Geometry!

Math and Physics Programming

Started by MohammadAhmed July 21, 2012 09:46 AM

10 comments, last by Krohm 11 years, 9 months ago

279

Author

July 21, 2012 09:46 AM

hello every one.

I had asked some one about linear algebra book to understand math in games but he says that you don't want that book you need geometric algebra so:

what is geometric algebra and how it relates to game?

what is computational geometry and how it relates to game ?

how geometric algebra and computational geometry aid game development?

I am a bit confused since I am not computer science student ,But I had good background in 3d graphics and game programming and development in general good

but math side especially those relate to computation and algebra make me confused.

At last any good books for both geometric algebra & computational geometry for beginners and dose they need other prerequisites books ?

sorry for lot questions

Krohm

5,051

July 21, 2012 10:28 AM

what is geometric algebra and how it relates to game?

what is computational geometry and how it relates to game ?

how geometric algebra and computational geometry aid game development?

You probably want to use the term "linear algebra" instead or "vector algebra" (vector spaces are referred as "linear spaces" in formal math). From a 10,000 ft view, linear algebra is just typical algebra, extended in multiple dimensions. However, it hides some interesting details such as matrix properties and manipulation or the fact that [font=courier new,courier,monospace]dot(u,v) = cos(AngleBetween(u, v)) * len(u) * len(v)[/font]. Geometric algebra, as introduced by the wiki page appears to be rubbish for computer usage.
Computational Geometry? It appears the wiki page is excellent resource. In general, you don't need to care much about those things, as libraries are here to help you although you must understand the concepts involved to avoid relying on assumptions which does not hold true.
They help game development in the same way arithmetics help you understanding how many months you need to work to buy a new car. It's the basic rules. Of the two, understanding linear spaces is very important, while you can focus less on computational geometry out of your picture for a while.

Previously "Krohm"

apatriarca

2,365

July 21, 2012 10:49 AM

Computational geometry and geometric algebra are two very different fields and they have basically nothing to do with each other.

Computational geometry, as the name suggest, is an applied maths field whose objective is to come up with algorithms to solve geometric problems. Examples of problems solved by this field can be finding the convex hull of a set of points or finding intersections or .. You probably already know some of these algorithms and it's probably a good field to know. I have read this book by O'Rourke. He has also written a new book recently which you may find interesting. Another good book is this book by de Berge at al.

Geometric algebra is, as far as I know, a generalization of linear algebra where higher dimensional vectors and new operators are defined. This isn't a really important field. It probably has its usage, but you can probably live without that. I do not know any book, but you can find several information by searching this keyword in Google.

MohammadAhmed

279

Author

July 21, 2012 11:52 AM

thanks krohm , apatriarca .

I know linear algebra (vectors , matrices , operations on them ....) I know this material well it's linear algebra , so as both of you says it's similar to Geometric algebra so I should not spend much time to learn it as I know basis (vectors , matrices , operations on them ....) is this right ?? and I should go for computational geometry as it's the best one for me now??

as I understand, computational geometry used to define good algorithms not for AI , Graphics but for geometry (lines , points ...etc) is this right ??!

what make me post this topic is that I had bought real-time collision detection book and it's heavily require (algorithims , computational geometry ) also another AI book which require heavily understanding of algorithims and while I am searching in google they says that computational geometry is very good for algorithims this is the story !!

thanks apatriarca for books , what is computational geometry prerequisites books( i think it's data structure,Algorithims)?

alvaro

21,604

July 21, 2012 12:17 PM

I don't know where you heard the term "Geometric Algebra", but you probably heard wrong. Algebras are important structures in several areas of Math and Physics, and one uses them indirectly in video-game programming for things like defining the cross product, but it's not the language that video-game programmers use, so you can safely ignore it.

Linear Algebra is very important, and you seem to know the basics already.

Computational Geometry is a large field, and I am sure parts of it are relevant to some video-game programmers, but not most.

apatriarca

2,365

July 21, 2012 01:39 PM

The prerequisites of computational geometry depends on the geometric problem you are trying to solve. The algorithms which are most relevant to videogame programmers generally only requires knowledge of data structures, algorithms, linear algebra and some basic discrete geometry and combinatorics. Not all algorithms are relavant to videogame programming and you can probably look for the relevant ones when trying to solve the particular problems they solve. There exists libraries who implement most of these algorithms anyway..

MohammadAhmed

279

Author

July 21, 2012 03:13 PM

thanks alvaro and thanks again apatriarca

ok 1: alvaro here where the term geometric algebra is ?? this is the book :

Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry book for daniel ?? so the term is used I don't know what he mean !!

2: apatriarca I want to learn real-time collision detection so what is the prerequisites of computational geometry I had to know in order to solve real-time collision detection problem ?

Iam so confused right now pls all what I need is that : I am developing AI and Collision system what I need for that what is the prerequisites : (I know linear algebra and discrete math and calculas ....etc I know all these stuff ) so :
for example some says you need good understanding of algorithims and computational geometry , but some says you need also good linear algebra not strong because all what I need is some vector and matrix operations ????

so what about members of this website what you know about this ??

alvaro

21,604

July 21, 2012 06:11 PM

You are probably ready to learn how to do collision detection already. You may want to make yourself familiar with the dot product, and that's about it.

MohammadAhmed

279

Author

July 21, 2012 10:20 PM

thansk alvaro

at last algorithims and computational geometry not important for me to develop AI , Collision detection systems and I should not care about them !

Krohm

5,051

July 23, 2012 07:36 AM

You are probably ready to learn how to do collision detection already. You may want to make yourself familiar with the dot product, and that's about it.

I disegree. Let's have a talk about convex hull extraction from an arbitrary shape without exceeding an error. Minowski sums. GJK and EPA algorithms. The fact SAT does not work on arbitrary geometry. Acceleration structures for broadphase rejections and narrowphase testing. The only reason to write collision detection at home is to better appreciate ready-to-go libraries IMHO.

Previously "Krohm"

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