By David H. Eberly
Game Physics is an advent to the tips and strategies had to create bodily reasonable 3D image environments. As a significant other quantity to Dave Eberly's usual 3D online game Engine Design, Game Physics stocks an analogous useful technique and structure. Dave comprises simulations to introduce the main difficulties concerned after which steadily finds the mathematical and actual ideas had to clear up them. He then describes all of the algorithmic foundations and makes use of code examples and dealing resource code to teach how they're applied, culminating in a wide choice of actual simulations. This ebook tackles the advanced, hard concerns that different books keep away from, together with Lagrangian dynamics, inflexible physique dynamics, impulse tools, resting touch, linear complementarity difficulties, deformable our bodies, mass-spring platforms, friction, numerical resolution of differential equations, numerical balance and its dating to actual balance, and Verlet integration tools. Dave even describes while genuine physics isn't necessary-and hacked physics will do.
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Sample text
Implementing a numerical method is only half the battle. 3 Examples and Exercises 11 the trade-offs between accuracy and computation time is the other half of the battle. Perhaps the most important part of Chapter 9 is the section on numerical stability and its relationship to physical stability of equilibrium solutions. You might think of this as an irrelevant mathematical exercise, but in fact I provide a stability analysis for a handful of methods when applied to the simple pendulum problem.
This material is the all-important foundation for the physics engines discussed in Chapter 5. The remainder of Chapter 2 is an introduction to the standard concepts that you see in a course on physics, starting with Newton's laws of motion. The topics of force, torque, equilibrium, linear and angular momentum, center of mass, moments and products of inertia, and kinetic and potential energy are discussed in detail with the goal of being able to calculate these quantities on a computer. Computing the center of mass and the inertia tensor for a solid convex polyhedron is necessary for the physics engines of Chapter 5.
13 14 Chapter 2 Basic Concepts from Physics The kinetic energy is an important quantity in the development of Lagrangian dynamics. The potential energy is important when dealing with conservative forces such as gravity. 1 RIGID BODY CLASSIFICATION A rigid body is characterized by the region that its mass lives in. The simplest body is a single particle of mass m that occupies a single location x. A particle system is a collection of a finite number of particles, say, p of them, the i th particle having mass mi and located at Xi' 1::S i ::s p.