# The "how's" and "why's"

#1

I’ve been reading around the net and trying to learn about the theory behind 3D ie. the maths and the physics.

It is all well and good to tell me that to find the length of the side that is perpendicular to one vector and meets the end of the other vector you use the dot product method, but the way I learn and I know many people also learn and remember this way is to UNDERSTAND what you are doing, ie.how and why, not just what…

So I am asking for people who have read good books or sites on the theory of 3D (maths AND physics) to recommend good books or sites that also explain WHY.

The site that i have been reading (struggling) is http://www.euclideanspace.com
it is the site the compelled me to write this post, a good site but no explanation…

#2

well it depends on what exactly you wanna learn its a broad field…if you understand vectors and all the linear algebra that goes with and wanna see how those theoriea are applied to 3d then i have a book that i enjoyed reading very much.

its called 3D GAMES: realtime and software rendering… now this book has gotten some bad reviews because people think its a book on making games…its more like an intro to game engine book… for example it goes into alot of detail to explain bezier surfaces bspline nurbs and then shows you how you would implent it in opengl…besides the code for a basic 3d engine its all mostly math… but its a good book to learn the hows and why’s.
you can find links to amazon, bn for both volumes at this site. http://www.fly3d.com.br

hope its what your looking for

#3

Originally posted by Isotope
but the way I learn and I know many people also learn and remember this way is to UNDERSTAND what you are doing, ie.how and why, not just what…

I would suggest going straight to “the bible”, Foley and Van Dam, Computer Graphics: Principles and Practice. It’s been the bible for 3D. I’ve only got some of the 1990 copies around and since then the new editions feature some examples in C.

It’ll give you both the fundamentals as well as a good dose of history, especially considering how long it’s been “the bible” in the 3D industry. Some of it will feel outdated and ancient but I think that is part what makes a lot of difference these days. Too many people focus on the “how” and not the “why” as if the younger generation entering the field only wants to know what buttons to press and how to get from A to B without actually digging into the history and fundamentals which are so important in even comprehending a lot of the more modern concepts that have their roots elsewhere and have evolved since.

It’s also a great hardcover doorstop that carries its weight with pride

#4

I second that. The Foley book is the bible of 3D maths for computer graphics.

3D math isn’t the easiest thing to get to grips with, but this book presents it in a really good way.

You can also get more specific books, such as 3D matrix math books. I have a good one at home, but forget the title. There’s also a lot of websites about 3d math, just check your local google for more info

#5

I have written a simple ray tracer and now I want to try adding G.I. to my renderer. But, I feel very diffcult to understand those equations, notations and terminology, and especially how to convert those integrals (differential area, volume.,etc) evaluation, rendering equations to C/C++. Sometime the upper limit of Diff eqaution is pi, or ohm or nothing; how to find dA, dt, dw,.etc I really have no idea about these as no detail explained.

I have read some general math books, but they only mention simple integral, say, the upper limit is 9 and lower limit is 0…
Any good math book for graphics programming? expecially integral , rendering equations, rather than Vector and matrix calcualations.

thanks

#6

Originally posted by sept94
Any good math book for graphics programming? expecially integral , rendering equations, rather than Vector and matrix calcualations.

If you are looking for good resources that combine the math with the code along with detailed overviews you may want to look into the “Graphics Gems” series (all five volumes).

For more than a decade, since the first volume, these guys have been an unmistakably valuable resource. It’s a shame that after the fifth volume somewhere in '95 or '96 they stopped publishing more of these. The content varies greatly and has chapters on rendering, geometry, motion, image processing, etc. and are not purely focussed on just rendering, though.

#7

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