Ebook: Guide to Dynamic Simulations of Rigid Bodies and Particle Systems

This book introduces the techniques needed to produce realistic simulations and animations of particle and rigid-body systems. The text focuses on both the theoretical and practical aspects of developing and implementing physically based dynamic-simulation engines. Each chapter examines numerous algorithms, describing their design and analysis in an accessible manner, without sacrificing depth of coverage or mathematical rigor. Features: examines the problem of computing an hierarchical representation of the geometric description of each simulated object, as well as the simulated world; discusses the use of discrete and continuous collision detection to handle thin or fast-moving objects; describes the computational techniques needed for determining all impulsive and contact forces between bodies with multiple simultaneous collisions and contacts; presents techniques that can be used to dynamically simulate articulated rigid bodies; concludes each chapter with exercises.

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Physically based modeling is widely used within the fields of computer graphics and mechanical engineering for complex systems that are difficult to analyze using conventional mechanics theory.

This book presents a comprehensive introduction to the techniques needed to produce realistic simulations and animations of particle and rigid-body systems. The book focuses on both the theoretical and practical aspects of developing and implementing physically based dynamic-simulation engines. Opening with an overview of the independent modules constituting a simulation engine, the text then provides detailed explanations for each technique, with more complex mathematical algorithms and associated implementations included in the second part of the book. Each chapter examines numerous algorithms, describing their design and analysis in an accessible manner, without sacrificing depth of coverage or mathematical rigor.

Topics and features:

• Examines the problem of computing an hierarchical representation of the geometric description of each simulated object, as well as the simulated world
• Discusses the use of discrete and continuous collision detection to handle thin or fast-moving objects, including a derivation of the conservative time advancement algorithm
• Describes the computational techniques needed for determining all impulsive and contact forces between bodies with multiple simultaneous collisions and contacts
• Presents techniques that can be used to dynamically simulate articulated rigid bodies
• Concludes each chapter with exercises, ranging from issues of algorithm enhancements to alternative approaches that complement the algorithms discussed in the book

Practical and easy-to-follow, this hands-on guide/reference is essential reading for software developers involved in computer graphics, computer animation, and computer-aided mechanical design and modeling.

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Physically based modeling is widely used within the fields of computer graphics and mechanical engineering for complex systems that are difficult to analyze using conventional mechanics theory.

This book presents a comprehensive introduction to the techniques needed to produce realistic simulations and animations of particle and rigid-body systems. The book focuses on both the theoretical and practical aspects of developing and implementing physically based dynamic-simulation engines. Opening with an overview of the independent modules constituting a simulation engine, the text then provides detailed explanations for each technique, with more complex mathematical algorithms and associated implementations included in the second part of the book. Each chapter examines numerous algorithms, describing their design and analysis in an accessible manner, without sacrificing depth of coverage or mathematical rigor.

Topics and features:

• Examines the problem of computing an hierarchical representation of the geometric description of each simulated object, as well as the simulated world
• Discusses the use of discrete and continuous collision detection to handle thin or fast-moving objects, including a derivation of the conservative time advancement algorithm
• Describes the computational techniques needed for determining all impulsive and contact forces between bodies with multiple simultaneous collisions and contacts
• Presents techniques that can be used to dynamically simulate articulated rigid bodies
• Concludes each chapter with exercises, ranging from issues of algorithm enhancements to alternative approaches that complement the algorithms discussed in the book

Practical and easy-to-follow, this hands-on guide/reference is essential reading for software developers involved in computer graphics, computer animation, and computer-aided mechanical design and modeling.

Content:
Front Matter....Pages I-XIV
Front Matter....Pages 1-1
Dynamic Simulations....Pages 3-27
Hierarchical Representation of 3D Polyhedra....Pages 29-88
Particle Systems....Pages 89-156
Rigid-Body Systems....Pages 157-243
Articulated Rigid-Body Systems....Pages 245-277
Front Matter....Pages 279-279
Appendix A: Useful 3D Geometric Constructions....Pages 281-289
Appendix B: Numerical Solution of Ordinary Differential Equations of Motion....Pages 291-305
Appendix C: Quaternions....Pages 307-315
Appendix D: Rigid-Body Mass Properties....Pages 317-328
Appendix E: Useful Time Derivatives....Pages 329-339
Appendix F: Convex Decomposition of 3D Polyhedra....Pages 341-349
Appendix G: Constructing Signed Distance Fields for 3D Polyhedra....Pages 351-364
Appendix H: Conservative Time Advancement for Convex Objects....Pages 365-368
Appendix I: The Linear-Complementarity Problem....Pages 369-394
Back Matter....Pages 395-399

---

Physically based modeling is widely used within the fields of computer graphics and mechanical engineering for complex systems that are difficult to analyze using conventional mechanics theory.

This book presents a comprehensive introduction to the techniques needed to produce realistic simulations and animations of particle and rigid-body systems. The book focuses on both the theoretical and practical aspects of developing and implementing physically based dynamic-simulation engines. Opening with an overview of the independent modules constituting a simulation engine, the text then provides detailed explanations for each technique, with more complex mathematical algorithms and associated implementations included in the second part of the book. Each chapter examines numerous algorithms, describing their design and analysis in an accessible manner, without sacrificing depth of coverage or mathematical rigor.

Topics and features:

• Examines the problem of computing an hierarchical representation of the geometric description of each simulated object, as well as the simulated world
• Discusses the use of discrete and continuous collision detection to handle thin or fast-moving objects, including a derivation of the conservative time advancement algorithm
• Describes the computational techniques needed for determining all impulsive and contact forces between bodies with multiple simultaneous collisions and contacts
• Presents techniques that can be used to dynamically simulate articulated rigid bodies
• Concludes each chapter with exercises, ranging from issues of algorithm enhancements to alternative approaches that complement the algorithms discussed in the book

Practical and easy-to-follow, this hands-on guide/reference is essential reading for software developers involved in computer graphics, computer animation, and computer-aided mechanical design and modeling.

Content:
Front Matter....Pages I-XIV
Front Matter....Pages 1-1
Dynamic Simulations....Pages 3-27
Hierarchical Representation of 3D Polyhedra....Pages 29-88
Particle Systems....Pages 89-156
Rigid-Body Systems....Pages 157-243
Articulated Rigid-Body Systems....Pages 245-277
Front Matter....Pages 279-279
Appendix A: Useful 3D Geometric Constructions....Pages 281-289
Appendix B: Numerical Solution of Ordinary Differential Equations of Motion....Pages 291-305
Appendix C: Quaternions....Pages 307-315
Appendix D: Rigid-Body Mass Properties....Pages 317-328
Appendix E: Useful Time Derivatives....Pages 329-339
Appendix F: Convex Decomposition of 3D Polyhedra....Pages 341-349
Appendix G: Constructing Signed Distance Fields for 3D Polyhedra....Pages 351-364
Appendix H: Conservative Time Advancement for Convex Objects....Pages 365-368
Appendix I: The Linear-Complementarity Problem....Pages 369-394
Back Matter....Pages 395-399
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