Course CGP103
Differential Equations for Computer Game Programmers
Differential Equations for Computer Game Programmers
Duration: 3 Days
Intended Audience
The course will be useful to a wide range of developers who need to update or enhance their understanding of differential equations - especially the computational aspects of differential equations in order to develop applications involving simulation of activities that can be modeled via differential equations. The emphasis is primarily on applicability, rather than rigorous mathematical understanding. interests related to using and applying 2D and 3D geometry to software applications
- computer game programmers
- graphics artists with an interest in "computer art"
- maths and science teachers who wish to develop educational software with a strong simulation and modeling component
- developers of modeling and simulation software
- developers of robotics systems software
A knowledge of maths up to about the level of the International Bacalaureate or A Level ( in the UK ) is assumed, as well as several years programming experience in C/C++. The course does not assume any detailed knowledge of differential equations and numerical analysis
Course Overview
The purpose of this course is to provide a sound foundation in the techniques and theory underlying modeling and simulation using differential equations In addition to covering the course also overviews
- applying structured programming techniques
- differential equations as they apply to Computer Game Physics Engines
- applying systems analysis techniques to computer game development
- overview of qualitative simulation and it uses in computer game development
- difference equations and their uses
Course Contents
Understanding the language of differentiation
Differential equations as a language for expressing ideas involving change and a language working with those ideas
testing them, using them to make predictions, and communicating them.
- Using the language of differential equations
- Looking at differential equations visually
- Estimating the solution of an initial value problem visually
- Estimating the solution of an initial value problem numerically
- Starting with a qualitative model and converting it to a differential equation model
Overview of Concepts and Techniques for Physics Based Modeling and Simulation
- Rigid body dynamics and motion
- Collision detection and response
- Particle system and interactions
- Deformable objects
- Continuum models
- Finite element methods
- Numerical integration techniques
- Constraint systems
Techniques - Theory and Practice
- Differential Equations
- Particle Systems Dynamics
- Implicit Methods for Differential Equations
- Constrained Dynamics
- Rigid Body Simulation
- Deformable Objects
- Fluid Simulation
- Shallow Water Equations
An Overview of Differential Equation and Physics Engine Based Systems Combined with OpenGL
- Introduction to Open GL
- Using the Open Dynamics Engind (ODE) with OpenGL
- Using OpenTissue with OpenGL
Numerical Methods and Differential Equations In Greater Depth
- First Order Equations
- Existence, Uniqueness and Continuous Dependence - Understanding the Concepts
- Second Order Equations
- General Order Differential Equations
- Linear Systems of Differential Equations
- Equilibria and Stability Issues
- Numerical Methods for Solving Differential Equations
- Euler's Method
- Taylor Methods of Higher Order
- Runge Kutta Methods
- Multistep Methods
- Predictor-Corrector Methods
- Extrapolation Methods
- Verlet Integration
- Physical Stability and Numerical Stability - Issues