
Linear algebra for game developers – Part 1 (2009) - maastaar
http://blog.wolfire.com/2009/07/linear-algebra-for-game-developers-part-1/
======
alexbock
I'm not sure how much someone who wasn't already familiar with vectors could
get out of this. This seems to be a common issue with informal lessons like
this[1].

The article starts seemingly assuming you have no idea what a vector is, but
after showing a few graphs opines "As you can see, a vector by itself is just
a set of numbers". I don't think someone who didn't already know what a vector
was and how to recognize a vector on a graph would see that. Reading the next
sentence about coordinate pairs and referring back to the graph might get you
somewhere I guess. It doesn't seem to know who the target audience is supposed
to be.

Trying to teach people things that you use every day and have throughly
internalized can be an eye-opening experience. If you're trying to teach
someone how to count in other bases and discover that they never learned about
exponentiation, you're not going to get away with just saying "it's repeated
multiplication and the top number is how many times you do it; oh also
anything to the zero power is one (except zero itself...), and also negative
numbers do this... and fractional exponents do that...". They're not going to
suddenly "get" exponentiation the way you do from years of experience from
three minutes of offhand remarks.

[1] [http://hentenaar.com/dont-learn-c-the-wrong-
way](http://hentenaar.com/dont-learn-c-the-wrong-way) (parts 3, 4, and 5 in
particular have similar complaints)

~~~
Aelinsaar
To be fair, if you're heading into linear algebra, you should have already
dealt with vectors and matrices.

~~~
esrauch
When did you deal with Matrices before taking linear algebra?

~~~
antjanus
uhm, Algebra in high school. That's where I first learned about matrices, dot
products, and other basic matrix manipulations.

I take it back, I first encountered matrices in 8th grade and then several
times in high school. Standard curriculum in the US at least (or at least
where I lived).

~~~
adrusi
Well there's no standard curriculum in the US, but based on my personal
experience in Virginia and Maryland, matrix math in Algebra I is common.

The problem is that that's never built upon and it seems many math teachers
don't have a firm grasp on why matrix math is useful, much less the ability to
explain its utility to typical ninth graders.

I encountered vectors later in Physics (which was the most popular class to
take as the one required science elective in my high school) and in one of the
AP Calculus classes (which a large majority never take)

Matrices were revisted in Algebra II, with nothing new relative to Algebra I
except that solving the matrix equations we were given required using Algebra
II-level techniques on scalars. I guess a bit of spaced repetition might mean
that more people remember it, but overall most students just forgot about
matrices right after the test.

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bastijn
If you want a deeper understanding of mathematics and physics for game dev I
would advice to read
[http://www.scratchapixel.com](http://www.scratchapixel.com). It has a good
entry guide which covers all the basics. As a bonus it lays the foundation for
rendering the objects, explaining them in the light of the just learned 3D
math. It has the structure and completeness missing in these articles to
create real understanding of the matter.

A good read if you didn't follow any CG classes, or if those classes are a
long time ago.

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kevindeasis
This is complementary:

[http://betterexplained.com/articles/linear-algebra-
guide/](http://betterexplained.com/articles/linear-algebra-guide/)

~~~
saeranv
Betterexplained.com is fantastic, even after years of thinking I understand a
concept, Khalid always manages to push my insight further.

In that link he mainly goes into matrices (if I recall) and to get into dot
product and cross product explanations check out his section on vector
calculus:

[http://betterexplained.com/articles/category/math/vector-
cal...](http://betterexplained.com/articles/category/math/vector-calculus/)

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damptowel
Another one for the list. Hands on introduction to a lot of basic concepts.

[https://m.youtube.com/user/codingmath](https://m.youtube.com/user/codingmath)

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tomrod
What a great idea! Thank you for sharing the article.

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kolapuriya
There seems to be a lot of complaining about this article being too simple.
Hopefully you all noticed that this was part 1 of 4, and it gets pretty
complicated and useful (to me at least) by the end.
part1:[http://blog.wolfire.com/2009/07/linear-algebra-for-game-
deve...](http://blog.wolfire.com/2009/07/linear-algebra-for-game-developers-
part-1/)

part2:[http://blog.wolfire.com/2009/07/linear-algebra-for-game-
deve...](http://blog.wolfire.com/2009/07/linear-algebra-for-game-developers-
part-2/)

part3:[http://blog.wolfire.com/2010/07/Linear-algebra-for-game-
deve...](http://blog.wolfire.com/2010/07/Linear-algebra-for-game-developers-
part-3)

part4:[http://blog.wolfire.com/2010/07/Linear-algebra-for-game-
deve...](http://blog.wolfire.com/2010/07/Linear-algebra-for-game-developers-
part-4)

~~~
detaro
curious, in what comments do you see "complaining about this article being to
simple"? I see complaints that it doesn't cover the underlying basics well,
but nothing that to me seems to be what you mention?

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Aelinsaar
It's useful for more than just QM!

~~~
maastaar
Definitely.

Can we find some similar tutorials that show other applications of linear
algebra?

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captnsamoil
I don't think this article got it wrong but having it like a TL;DR of maths is
a bad way to do it.

Just check the maths courses at gameinstitute.com.

~~~
RaitoBezarius
I don't agree, this is not exactly the same as a tl;DR for maths.

IMHO, this is more a way to make people (game developers) feel mathematics
intuitively.

It is somehow the same as the setosa.io approach which is all about visual
explanations.

This is pretty cool.

~~~
ams6110
It may also whet the appetite for more deliberate study of the mathematics
involved. I have always been one to struggle a bit with math concepts if they
are too abstract. Tie them into somthing I have real-world interest in, and
it's much easier to engage and stay motivated to learn.

~~~
tjl
When I was going through undergrad engineering we were taught linear algebra
in first year but didn't really have a lot of the other background for the
different applications.

As a grad student, I had a friend of mine who was teaching that same linear
algebra course. I provided her with a lot of materials (similar to this) to
help her students better understand different aspects of the material. There's
a reason why the different introductory topics are taught, but often you don't
really understand the topic until you get deeper into the applied material in
3rd and 4th year.

