game physics engine development:

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Bibliographic Details
Main Author:	Millington, Ian (Author)
Format:	Book
Language:	English
Published:	Amsterdam [u.a.] Elsevier[u.a.] 2007
Series:	The Morgan Kaufmann series in interactive 3D technology
Subjects:	Computerspiel Maschine Programmierung Computerphysik Gesetz > Physik
Online Access:	Inhaltsverzeichnis
Physical Description:	XXI, 456 S. Ill., graph. Darst. 1 CD-ROM (12 cm)
ISBN:	9780123694713 012369471X 9780123737229 0123737222

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adam_text	Contents List of Figures xvi Preface xix Chapter J. Introduction і 1.1 What Is Game Physics? 2 1.2 What Is a Physics Engine? 2 1.2.1 Advantages of a Physics Engine 3 1.2.2 Weaknesses of a Physics Engine 4 1.3 Approaches to Physics Engines 5 1.3.1 Types of Object 5 1.3.2 Contact Resolution 5 1.3.3 Impulses and Forces 6 1.3.4 What We re Building 7 1.4 The Mathematics of Physics Engines 7 1.4.1 The Math You Need to Know 8 1.4.2 The Math We ll Review 9 1.4.3 The Math We ll Introduce 10 1.5 The Source Code in This Book 10 1.6 How this Book Is Structured 11 Part I Particle Physics 13 Chapter jLi The Mathematics of Particles 15 2.1 Vectors 15 2.1.1 The Handedness of Space 19 2.1.2 Vectors and Directions 2.1.3 Scalar and Vector Multiplication 2.1.4 Vector Addition and Subtraction 2.1.5 Multiplying Vectors 2.1.6 The Component Product 2.1.7 The Scalar Product 2.1.8 The Vector Product 2.1.9 The Orthonormal Basis 2.2 Calculus 2.2.1 Differential Calculus 2.2.2 Integral Calculus 2.3 Summary 20 23 24 27 28 29 31 35 35 36 40 42 Chapter The Laws of Motion 3.1 A Particle 3.2 The First Two Laws 3.2.1 The First Law 3.2.2 The Second Law 3.2.3 The Force Equations 3.2.4 Adding Mass to Particles 3.2.5 Momentum and Velocity 3.2.6 The Force of Gravity 3.3 The Integrator 3.3.1 The Update Equations 3.3.2 The Complete Integrator 3.4 Summary 43 43 44 45 46 46 47 48 48 50 51 52 54 Chapter The Particle Physics Engine 4.1 Ballistics 4.1.1 Setting Projectile Properties 4.1.2 Implementation 4.2 Fireworks 4.2.1 The Fireworks Data 4.2.2 The Fireworks Rules 4.2.3 The Implementation 4.3 Summary 55 55 56 57 60 60 61 63 66 Part II Mass-Aggregate Physics 67 Chapter Adding General Forces 5.1 D Alembert s Principle 5.2 Force Generators 5.2.1 Interfaces and Polymorphism 5.2.2 Implementation 5.2.3 A Gravity Force Generator 5.2.4 A Drag Force Generator 5.3 Built-in Gravity and Damping 5.4 Summary Chapter Springs and Springlike Things 6.1 Hook s Law 6.1.1 The Limit of Elasticity 6.1.2 Springlike Things 6.2 Springlike Force Generators 6.2.1 A Basic Spring Generator 6.2.2 An Anchored Spring Generator 6.2.3 An Elastic Bungee Generator 6.2.4 A Buoyancy Force Generator 6.3 Stiff Springs 6.3.1 The Problem of Stiff Springs 6.3.2 Faking Stiff Springs 6.4 Summary Chapter Hard Constraints 7.1 Simple Collision Resolution 7.1.1 The Closing Velocity 7.1.2 The Coefficient of Restitution 7.1.3 The Collision Direction and the Contact Normal 7.1.4 Impulses 69 69 72 73 73 76 77 79 79 81 81 83 83 83 84 86 87 89 93 93 95 101 103 103 104 105 105 107 7.2 Collision Processing 108 7.2.1 Collision Detection 111 7.2.2 Resolving Interpénétration 112 7.2.3 Resting Contacts 116 7.3 The Contact Resolver Algorithm 119 7.3.1 Resolution Order 120 7.3.2 Time-Division Engines 124 7.4 COLLISIONLIKE THINGS 125 7.4.1 Cables 126 7.4.2 Rods 128 7.5 Summary 131 Chapter 8 The Mass-Aggregate Physics Engine ізз 8.1 Overview of the Engine 133 8.2 Using the Physics Engine 139 8.2.1 Rope-Bridges and Cables 139 8.2.2 Friction 140 8.2.3 Blob Games 141 8.3 Summary 142 Part III Rigid-Body Physics 143 Chapter Zr The Mathematics of Rotations 145 9.1 Rotating Objects in Two Dimensions 145 9.1.1 The Mathematics of Angles 146 9.1.2 Angular Speed 148 9.1.3 The Origin and the Center of Mass 148 9.2 Orientation in Three Dimensions 152 9.2.1 Euler Angles 153 9.2.2 Axis-Angle 155 9.2.3 Rotation Matrices 156 9.2.4 Quaternions 157 9.3 Angular Velocity and Acceleration 159 9.3.1 The Velocity of a Point 160 9.3.2 Angular Acceleration 160 9.4 Implementing the Mathematics 161 9.4.1 The Matrix Classes 161 9.4.2 Matrix Multiplication 162 9.4.3 The Matrix Inverse and Transpose 171 9.4.4 Converting a Quaternion to a Matrix 178 9.4.5 Transforming Vectors 180 9.4.6 Changing the Basis of a Matrix 184 9.4.7 The Quaternion Class 186 9.4.8 Normalizing Quaternions 187 9.4.9 Combining Quaternions 188 9.4.10 Rotating 189 9.4.11 Updating by the Angular Velocity 190 9.5 Summary 191 Chapter 10 Laws of Motion for Rigid Bodies 193 10.1 The Rigid Body 193 10.2 Newton 2 for Rotation 196 10.2.1 Torque 197 10.2.2 The Moment of Inertia 198 10.2.3 The Inertia Tensor in World Coordinates 202 10.3 D Alembert for Rotation 205 10.3.1 Force Generators 208 10.4 The Rigid-Body Integration 210 10.5 Summary 212 Chapter 11 The Rigid-Body Physics Engine 213 11.1 Overview of the Engine 213 11.2 Using the Physics Engine 216 11.2.1 A Flight Simulator 216 11.2.2 A Sailing Simulator 222 11.3 Summary 227 Chapter 12 Collision Detection 23 і 12.1 Collision Detection Pipeline 232 12.2 Coarse Collision Detection 232 12.3 Bounding Volumes 233 12.3.1 Hierarchies 235 12.3.2 Building the Hierarchy 241 12.3.3 Sub-Object Hierarchies 250 12.4 Spatial Data Structures 251 12.4.1 Binary Space Partitioning 251 12.4.2 Oct-Trees and Quad-Trees 255 12.4.3 Grids 258 12.4.4 Multi-Resolution Maps 260 12.5 Summary 261 Chapter 13 Generating Contacts 263 13.1 Collision Geometry 264 13.1.1 Primitive Assemblies 264 13.1.2 Generating Collision Geometry 265 13.2 Contact Generation 265 13.2.1 Contact Data 267 13.2.2 Point-Face Contacts 269 13.2.3 Edge-Edge Contacts 269 13.2.4 Edge-Face Contacts 271 13.2.5 Face-Face Contacts 271 13.2.6 Early-Outs 272 13.3 Primitive Collision Algorithms 273 13.3.1 Colliding Two Spheres 274 13.3.2 Colliding a Sphere and a Plane 276 13.3.3 Colliding a Box and a Plane 279 13.3.4 Colliding a Sphere and a Box 282 13.3.5 Colliding Two Boxes 287 13.3.6 Efficiency and General Polyhedra 297 13.4 SUMMARY 297 Part V Contact Physics 299 Chapter 14 Collision Resolution зо і 14.1 Impulses and Impulsive Torques 301 14.1.1 Impulsive Torque 302 14.1.2 Rotating Collisions 304 14.1.3 Handling Rotating Collisions 305 14.2 Collision Impulses 306 14.2.1 Change to Contact Coordinates 306 14.2.2 Velocity Change by Impulse 313 14.2.3 Impulse Change by Velocity 317 14.2.4 Calculating the Desired Velocity Change 318 14.2.5 Calculating the Imp ulse 319 14.2.6 Applying the Impulse 320 14.3 Resolving Interpénétration 321 14.3.1 Choosing a Resolution Method 321 14.3.2 Implementing Nonlinear Projection 325 14.3.3 Avoiding Excessive Rotation 328 14.4 The Collision Resolution Process 330 14.4.1 The Collision Resolution Pipeline 331 14.4.2 Preparing Contact Data 333 14.4.3 Resolving Penetration 337 14.4.4 Resolving Velocity 344 14.4.5 Alternative Update Algorithms 346 14.5 Summary 349 Chapter 15 Resting Contacts and Friction 351 15.1 Resting Forces 352 15.1.1 Force Calculations 353 15.2 Micro-collisions 354 15.2.1 Removing Accelerated Velocity 356 15.2.2 Lowering the Restitution 357 15.2.3 The New Velocity Calculation 357 15.3 Types of Friction 358 15.3.1 Static and Dynamic Friction 359 15.3.2 Isotropie and Anisotropie Friction 361 15.4 Implementing Friction 362 15.4.1 Friction as Impulses 363 15.4.2 Modifying the Velocity Resolution Algorithm 365 15.4.3 Putting It All Together 371 15.5 Friction and Sequential Contact Resolution 373 15.6 Summary 374 Chapter 16 Stability and Optimization 375 16.1 stability 375 16.1.1 Quaternion Drift 376 16.1.2 Interpénétration on Slopes 377 16.1.3 Integration Stability 379 16.1.4 The Benefit of Pessimistic Collision Detection 380 16.1.5 Changing Mathematical Accuracy 381 16.2 Optimizations 383 16.2.1 Sleep 383 16.2.2 Margins of Error for Penetration and Velocity 390 16.2.3 Contact Grouping 393 16.2.4 Code Optimizations 394 16.3 Summary 397 Chapter 17 Putting It All Together 399 17.1 overview of the engine 399 17.2 Using the Physics Engine 401 17.2.1 Ragdolls 402 17.2.2 Fracture Physics 405 17.2.3 Explosive Physics 411 17.3 LIMITATIONS OF THE ENGINE 418 17.3.1 Stacks 418 17.3.2 Reaction Force Friction 419 17.3.3 Joint Assemblies 419 17.3.4 Stiff Springs 419 17.4 Summary 419 Part VI What Comes Next? 42 1 Chapter 18 Other Types of Physics 423 18.1 Simultaneous Contact Resolution 423 18.1.1 Thejacobian 424 18.1.2 The Linear Complementary Problem 425 18.2 Reduced Coordinate Approaches 428 18.3 Summary 429 Appendices В D Common Inertia Tensors 43 і A.I Discrete Masses 431 A.2 Continuous Masses 432 A.3 Common Shapes 432 A.3.1 Cuboid 432 A.3.2 Sphere 432 A.3.3 Cylinder 433 A.3.4 Cone 433 Useful Friction Coefficients for Games 434 Other Programming Languages 435 Cl C 435 C.2 Java 436 C.3 Common Language Runtime (.NET) 436 C.4 L и а 436 Mathematics Summary 438 D.I Vectors 438 D.2 Quaternions 439 D.3 Matrices 440 D.4 Integration 441 D.5 Physics 442 D.6 Other Formulae 443 Bibliography 445 Index 447
adam_txt	Contents List of Figures xvi Preface xix Chapter J. Introduction і 1.1 What Is Game Physics? 2 1.2 What Is a Physics Engine? 2 1.2.1 Advantages of a Physics Engine 3 1.2.2 Weaknesses of a Physics Engine 4 1.3 Approaches to Physics Engines 5 1.3.1 Types of Object 5 1.3.2 Contact Resolution 5 1.3.3 Impulses and Forces 6 1.3.4 What We're Building 7 1.4 The Mathematics of Physics Engines 7 1.4.1 The Math You Need to Know 8 1.4.2 The Math We'll Review 9 1.4.3 The Math We'll Introduce 10 1.5 The Source Code in This Book 10 1.6 How this Book Is Structured 11 Part I Particle Physics 13 Chapter jLi The Mathematics of Particles 15 2.1 Vectors 15 2.1.1 The Handedness of Space 19 2.1.2 Vectors and Directions 2.1.3 Scalar and Vector Multiplication 2.1.4 Vector Addition and Subtraction 2.1.5 Multiplying Vectors 2.1.6 The Component Product 2.1.7 The Scalar Product 2.1.8 The Vector Product 2.1.9 The Orthonormal Basis 2.2 Calculus 2.2.1 Differential Calculus 2.2.2 Integral Calculus 2.3 Summary 20 23 24 27 28 29 31 35 35 36 40 42 Chapter The Laws of Motion 3.1 A Particle 3.2 The First Two Laws 3.2.1 The First Law 3.2.2 The Second Law 3.2.3 The Force Equations 3.2.4 Adding Mass to Particles 3.2.5 Momentum and Velocity 3.2.6 The Force of Gravity 3.3 The Integrator 3.3.1 The Update Equations 3.3.2 The Complete Integrator 3.4 Summary 43 43 44 45 46 46 47 48 48 50 51 52 54 Chapter The Particle Physics Engine 4.1 Ballistics 4.1.1 Setting Projectile Properties 4.1.2 Implementation 4.2 Fireworks 4.2.1 The Fireworks Data 4.2.2 The Fireworks Rules 4.2.3 The Implementation 4.3 Summary 55 55 56 57 60 60 61 63 66 Part II Mass-Aggregate Physics 67 Chapter Adding General Forces 5.1 D'Alembert's Principle 5.2 Force Generators 5.2.1 Interfaces and Polymorphism 5.2.2 Implementation 5.2.3 A Gravity Force Generator 5.2.4 A Drag Force Generator 5.3 Built-in Gravity and Damping 5.4 Summary Chapter Springs and Springlike Things 6.1 Hook's Law 6.1.1 The Limit of Elasticity 6.1.2 Springlike Things 6.2 Springlike Force Generators 6.2.1 A Basic Spring Generator 6.2.2 An Anchored Spring Generator 6.2.3 An Elastic Bungee Generator 6.2.4 A Buoyancy Force Generator 6.3 Stiff Springs 6.3.1 The Problem of Stiff Springs 6.3.2 Faking Stiff Springs 6.4 Summary Chapter Hard Constraints 7.1 Simple Collision Resolution 7.1.1 The Closing Velocity 7.1.2 The Coefficient of Restitution 7.1.3 The Collision Direction and the Contact Normal 7.1.4 Impulses 69 69 72 73 73 76 77 79 79 81 81 83 83 83 84 86 87 89 93 93 95 101 103 103 104 105 105 107 7.2 Collision Processing 108 7.2.1 Collision Detection 111 7.2.2 Resolving Interpénétration 112 7.2.3 Resting Contacts 116 7.3 The Contact Resolver Algorithm 119 7.3.1 Resolution Order 120 7.3.2 Time-Division Engines 124 7.4 COLLISIONLIKE THINGS 125 7.4.1 Cables 126 7.4.2 Rods 128 7.5 Summary 131 Chapter 8 The Mass-Aggregate Physics Engine ізз 8.1 Overview of the Engine 133 8.2 Using the Physics Engine 139 8.2.1 Rope-Bridges and Cables 139 8.2.2 Friction 140 8.2.3 Blob Games 141 8.3 Summary 142 Part III Rigid-Body Physics 143 Chapter Zr The Mathematics of Rotations 145 9.1 Rotating Objects in Two Dimensions 145 9.1.1 The Mathematics of Angles 146 9.1.2 Angular Speed 148 9.1.3 The Origin and the Center of Mass 148 9.2 Orientation in Three Dimensions 152 9.2.1 Euler Angles 153 9.2.2 Axis-Angle 155 9.2.3 Rotation Matrices 156 9.2.4 Quaternions 157 9.3 Angular Velocity and Acceleration 159 9.3.1 The Velocity of a Point 160 9.3.2 Angular Acceleration 160 9.4 Implementing the Mathematics 161 9.4.1 The Matrix Classes 161 9.4.2 Matrix Multiplication 162 9.4.3 The Matrix Inverse and Transpose 171 9.4.4 Converting a Quaternion to a Matrix 178 9.4.5 Transforming Vectors 180 9.4.6 Changing the Basis of a Matrix 184 9.4.7 The Quaternion Class 186 9.4.8 Normalizing Quaternions 187 9.4.9 Combining Quaternions 188 9.4.10 Rotating 189 9.4.11 Updating by the Angular Velocity 190 9.5 Summary 191 Chapter 10 Laws of Motion for Rigid Bodies 193 10.1 The Rigid Body 193 10.2 Newton 2 for Rotation 196 10.2.1 Torque 197 10.2.2 The Moment of Inertia 198 10.2.3 The Inertia Tensor in World Coordinates 202 10.3 D'Alembert for Rotation 205 10.3.1 Force Generators 208 10.4 The Rigid-Body Integration 210 10.5 Summary 212 Chapter 11 The Rigid-Body Physics Engine 213 11.1 Overview of the Engine 213 11.2 Using the Physics Engine 216 11.2.1 A Flight Simulator 216 11.2.2 A Sailing Simulator 222 11.3 Summary 227 Chapter 12 Collision Detection 23 і 12.1 Collision Detection Pipeline 232 12.2 Coarse Collision Detection 232 12.3 Bounding Volumes 233 12.3.1 Hierarchies 235 12.3.2 Building the Hierarchy 241 12.3.3 Sub-Object Hierarchies 250 12.4 Spatial Data Structures 251 12.4.1 Binary Space Partitioning 251 12.4.2 Oct-Trees and Quad-Trees 255 12.4.3 Grids 258 12.4.4 Multi-Resolution Maps 260 12.5 Summary 261 Chapter 13 Generating Contacts 263 13.1 Collision Geometry 264 13.1.1 Primitive Assemblies 264 13.1.2 Generating Collision Geometry 265 13.2 Contact Generation 265 13.2.1 Contact Data 267 13.2.2 Point-Face Contacts 269 13.2.3 Edge-Edge Contacts 269 13.2.4 Edge-Face Contacts 271 13.2.5 Face-Face Contacts 271 13.2.6 Early-Outs 272 13.3 Primitive Collision Algorithms 273 13.3.1 Colliding Two Spheres 274 13.3.2 Colliding a Sphere and a Plane 276 13.3.3 Colliding a Box and a Plane 279 13.3.4 Colliding a Sphere and a Box 282 13.3.5 Colliding Two Boxes 287 13.3.6 Efficiency and General Polyhedra 297 13.4 SUMMARY 297 Part V Contact Physics 299 Chapter 14 Collision Resolution зо і 14.1 Impulses and Impulsive Torques 301 14.1.1 Impulsive Torque 302 14.1.2 Rotating Collisions 304 14.1.3 Handling Rotating Collisions 305 14.2 Collision Impulses 306 14.2.1 Change to Contact Coordinates 306 14.2.2 Velocity Change by Impulse 313 14.2.3 Impulse Change by Velocity 317 14.2.4 Calculating the Desired Velocity Change 318 14.2.5 Calculating the Imp ulse 319 14.2.6 Applying the Impulse 320 14.3 Resolving Interpénétration 321 14.3.1 Choosing a Resolution Method 321 14.3.2 Implementing Nonlinear Projection 325 14.3.3 Avoiding Excessive Rotation 328 14.4 The Collision Resolution Process 330 14.4.1 The Collision Resolution Pipeline 331 14.4.2 Preparing Contact Data 333 14.4.3 Resolving Penetration 337 14.4.4 Resolving Velocity 344 14.4.5 Alternative Update Algorithms 346 14.5 Summary 349 Chapter 15 Resting Contacts and Friction 351 15.1 Resting Forces 352 15.1.1 Force Calculations 353 15.2 Micro-collisions 354 15.2.1 Removing Accelerated Velocity 356 15.2.2 Lowering the Restitution 357 15.2.3 The New Velocity Calculation 357 15.3 Types of Friction 358 15.3.1 Static and Dynamic Friction 359 15.3.2 Isotropie and Anisotropie Friction 361 15.4 Implementing Friction 362 15.4.1 Friction as Impulses 363 15.4.2 Modifying the Velocity Resolution Algorithm 365 15.4.3 Putting It All Together 371 15.5 Friction and Sequential Contact Resolution 373 15.6 Summary 374 Chapter 16 Stability and Optimization 375 16.1 stability 375 16.1.1 Quaternion Drift 376 16.1.2 Interpénétration on Slopes 377 16.1.3 Integration Stability 379 16.1.4 The Benefit of Pessimistic Collision Detection 380 16.1.5 Changing Mathematical Accuracy 381 16.2 Optimizations 383 16.2.1 Sleep 383 16.2.2 Margins of Error for Penetration and Velocity 390 16.2.3 Contact Grouping 393 16.2.4 Code Optimizations 394 16.3 Summary 397 Chapter 17 Putting It All Together 399 17.1 overview of the engine 399 17.2 Using the Physics Engine 401 17.2.1 Ragdolls 402 17.2.2 Fracture Physics 405 17.2.3 Explosive Physics 411 17.3 LIMITATIONS OF THE ENGINE 418 17.3.1 Stacks 418 17.3.2 Reaction Force Friction 419 17.3.3 Joint Assemblies 419 17.3.4 Stiff Springs 419 17.4 Summary 419 Part VI What Comes Next? 42 1 Chapter 18 Other Types of Physics 423 18.1 Simultaneous Contact Resolution 423 18.1.1 Thejacobian 424 18.1.2 The Linear Complementary Problem 425 18.2 Reduced Coordinate Approaches 428 18.3 Summary 429 Appendices В D Common Inertia Tensors 43 і A.I Discrete Masses 431 A.2 Continuous Masses 432 A.3 Common Shapes 432 A.3.1 Cuboid 432 A.3.2 Sphere 432 A.3.3 Cylinder 433 A.3.4 Cone 433 Useful Friction Coefficients for Games 434 Other Programming Languages 435 Cl C 435 C.2 Java 436 C.3 Common Language Runtime (.NET) 436 C.4 L и а 436 Mathematics Summary 438 D.I Vectors 438 D.2 Quaternions 439 D.3 Matrices 440 D.4 Integration 441 D.5 Physics 442 D.6 Other Formulae 443 Bibliography 445 Index 447
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id	DE-604.BV022476642
illustrated	Illustrated
index_date	2024-07-02T17:46:47Z
indexdate	2024-07-09T20:58:26Z
institution	BVB
isbn	9780123694713 012369471X 9780123737229 0123737222
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-015684052
oclc_num	634312276
open_access_boolean
owner	DE-Aug4 DE-29T DE-739 DE-703 DE-634
owner_facet	DE-Aug4 DE-29T DE-739 DE-703 DE-634
physical	XXI, 456 S. Ill., graph. Darst. 1 CD-ROM (12 cm)
publishDate	2007
publishDateSearch	2007
publishDateSort	2007
publisher	Elsevier[u.a.]
record_format	marc
series2	The Morgan Kaufmann series in interactive 3D technology
spelling	Millington, Ian Verfasser aut Game physics engine development Ian Millington Amsterdam [u.a.] Elsevier[u.a.] 2007 XXI, 456 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier The Morgan Kaufmann series in interactive 3D technology Computerspiel (DE-588)4010457-6 gnd rswk-swf Maschine (DE-588)4037786-6 gnd rswk-swf Programmierung (DE-588)4076370-5 gnd rswk-swf Computerphysik (DE-588)4273564-6 gnd rswk-swf Gesetz Physik (DE-588)4139909-2 gnd rswk-swf Computerspiel (DE-588)4010457-6 s Maschine (DE-588)4037786-6 s Programmierung (DE-588)4076370-5 s Gesetz Physik (DE-588)4139909-2 s DE-604 Computerphysik (DE-588)4273564-6 s 1\p DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015684052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Millington, Ian Game physics engine development Computerspiel (DE-588)4010457-6 gnd Maschine (DE-588)4037786-6 gnd Programmierung (DE-588)4076370-5 gnd Computerphysik (DE-588)4273564-6 gnd Gesetz Physik (DE-588)4139909-2 gnd
subject_GND	(DE-588)4010457-6 (DE-588)4037786-6 (DE-588)4076370-5 (DE-588)4273564-6 (DE-588)4139909-2
title	Game physics engine development
title_auth	Game physics engine development
title_exact_search	Game physics engine development
title_exact_search_txtP	Game physics engine development
title_full	Game physics engine development Ian Millington
title_fullStr	Game physics engine development Ian Millington
title_full_unstemmed	Game physics engine development Ian Millington
title_short	Game physics engine development
title_sort	game physics engine development
topic	Computerspiel (DE-588)4010457-6 gnd Maschine (DE-588)4037786-6 gnd Programmierung (DE-588)4076370-5 gnd Computerphysik (DE-588)4273564-6 gnd Gesetz Physik (DE-588)4139909-2 gnd
topic_facet	Computerspiel Maschine Programmierung Computerphysik Gesetz Physik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015684052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT millingtonian gamephysicsenginedevelopment

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