Math for CG

[Srek]

This depends heavily on what area you are planning to work in. Rendering, Animation and modelling require pretty different know how and each in itself can be complex enough to get you busy for years.
Personaly i'm mostly concerned with some animation stuff where i make heavy use of vector and matrix operations.
Cheers
Björn

[Hezza]

I think Vector and Matrix maths would be great to learn (it was actually looking into vector math a couple of months back that prompted this whole thing), and just general/intermediate algebra, how to calculate angles, distances in 3d space etc.

I've started watching the Fahrenhiet rigging dvd's for maya, and they go into how to make the rig in mel, I just feel a greater understanding of the maths of 3d space would be majorly beneficial, even if I don't end up using alot of it, actually understanding some of the behind the scenes stuff would be great.

Anyone thats from the UK, would you think an A-level maths course would be useful? Or is there a Maths of CG book that i've missed

[Carina]

To be honest, I'm not sure how much an A-level course would give you that you couldn't get from a book.. Especially if the book in question is aimed particularly towards computer graphics! Obviously it depends on how far the GCSE maths went, I can't for the life of me remember when certain things were first taught;)

Something like this (http://www.amazon.co.uk/Essential-Mathematics-Computer-Graphics-Fast/dp/1852333804/ref=sr_1_2?ie=UTF8&s=books&qid=1197979890&sr=1-2) would probably do.. That covers the absolute essentials. Once you're comfortable with those, you may, like Björn says, find your particular field of choice will need you to get into other types of math ontop of that, for example lighting and rendering can be very heavy on statistics and differential/integral equations.

[Hezza]

Cheers for the pointers Carina, that was one thing i was wondering, how much of an A-level would be useful. The book you linked looks very interesting and covers most of the stuff i'd like to get my head round, i'm just going to have to try and find somewhere with it abit cheaper, £120 second hand :eek:

I think that'll be my plan, brush up on my gcse math and see if that will be advanced enough to go through a book similar to that.

How's Bath this fine morning? I'm just up the road in Bristol, bloody freezing but not as bad as yesterday :)

EDIT:
Just had a read of the intro on amazon and its exactly what i'm after. Big thumbs up Carina!

[Carina]

The book you linked looks very interesting and covers most of the stuff i'd like to get my head round, i'm just going to have to try and find somewhere with it abit cheaper, £120 second hand :eek:

Ack.. heh.. didn't see the price, maybe try this (http://www.amazon.co.uk/Mathematics-Computer-Graphics-John-Vince/dp/1846280346/ref=sr_1_1?ie=UTF8&s=books&qid=1197982435&sr=1-1), it's by the same author;)

Bath is okay, though yeah, it's windy and not very pleasant :rolleyes:

[Hezza]

Second edition of the book for anyone interested:
http://www.amazon.co.uk/Mathematics-Computer-Graphics-John-Vince/dp/1846280346/ref=sr_1_1?ie=UTF8&s=books&qid=1197982690&sr=1-1

£19.50

EDIT:

Musta been posting at the same time, thanks again :thumbsup:

[Robert Bateman]

John Vince used to teach at the NCCA in Bournemouth (he's retired recently, but still pops his head in from time to time) - Mind you i'm no longer there either. The books pretty good at going through most concepts.

I'd strongly recommend an A-level course in maths. It makes most of the basic 3D maths seem fairly straightforward and simple (interpolation, matrices, vectors etc), however as you start delving deeper into 3D (dynamics, particles, fluids, cloth etc), you will basically hit a brick wall in your understanding if you have not a decent understanding of maths. A quick list off the top of my head.......

The most important bits of an a-level sylabuss are: (with what they relate to in CG in brackets)

mechanics (dynamics)
matrices (transformations)
trigonometry (triangles)
vectors (vertices, normals)

Other things that are particularly of note are,

polynomials (parametric curves)
differentiation & integration (pretty much any CG paper from siggraph)
simulataneous equations (IK, evaluating 2d anim curves)
complex numbers (quaternions, sine, cosine)
statistics (data compression schemes, lighting models, distributions etc).

[Hezza]

Cheers for the extra info Robert. I think i'm going to see how it goes with the book for now, should be here this afternoon actually if amazon are on the ball, fun xmas train reading :wise:. If I really struggle with it then I'll look into an A-Level course, I think i'm motivated enough to learn it by myself though.

I did apply for the NCCA when I was looking at universities (5 or 6 years ago now) But I actually failed the life drawing test and didn't have much of a portfolio to show. Been doing life drawing classes the past few years to make up for it though :) . I ended up at Swansea Institute on their BA 3D Computer Animation course. Looking back I really should have done the BSc but ah well, things are clearer with hindsite :)

I think i've been very lucky with my first year in the industry, I've mainly been at a smallish studio so get to work on every aspect of 3D, normally thrown in at the deep end but i'm enjoying it :) I think its giving me a good generalist grounding and over the next year i'm going to try and figure out what I want to specialise in. There's just too many interesting areas :)

[Donio]

Yeh, don't underestimate the power of books...i'm studying at the university at the moment and i'm not even following a single of my math courses...just read the books at your own pace. As long as you have a bit of a spine and as long as you aren't too easy-going on yourself you'll do just fine.

[Kuroyume0161]

If you decide to go the 'book route', it'd be best to get something that is more akin to a textbook with examples and exercises (but not those Schaum type books - more confusing than illuminating). I would have never understood Chaos Theory without going through "Chaos and Fractals" and doing the exercises (usually involving some programming). But probably not a full-on college textbook unless you have the wherewithall to understand all of the primary concepts without some to fill in the gaps and explain the details. Start with Trigonometry, vectors, matrices. Move onto Linear Algebra, Calculus. If you intend on programming, a good dose of Boolean Algebra and logic theory wouldn't hurt.

A couple of good reference books (a bit explanatory but more reference) that can be used for guidance into what you might need to learn are "Computer Graphics: Practice and Principles", "Essential Mathematics for Games", "Mathematics for 3D Game Programming & Computer Graphics", "3D Game Engine Architecture". There are tons to choose from. Avoid the "Make a 3D Game using C#" type books - these are too narrow, seldom useful beyond their target audience, and sometimes more confusing than illuminating (as noted above for the others).

[seadonghai]

"physics for game developers" .try this , it si very nice book .

[Robert Bateman]

"physics for game developers" .try this , it si very nice book .

No it's not, it is quite literally the worst book ever written on the subject. Do not by that book. by this one instead - it actually makes sense - http://www.charlesriver.com/books/BookDetail.aspx?productID=84482

\edit

I should probably qualify why that book is crap. In Europe:

feet = things at the end of your legs
ounces = things you get arrested and sent to jail for
slugs = things that eat your cabbage in your garden
pounds = money
inches = something your girlfriend wants a few more of

In Europe, we don't buy guns, or bullets for that matter. So when someone starts describing momentum in units of "slug feet per second", it's almost inconprehensible. For him then to explain what a slug is in ounces still makes no sense what so ever. I've got that book, and almost every line was incomprehensible due to the choice of units, and the fact that he regularly changes between units, sometimes within the same sentance. At one point in the book, he then says "of course, make sure you don't get your units confused" - which is a bit ironic.

If the book had been written using meters and kilograms, it may have been OK. If however you have no problem using the imperial units, then it may be ok. I still say that the other book i linked to is far superior to the crap o'reilly offering.

[Hezza]

No it's not, it is quite literally the worst book ever written on the subject. Do not by that book. by this one instead - it actually makes sense - http://www.charlesriver.com/books/BookDetail.aspx?productID=84482

\edit

I should probably qualify why that book is crap.

Hehe, great discription Robert, I shall avoid that book :) To be honest i'm not really looking into the programming side of it just yet. Was just interested more in the pure maths behind it. I got the 'Mathematics for Computer Graphics' book mentioned and its what I was looking for. Not properly attacked it yet but it looks good.

[RobotClayton]

I should probably qualify why that book is crap. In Europe:

feet = things at the end of your legs
ounces = things you get arrested and sent to jail for
slugs = things that eat your cabbage in your garden
pounds = money
inches = something your girlfriend wants a few more of


What really bothers me, is that hardly no one in the US uses these units (other than in manufacturing). Meters, Kilograms, Netwon * Meters; that's all you need.

I can't believe somone is using slugs in a 'physics book'...

Oh, I'd highly reccomend taking a linear algebra course.

[Kuroyume0161]

If I remember correcrtly, people in England don't exactly use these units extensively either. They tend to still give their weight in stones not kilograms, for instance. Of course, the US is worse. But a book describing Physics should be using scientific units of measure: second, meter, gram, Newton, joules, Hertz, volts, etc..

Here, we think:

meter - a device that measures something
gram - short for 'telegram' or grandmother
joules - Verne
Hertz - ouch
Newton - fig
second - someone who isn't first
amp(ere) - a box through which to play electric guitar
kilometer - a distance shorter than a mile which makes Europeans feel like they are moving faster. ;P
...

[Carina]

If I remember correcrtly, people in England don't exactly use these units extensively either. They tend to still give their weight in stones not kilograms, for instance. Of course, the US is worse.

Not sure the US is worse.. what amuses me in the UK is the fact that most people I know don't even know how many pounds are in a stone.. Still they keep going on about how imperial is the way to go :shrug:

Anyhow..I've never seen imperial used much in science, even here, for very obvious reasons. No point in confusing yourself unnecessarily.

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