Behavioral Mathematics for Game AI

480 Pages·2009·4.06 MB·English

by  Dave Mark

B M
EHAVIORAL ATHEMATICS
G AI
FOR AME
D M
AVE ARK
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Dave Mark
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A Little History
and a Lot of Dedication
Ifirst got into computers in the early 1980s. By the late 1980s, my very nontech-
nical grandfather, Gilbert Todd, advised me to “grab onto them computers and
stick with ’em… that’s where the future is.” I did just that, but more out of my
own inexorable need to be involved in technology than from his encouragement.
After a brief spin in the music business, I got back into computers in the mid-
1990s by doing all manner of IT consulting.
In 2002, my wife Laurie and I had just started dipping into the game business
by forming Intrinsic Algorithm. On May 20 of that year, my dad drove me to the
airport to head off to what was my first Electronics Entertainment Expo (E3) con-
ference. My 88-year-old grandfather wanted to come along for the ride. As an ex-
pilot, he enjoyed watching the planes. He knew that I was going out to Los Angeles
to some sort of computer game–related conference, although he probably believed
that it was a little more of a heady event than what the then-ubiquitous loud music,
spectacular lights, and “booth babes” would have suggested to him.
As I got out of the car in front of the terminal and retrieved my luggage from
the trunk, my grandfather gave me the best handshake his aging body could gener-
ate and told me, “You head out there and tell ’em how it’s done.”
I didn’t have the heart to argue with my grandfather and say that I wasn’t going
to E3 to tellanyone anything, but rather to soak up as much of the state of the in-
dustry as I could. I simply thanked him for the encouragement and told him that I
would do my best to “set ’em straight.”
Those words were the last thing my grandfather said to me. On May 25, 2002,
the Saturday after the show and the night before I was due to fly back, he had a heart
attack and died.
My grandfather’s final words to me—which none of us knew at the time would
be so—have rattled around in my brain for the past six years. Just like the trip that
I left for on that day, I have spent more time listening and learning than telling any-
one how anything is done. However, as I started writing this book, my grandfather’s
iii
iv Dedications
words came back to me once again. I couldn’t help but think that, perhaps, his
advice was more timeless than the handful of days that I spent wandering through
the expansive LA Convention Center. Maybe his encouragement was issued without
an expiration date. Or maybe I should just assume that it is still in effect.
Regardless, here I am six years later writing a book on game AI. So, PawPa, I
may be a bit late, but I’m ready to head out there and tell ’em how it’s done. Thank
you.
In the meantime, there are others who have been helping me along the way
who deserve some thanks:
To my parents, who bought me my first Apple IIc back in 1984—although
they were a bit less enthusiastic when I used it to play games. See? I told you I could
make something out of that!
To my best friend in my teen years, Gregg Bieser, who did more than simply
play games with me on our respective Apples. It was with Gregg that I made my first
awkward—evenabortive—efforts to make my own games.
To my AP Computer sidekicks and friends, Phil, Bob, Scott, and Rick, whose
love of strategy board games and RPGs (fueled by the strangely never-diminishing
supply of caffeine at Phil’s house) helped crystallize in me what I wanted my own
games to look and play like some day.
To my younger brothers, Jared and Kevin, who, at elementary school ages in
the 1980s, were my guinea pigs as AD&D players. In retrospect, being a Dungeon
Master at 15 years old was the first time I turned mathematics into behaviors.
To the late Eric Dybsand, who, at the 2003 GDC, told me I knew what I was
talking about—even when I didn’t think I did. Respawn soon, my friend! In the
meantime, I hope you can get this book delivered to wherever you are. It seems like
you were right. Oh, do me a favor and loan a copy to PawPa while you are at it. He
won’t understand a word of it, but it will make him proud.
To Steve Woodcock, not only for being there from the beginning, but for stick-
ing around during the hard part, and then telling me it was time to get back on the
horse after I had fallen off.
To Alex Champandard for both giving me plenty of good advice and handing
me the “megaphone and soapbox” that a weekly column can turn into.
To Steve Rabin for his supply of wisdom regarding “AI Wisdom” and trusting
me to help hold the reins to something bigger than both of us.
To Heather Hurley and Karen Gill at Charles River Media for helping me make
the jump from 13 pages to 500.
Dedications v
To my tech editor, Kevin Dill, for reading every word and number—and
reminding me about the geometry of triangles.
To my in-laws, Larry and Lenora Reynolds, who loaned Laurie and me some
bootstraps they had lying around—and were patient with us when we wore them
out.
To my son Steven, who constantly reminds me that games can bridge generations
—and teaches me that my thumbs are too slow.
To my daughter, Kathy, who constantly reminds me that games can be about
more than shooting stuff—and teaches me how to observe people in ways that
continue to amaze me.
To my son Aaron, who constantly reminds me of what I was like when I was his
age—which kinda scares both of us.
To my stepdaughter Beth, who constantly reminds me that it can be fun to
completely beat the snot out of an opponent.
And, finally, thanks must go out to my wife and business partner, Laurie.
Starting Intrinsic Algorithm was my dream. Her dream was helping me achieve
mine. During the conversation at a restaurant in late 2001 that launched us into the
game business, she gave me the best bit of advice I’ve ever had. When I asked her,
“But what if I can’t do it? What if I fail?” she simply shrugged and said, “Well, then
we’ll know.”
Thanks, dear. You don’t know what that meant to me, then and now. This
book is dedicated to yourdedication.
Thank you all,
Dave Mark
About the Author
Dave Markis the president and lead designer of Intrinsic Algorithm, LLC, an
independent game development studio and AI consulting company in Omaha,
Nebraska. He has been programming since 1984 when he was in high school where,
much to the dismay of his teacher, he wrote his first text adventure on the school’s
DEC PDP-1144.
After a brief detour in the music business as a composer/arranger, keyboard
player, and recording engineer during the early 1990s, Dave re-entered the technol-
ogyarena in 1995. In 2002, he came to the startling realization that the corporate IT
consulting and development world is a little short on creativity and fun. As a result,
Dave left to start Intrinsic Algorithm LLC with his wife, Laurie.
He is a contributor to the AI Game Programming Wisdom series of books, a
regular columnist at AIGameDev.com, and a founding member of the AI Game
Programmers Guild.
Dave continues to attend the University of Life. He does not plan to graduate
anytime soon.
vi
Author’s Preface
As I have read different books on a variety of subjects over the years, I have
found a variety of styles to be effective for communicating ideas. In addition
to simply reading the text of a book on a technical subject, I have often
appreciated the extra effort that went into creating examples of the concept. I enjoy
diagrams and graphs so that I can simply have a place to anchor my thoughts as
I ponder the issue. Where appropriate, I like seeing the formulas used, already
normalized into a form that can be dropped into code. And, of course, I find actual
code snippets very helpful when the problem is one of programming.
Some of these elements have been more helpful than others. Some of them
have been used to the point of overkill such that it was next to impossible to extract
meaningful content from the clutter. On the other hand, I have often felt that I have
been left wanting a diagram, a table, or a bit of code so that I could put things into
perspective.
To that end, as I set out to write this book, I made myself a promise to attempt
to find the balance that would be the most helpful to you, the reader. Throughout
this work, I attempt to cover four different approaches: theory, math, examples,
and code.
Much of the discussion in this book will be about the theory behind the con-
cepts. This will be where I lay out the concept of a point as groundwork. While this
might seem to be the part of the book that is the least directly relevant to game pro-
gramming, it is also where much of the important material is. Everything spills out
of these ideas. Rather than bland recitation, I try to make the theory accessible
through example and anecdote.
If necessary, the theory sections will show the relevant mathematics of the
concepts. Please note that, unlike some other books, my goal is not to overwhelm
you with esoteric proofs of howI got to where I did, but to give you as a developer
an end product that you can find useful in production.
vii
viii Author’s Preface
IN THE GAME
Very often throughout the book, I will lay out hypothetical game-like situations
that show how to use a theoretical concept. While these examples may be game
genre–specific, the concepts themselves can usually be applied universally. You will
be able to quickly identify these sections by the icon at the left that will appear at the
beginning of each in-game example. Note that there’s a listing of all the In the Games
following the table of contents.
PUTTING IT IN CODE
Where appropriate, I will offer up examples of how tools are used in programming
situations. Sometimes these functions will be ones that you can use in your own
projects. In these cases, you can find the code on the book’s Web site at
http://www.courseptr.com/downloads.
For clarity’s sake, I list some of the naming conventions that I use in my pro-
jects and, therefore, in this book.
Type and structnames are in all caps: MY_TYPE.
Structnames are preceded by a lowercase “s”: sMY_STRUCT.
Variables and functions are in initial caps: MyFunction( MyVariable ).
Member variables of a class are generally preceded with a lowercase “m”:
mMyMemberVariable.
List and vector names are preceded by a lowercase “l” and “v,” respectively. I
combine these when necessary, such as in a member of a class that is also a vector.
In this case, the name is preceded by “mv,” such as in mvMyMemberVector.
Given that discussions of differences in programming style are often likened to
religious wars, I hope my naming conventions do not cause you to view me as a
heretic or to lob this book onto a blazing pyre of sacrilegious tomes with evil code-
naming conventions.
Oh yeah, open and close braces for functions belong in the same column, but
open braces for ifandwhilestatements belong at the endof the iforwhileline.
I want to follow the column from the end brace to the command that started it all.
If you think differently, then you… you… you’re just wrong!So there!
Author’s Preface ix
OK… sorry. That was uncalled for. I truly hope that my quirks don’t annoy you
or make this book harder to understand. I’m just old. I learned some of these habits
in 1984. Blame my high school computer teacher.
*sigh*
Throughout all of the sections, we will encounter terms that are worth noting.
To help you locate and remember these items, they will be bolded and marked with
theimportant lingoarrow in the margin.
Sometimes, I will add a cautionary note or an aside of some sort. This will be
set apart with the stylized, yet familiar comment brackets you see here.
In addition to seeing in-game examples, you will encounter numerous exam-
ples from “life”—mine as well as those around me. Since, as AI programmers, we
are often in the business of re-creating lifelike situations and behaviors, I find this
approach fitting. Also, I hope that you forgive me for a sense of humor. It is my at-
tempt to keep you from falling into the mind-numbing stupor that technical books
have been known to induce. In a manner of speaking, I’m doing it for your own
good. Don’t just learn—enjoy!