Where can I get a more intuitive understanding of these 3d related maths?

[....]

The trig functions.

I've seen and understand the regular pi using graphs, the triangle side angle relationships, etc.

What I wan't to know is a reason why those connections exist with the functions(angles to sides), what the functions and inverse functions are doing to transform values from one thing to another, and a deeper understanding of the why and how they came about.

I know how to do powers in functions by multiplication, multiplication by using addition, division by doing substractions, but I'm not sure how to do square, cubic, etc roots with simpler math in functions.


Also I've read and seen info on the dot product, but would like additional intuitive info.

 

[Davros]

any good to you?
http://illuminations.nctm.org/LessonsList.aspx?grade=4&standard=3

 

[PellePlutt]

In order to get a fairly deep and intuitive understanding, the simplest way would probably be to simply be to study these topics at a university, or read university textbooks. High-school might work for basic trigonometry though.

For computing square-roots I'd use Taylor series, a fairly advanced calculus topic. Might be a bit overkill to learn if you're only interested in 3d.

Dot products are part of linear algebra, a very important (almost the only important?) field for 3d-graphics. A linear algebra textbook would probably be a good start, and probably starts off with some trigonometry anyway.

 

[Dominik D]

Take a grid paper, ruler and a pencil. Draw triangles and look at their angles. Represent angles using side_one/side_two values. Toy around with it while reading any reasonable book about math. But please, polish your basic math first, ok?

 

[....]

In order to get a fairly deep and intuitive understanding, the simplest way would probably be to simply be to study these topics at a university, or read university textbooks. High-school might work for basic trigonometry though.

For computing square-roots I'd use Taylor series, a fairly advanced calculus topic. Might be a bit overkill to learn if you're only interested in 3d.

Dot products are part of linear algebra, a very important (almost the only important?) field for 3d-graphics. A linear algebra textbook would probably be a good start, and probably starts off with some trigonometry anyway.

I've taken university math courses. But at least up to know no one has gone into the inner details and workings of such things. Calculators are used, and the basic diagrams and relations given. What the calculator does to do a sine, cos, etc, or a square or cubic root, etc. remains unknown.

 

[nutball]

What the calculator does to do a sine, cos, etc, or a square or cubic root, etc. remains unknown.

They tend to use series expansions as far as I'm aware.

Look here

http://mathworld.wolfram.com/Sine.html

and other pages on that site. All the equations you'll ever need (albeit somewhat terse)!

 

[silent_guy]

They tend to use series expansions as far as I'm aware.

Look here

http://mathworld.wolfram.com/Sine.html

and other pages on that site. All the equations you'll ever need (albeit somewhat terse)!

Series expansions are very often not what you need: for a lot of cases, they require a lot of iterations before you get the required accuracy. Too little bang for buck.

For hand calculators, the CORDIC algorithm used to be very popular. Slow, but it doesn't require a multiplier, so the amount of logic required is minimal.

For square roots, there are a whole lot of ways. For HW, it's usually done by some Newton-Raphson method or equivalent. The same link shows you the fast famous reciprocal sqrt formula. According to this posting in the CUDA forums, GPU accelerates 1/sqrt in hardware instead of sqrt, so they do sqrt by doing x/sqrt(x) to get to sqrt(x).

This post by Arun talks about special functions in G80, which are based on quadratic table. In this case, you use result = ax2+bx+c, which a different table per special function. Here is some info on quadratic minimax. (It's a View as Text of a postscript document on Google. )
Look in the CUDA documentation to get an idea about the accuracy you can get this way. You often have 2 options when writing CUDA programs: either use sin(x) or use _sin(x). The former does stuff in addition to the hardware function, the latter uses the straight hardware result, so it's faster, but also lower precision (I believe.)

There are a lot of different ways to calculate special functions. As usual Google is your friend...

 

[....]

Thanks for all the info and help! edited