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• Read Me First Why Does This Book Exist? Preconditions Postconditions Programming Style Supplementary Material
• I Introduction to Game Physics Mathematics for Game Physics Geometry and Linear Algebra Reflections on Reflection Digital Calculus Relaxation
• A Rigid Body Physics Game The 8-Ball Pool End Game Code Run-Through Render World Object World Objects
• A Soft Body Physics Toy Particles Springs Soft Bodies Ragdoll Physics
• II Game Physics with Box2D Getting Started Download and Set Up Box2D Overview of Box2D Units Our First Box2D App
• A Tale of Three Modules The Common Module The Math Library The Collision Module Shapes The Dynamics Module Joints
• The Cannon Game The Platform and the Tower The Heads-Up Display The Object World The Cannon Object The Frame Loop and the Keyboard Handler Son et Lumiere
• The Collision Module Contacts and Manifolds Contact Listeners AABBs Dynamic Trees
• III Appendices For Math Geeks Only
• The Blacke Arte of Program Debugging The Debug printf Zen and the Art of Debugging
• There Are, In Fact, Dumb Questions Lies of Quis Custodiet Ipsos Auditores?
• Bullet Physics Getting Started The Dynamics World Adding Objects Rigid Body Dynamics Motion States Render Frames and Physics Frames
• Bibliography
• Index
• Exercises appear at the end of each chapter.
• (source: Nielsen Book Data)

Written by a pioneer of game development in academia, Introduction to Game Physics with Box2D covers the theory and practice of 2D game physics in a relaxed and entertaining yet instructional style. It offers a cohesive treatment of the topics and code involved in programming the physics for 2D video games. Focusing on writing elementary game physics code, the first half of the book helps you grasp the challenges of programming game physics from scratch, without libraries or outside help. It examines the mathematical foundation of game physics and illustrates how it is applied in practice through coding examples. The second half of the book shows you how to use Box2D, a popular open source 2D game physics engine. A companion website provides supplementary material, including source code and videos. This book helps you become a capable 2D game physics programmer through its presentation of both the theory and applications of 2D game physics. After reading the book and experimenting with the code samples, you will understand the basics of 2D game physics and know how to use Box2D to make a 2D physics-based game.
(source: Nielsen Book Data)

• Computers and computation
• the discrete neuron
• the Boolean neuron
• alternating circuits
• small, shallow alternating circuits
• threshold circuits
• cyclic networks
• probabilistic neural networks.
• (source: Nielsen Book Data)

Neural networks usually work adequately on small problems but can run into trouble when they are scaled up to problems involving large amounts of input data. Circuit Complexity and Neural Networks addresses the important question of how well neural networks scale - that is, how fast the computation time and number of neurons grow as the problem size increases. It surveys recent research in circuit complexity (a robust branch of theoretical computer science) and applies this work to a theoretical understanding of the problem of scalability.Most research in neural networks focuses on learning, yet it is important to understand the physical limitations of the network before the resources needed to solve a certain problem can be calculated. One of the aims of this book is to compare the complexity of neural networks and the complexity of conventional computers, looking at the computational ability and resources (neurons and time) that are a necessary part of the foundations of neural network learning.Circuit Complexity and Neural Networks contains a significant amount of background material on conventional complexity theory that will enable neural network scientists to learn about how complexity theory applies to their discipline, and allow complexity theorists to see how their discipline applies to neural networks.
(source: Nielsen Book Data)
Neural networks usually work adequately on small problems but can run into trouble when they are scaled up to problems involving large amounts of input data. Circuit Complexity and Neural Networks addresses the important question of how well neural networks scale - that is, how fast the computation time and number of neurons grow as the problem size increases. It surveys recent research in circuit complexity (a robust branch of theoretical computer science) and applies this work to a theoretical understanding of the problem of scalability.
(source: Nielsen Book Data)

• Computers and computation
• the discrete neuron
• the Boolean neuron
• alternating circuits
• small, shallow alternating circuits
• threshold circuits
• cyclic networks
• probabilistic neural networks.
• (source: Nielsen Book Data)

Neural networks usually work adequately on small problems but can run into trouble when they are scaled up to problems involving large amounts of input data. Circuit Complexity and Neural Networks addresses the important question of how well neural networks scale - that is, how fast the computation time and number of neurons grow as the problem size increases. It surveys recent research in circuit complexity (a robust branch of theoretical computer science) and applies this work to a theoretical understanding of the problem of scalability. Most research in neural networks focuses on learning, yet it is important to understand the physical limitations of the network before the resources needed to solve a certain problem can be calculated. One of the aims of this book is to compare the complexity of neural networks and the complexity of conventional computers, looking at the computational ability and resources (neurons and time) that are a necessary part of the foundations of neural network learning. Circuit Complexity and Neural Networks contains a significant amount of background material on conventional complexity theory that will enable neural network scientists to learn about how complexity theory applies to their discipline, and allow complexity theorists to see how their discipline applies to neural networks.
(source: Nielsen Book Data)

• Cartesian Coordinate Systems 1D Mathematics 2D Cartesian Space 3D Cartesian Space Odds and ends
• Vectors Vector - mathematical definition and other boring stuff Vector - a geometric definition Specifying vectors using Cartesian coordinates Vectors vs. points Negating a vector Vector multiplication by a scalar Vector addition and subtraction Vector magnitude (length) Unit vectors The distance formula Vector dot product Vector cross product Linear algebra identities
• Multiple Coordinate Spaces Why multiple coordinate spaces? Some useful coordinate spaces Coordinate space transformations Nested coordinate spaces In defense of upright space
• Introduction to Matrices Matrix - a mathematical definition Matrix - a geometric interpretation The bigger picture of linear algebra
• Matrices and Linear Transformations Rotation Scale Orthographic projection Reection Shearing Combining transformations Classes of transformations
• More on Matrices Determinant of a matrix Inverse of a matrix Orthogonal matrices 4 x 4 homogeneous matrices 4 x 4 matrices and perspective projection
• Polar Coordinate Systems 2D Polar Space Why would anybody use Polar coordinates? 3D Polar Space Using polar coordinates to specify vectors
• Rotation in Three Dimensions What exactly is "orientation?" Matrix form Euler angles Axis-angle and exponential map representations Quaternions Comparison of methods Converting between representations
• Geometric Primitives Representation techniques Lines and rays Spheres and circles Bounding boxes Planes Triangles Polygons
• Mathematical Topics from 3D Graphics How graphics works Viewing in 3D Coordinate spaces Polygon meshes Texture mapping The standard local lighting model Light sources Skeletal animation Bump mapping The real-time graphics pipeline Some HLSL examples Further reading
• Mechanics 1: Linear Kinematics and Calculus Overview and other expectation-reducing remarks Basic quantities and units Average velocity Instantaneous velocity and the derivative Acceleration Motion under constant acceleration Acceleration and the integral Uniform circular motion
• Mechanics 2: Linear and Rotational Dynamics Newton's three laws Some simple force laws Momentum Impulsive forces and collisions Rotational dynamics Real-time rigid body simulators Suggested reading
• Curves in 3D Parametric polynomial curves Polynomial interpolation Hermite curves Bezier curves Subdivision Splines Hermite and Bezier splines Continuity Automatic tangent control
• Afterword What next?
• Appendix A: Geometric Tests Appendix B: Answers to the Exercises
• Bibliography
• Index
• Exercises appear at the end of each chapter.
• (source: Nielsen Book Data)

• Cartesian Coordinate Systems. Vectors. Multiple Coordinate Spaces. Introduction to Matrices. Matrices and Linear Transformations. More on Matrices. Polar Coordinate Systems. Rotation in Three Dimensions. Geometric Primitives. Mathematical Topics from 3D Graphics. Mechanics
• 1: Linear Kinematics and Calculus. Mechanics
• 2: Linear and Rotational Dynamics. Curves in 3D. Afterword. Appendices. Bibliography. Index.
• (source: Nielsen Book Data)

This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.
(source: Nielsen Book Data)
This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for.
(source: Nielsen Book Data)