1.1 Game 2302-0105: getting started

Table of contents

• Preface
  • General
  • Viewing tip
    • Figures
    • Listings
• Preview
• Discussion and sample code
  • Points, lines, and vectors
  • Writing, compiling, and running Java programs
  • The program named PointLine01
  • But wait, there's something wrong here
  • The program named PointLine02 and the library named GM2D01
    • The GM2D01.ColMatrix class
    • The GM2D01.Point class
    • The GM2D01.Vector class
    • The GM2D01.Line class
• The GM2D01 library is purely mathematical
• Documentation for the GM2D01 library
• Homework assignment
• Run the programs
• Summary
• What's next?
• Miscellaneous
• Complete program listings
• Exercises
  • Exercise 1
  • Exercise 2
  • Exercise 3

Preface

This module is one in a collection of modules designed for teaching GAME2302 Mathematical Applications for Game Development at Austin Community College in Austin, TX.

General

Good math skills are required

In order to be a successful game programmer you must be skilled in technologies other than simply programming. Those technologies includemathematics. My purpose in writing this module is to help you to gain mathematical strengths in addition to your other strengths.

This collection is designed to teach you some of the mathematical skills that you will need (in addition to good programming skills) to become a successful game programmer. In addition to helping you with your math skills, I will also teach you how to incorporate those skillsinto object-oriented programming using Java. If you are familiar with other object-oriented programming languages such as C#, you should have nodifficulty porting this material from Java to those other programming languages.

Lots of graphics

Since most computer games make heavy use of either 2D or 3D graphics, you will need skills in the mathematical areas that are required for success in 2Dand 3D graphics programming. As a minimum, this includes but is not limitedto skills in:

1. Geometry
2. Trigonometry
3. Vectors
4. Matrices
5. 2D and 3D transforms
6. Transformations between coordinate systems
7. Projections

Game programming requires mathematical skills beyond those required for graphics. This collection willconcentrate on items 3, 4, and 5 in the above list. (I will assume that you either already have, or can gain the required skills in geometryand trigonometry on your own. There are many tutorials available on the web to help you in that quest including the Brief Trigonometry Tutorial at (External Link) .)

Insofar as vectors and matrices are concerned, I will frequently refer you to an excellent interactive tutorial titled Vector Math for 3D Computer Graphics by Dr. Bradley P. Kjell for therequired technical background. I will then teach you how to incorporate the knowledge that you gain from Kjell's tutorial into Java code with a heavyemphasis on object-oriented programming.

In the process, I will develop and explain a game-programming math library that you can use to experiment with and to confirm what you learn about vectorsand matrices from the Kjell tutorial. The library will start out small and grow as we progress through more and more material in subsequent modules.