Beginning Math Concepts for Game Developers

by Flynt, Ph.D., John P; Meltreger, Boris

• ISBN13: 9781598632903
• ISBN10: 1598632906
• Edition: CD
• Format: Paperback
• Copyright: 2006-10-10
• Publisher: Cengage Learning PTR

Summary

Successful game programmers understand that in order to take their skills beyond the basics, they must have an understanding of central math topics; however, finding a guide that explains how these topics relate directly to games is not always easy. Beginning Math Concepts for Game Developers is the solution! It includes several hands-on activities in which basic math equations are used for the creation of graphs and, ultimately, animations. By the time you finish, you will have developed a complete application from the ground up that allows you to endlessly explore game development scenarios for 2D games. If you have a basic understanding of programming essentials and a desire to hone your math skills, then get ready to take a unique journey that examines what is possible when you combine game development with basic math concepts.

Table of Contents

Introduction	xii
Getting Started	1	(18)
Game Contexts	2	(5)
Extending the Game	4	(2)
Heuristics	6	(1)
Alternative Models	7	(5)
A Framework for Exploration	8	(2)
Nodes and Values	10	(2)
Mathematics and Functionality	12	(2)
Development Strategies	14	(2)
Conclusion	16	(3)
Functions and Methods	19	(22)
Patterns	20	(1)
Rules, Domains, and Ranges	21	(10)
Lab Work for the CO2 Table	26	(2)
Generating a Table	28	(1)
Calling a Method from the Functions Class	29	(1)
Using Repetition	30	(1)
Writing to a Table	30	(1)
Programming a Function	31	(4)
The Functions Class	35	(5)
Defining a Field	36	(1)
Defining a Constructor	36	(1)
Using a Method to Implement a Math Function	37	(3)
Conclusion	40	(1)
Working with Functions	41	(24)
Domains and Functions	42	(6)
Starting Values	43	(3)
All Real Numbers	46	(1)
Restricting the Domain	47	(1)
Specific Values	48	(1)
Methods That Use Restricted Domain Values	48	(13)
Single Selection and Throwing Exceptions	49	(2)
Generating Values and Catching Exceptions	51	(5)
The List Collection	56	(2)
Iterations and Retrieval of Error Messages	58	(1)
Events and Displays	59	(2)
Division by Zero	61	(3)
Conclusion	64	(1)
Extending the Lab	65	(30)
Graphing Functions	66	(4)
Aggregation and Composition	67	(2)
Dependencies	69	(1)
Adding a Struct	70	(2)
Adding a Static List to the DataForm Class	72	(2)
Using the List Object	74	(1)
Using the List Object for Display Purposes	75	(2)
Setting and Using a Flag	77	(2)
Initializing the Flag	78	(1)
Clear and Reset	79	(1)
Defining the Run Property	79	(1)
Defining the Vals Property	80	(1)
Opening the Graphics Window	80	(4)
The CartForm Class	84	(9)
The CartForm Code	87	(2)
Painting	89	(2)
Plotting	91	(1)
Calling the CoordSystem Methods	92	(1)
Closing	93	(1)
Conclusion	94	(1)
Plotting Points and Curves	95	(24)
Creating a Cartesian Plane	96	(9)
Planning the Grid	99	(2)
Drawing a Grid	101	(2)
Adding the Axes	103	(2)
Creating the CoordSystem Class	105	(13)
Plotting a Point	108	(2)
Plotting a Line	110	(3)
Plotting a Curve	113	(5)
Conclusion	118	(1)
Lines, Slopes, and Methods	119	(34)
Valid Functions	120	(1)
Constant Functions	120	(9)
Profits	121	(2)
Coding the Function	123	(1)
Generating the Table	123	(1)
Generating a Graph	124	(4)
Grid Adjustments in the CoordSystem Class	128	(1)
Composition of Functions	129	(5)
Back to the Factory	130	(1)
Coding the Function	131	(1)
Generating the Table	131	(2)
Generating a Graph	133	(1)
Linear Functions and the Slopes of Functions	134	(4)
Standard Form	134	(1)
Coding the Function	135	(1)
Generating the Table	136	(1)
Generating a Graph	137	(1)
Rise and Run	138	(10)
More on Temperatures	140	(1)
Coding a Method to Find a Slope	141	(1)
Creating Output with the Slope Method	142	(2)
Coding a Method to Convert Celsius to Fahrenheit	144	(1)
Generating a Graph	145	(1)
Method Overloading	146	(2)
Slope Characteristics	148	(2)
Slope Gradients and Negative Slopes	149	(1)
Perpendicular Lines	150	(1)
Shifting on the y Axis	150	(1)
Conclusion	150	(3)
Quadratics	153	(38)
Quadratic Functions	154	(1)
Parabolas	155	(6)
Completing the Square	155	(2)
Shifting Left and Right	157	(2)
Flipping	159	(1)
Shifting Up and Down	160	(1)
Tangent Lines	161	(4)
Minimum and Maximum	165	(6)
Coding the Function	166	(1)
Generating a Table	167	(2)
Generating a Graph	169	(2)
Absolute Values	171	(14)
Coding a Method for an Absolute Value	172	(3)
Generating a Table	175	(2)
Generating a Graph	177	(4)
Translating Coordinate Values	181	(1)
Reference Arguments	182	(3)
Discontinuous Lines	185	(4)
Writing the Method	185	(1)
Generating a Table	186	(1)
Generating a Graph	187	(2)
Conclusion	189	(2)
Limits and Methods	191	(30)
Talk of Limits	191	(8)
Programming to Define a Limit	192	(6)
Formal Definitions	198	(1)
Limits and Bicycle Tires	199	(17)
Coding the Functions	203	(2)
Generating a Table of Values	205	(2)
Generating a Graphical Representation	207	(4)
Differing Forms of Limits	211	(1)
Left-Hand Limits	212	(1)
Right-Hand Limits	213	(3)
Unrestricted Limits	216	(1)
Continuity	216	(2)
Infinity	218	(2)
Conclusion	220	(1)
Animations	221	(38)
Graphs and Animation	222	(13)
Adding a Text Area and Buttons	222	(1)
Anticipating Development	223	(1)
Invoking the Animation Form	224	(1)
Adding a Timer	225	(2)
Timer Methods	227	(1)
Setting Up the Basic Timer	228	(1)
Attending to Preliminaries	229	(1)
Implementing the Code for the Timer Actions	230	(5)
Creating a No-Flicker Panel	235	(3)
Deriving One Class from Another	236	(1)
Specifics of Derivation	236	(2)
Adding the Panel	238	(4)
Adding the Axes	239	(1)
Adding an Animated Point	239	(3)
Adding a Continuous Array	242	(2)
Generating Coordinates	244	(5)
Queues and Coordinates	249	(9)
Cardinal Directions	249	(3)
Generating Coordinates	252	(1)
Plotting the Point	253	(1)
Event Detection	254	(4)
Conclusion	258	(1)
More Animations	259	(24)
Random Numbers	260	(2)
A Function for Random Values	260	(2)
Generating a Table of Values	262	(3)
Random Events	263	(2)
Restoring Glow	265	(3)
Implementing a Nonrandom Method	265	(1)
Generating Nonrandom Values	266	(2)
Modifying AniForm5	268	(7)
Pattern-Driven Activities	269	(2)
Fields and Initialization	271	(1)
Basic Point Events	271	(2)
V2 Events	273	(2)
Event Contexts	275	(6)
Setting Events	276	(2)
Event Execution	278	(3)
Conclusion	281	(2)
Appendix A Obtaining and Installing C#	283	(12)
Appendix B Visual Formula Setup and Use	295	(14)
Index	309