Is it me or is matrix math incredibly confusing?
Author
I''m reading "Mathematics for 3d Game Programming and Computer Graphics" by Lengyel. I am on the matrix chapter and just about everything is confusing and takes forever to read and understand. Has anyone else had problems with matrices? Also the proofs give me trouble sometimes. Do I really need to know the proofs of the theroems or can i just learn definitions and algorithms?
A game programming book that gives proofs? I don''t think you need the proofs. 
If the book is sacrificing examples for proofs, and you want to get more profeccient with matrix algebra you can go to Barnes and Noble and take a look at a Schaum''s outline on Linear Algebra. They have the pertinent theorems in outline form and lots of problems to work out with answers, and they''re only about $15. Otherwise you can buy a text book on Linear Algebra but that would be about $100.
If the book is sacrificing examples for proofs, and you want to get more profeccient with matrix algebra you can go to Barnes and Noble and take a look at a Schaum''s outline on Linear Algebra. They have the pertinent theorems in outline form and lots of problems to work out with answers, and they''re only about $15. Otherwise you can buy a text book on Linear Algebra but that would be about $100.
If you just want code and not any theories behind the code, then that book is probably not for you. It''s more like a text book with excercies for you to work on. But if you can go through the entire book without breaking a sweat, you''d have become a pretty competent 3D programmer. Most of the book is about 2nd to 3rd year university lvel.
Of course, it''s always better to understand what the code is doing and why it works than just to blindly use it as a black box.
Premature optimizations can only slow down your project even more.
>> everything is confusing and takes forever to read and understand <<
This is always true even if you''re an expert in one thing there will always be something new that will be confusing in first stages. Recently I had the same confusion when playing with microsoft''s windows installer and orca database editor. After a week I finally understood it. The same happened when I was learning c. Complete confusion. But stick with it. Read it over and over, go on the internet and look at some math sites out there. There are plenty. You can also get free college notes or lectures that way. Matrices are tough but there will be much tougher things to come I guarantee it. Btw, this site plus flipcode might have some tutorials on matrices. Read as many as you can and don''t rely on one unless it explains everything however I haven''t found a single source that explains it all. Real-Time Rendering book is my reference.
In computer graphics there are other things that you will need to concentrate on not just matrices. Thousand of different things. You don''t need to concentrate on proofs but it''s the best way to train your mind how to think when problems to which no one has solution crop up. There will be other problems that will have nothing to do with math proofs though. Good luck!
ForgEd3D world editor
This is always true even if you''re an expert in one thing there will always be something new that will be confusing in first stages. Recently I had the same confusion when playing with microsoft''s windows installer and orca database editor. After a week I finally understood it. The same happened when I was learning c. Complete confusion. But stick with it. Read it over and over, go on the internet and look at some math sites out there. There are plenty. You can also get free college notes or lectures that way. Matrices are tough but there will be much tougher things to come I guarantee it. Btw, this site plus flipcode might have some tutorials on matrices. Read as many as you can and don''t rely on one unless it explains everything however I haven''t found a single source that explains it all. Real-Time Rendering book is my reference.
In computer graphics there are other things that you will need to concentrate on not just matrices. Thousand of different things. You don''t need to concentrate on proofs but it''s the best way to train your mind how to think when problems to which no one has solution crop up. There will be other problems that will have nothing to do with math proofs though. Good luck!
ForgEd3D world editor
One trick to getting a handle on matrices (and there are many... tricks that is) is to realise that matrix algebra is just a compact way of representing a set of mathematical equations. For example, the formula Ax = B might expand as
and this might seem confusing, but all this is stating is a system of 3 linear equations in the variables (x1, x2 and x3) in a compact manner. In a less compact manner, the three equations would be:
and a solution of this system of equations (i.e., values for (x1, x2 and x3 that are consistent with the equations) might represent the intersection of 3 spatial planes (as in a corner of a room) or perhaps the translation of an object in 3-dimensional space.
The thing to hold in your mind while you are struggling with all of the symbols is what the symbols represent. Use the examples in the book to get a grasp of this and then go back and re-read the text with a specific example in mind.
I hope this helps.
Cheers,
Timkin
Edited by - Timkin on February 3, 2002 11:21:59 PM
|a11 a12 a13||x1| |b1||a21 a22 a23||x2| = |b2||a31 a32 a33||x3| |b2| and this might seem confusing, but all this is stating is a system of 3 linear equations in the variables (x1, x2 and x3) in a compact manner. In a less compact manner, the three equations would be:
a11x1 + a12x2 + a13x3 = b1a21x1 + a22x2 + a23x3 = b2a31x1 + a32x2 + a33x3 = b3 and a solution of this system of equations (i.e., values for (x1, x2 and x3 that are consistent with the equations) might represent the intersection of 3 spatial planes (as in a corner of a room) or perhaps the translation of an object in 3-dimensional space.
The thing to hold in your mind while you are struggling with all of the symbols is what the symbols represent. Use the examples in the book to get a grasp of this and then go back and re-read the text with a specific example in mind.
I hope this helps.
Cheers,
Timkin
Edited by - Timkin on February 3, 2002 11:21:59 PM
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