Re: Programming question : Newton's method

I noticed the conversation. Since nobody mentioned it. I will.

I good method for solving many equations is "Newton's method". I can get a
math book out on this, but it more or less involves this:

Make a guess of the square root based on whatever simple criteria.
square it
what is the difference between that and the expected answer?
adjust the number according to how far off you are
square it
what is the difference between that and the expected answer?
adjust the number according to how far off you are
square it
what is the difference between that and the expected answer?
adjust the number according to how far off you are
square it

Generally, if correctly implemented, it is accurate to several decimal
places after 3 iterations.
This is probably more code than a look up table, but you should be familiar
with this technique for solving complex equations.

James

----- Original Message -----
From: jeff hendrix <jhendrix@Quark.Com>
To: <vectorlist@lists.cc.utexas.edu>
Sent: Thursday, October 28, 1999 5:14 PM
Subject: RE: Programming question

> Thanks for all the replies.
> These posts have got some of the wheels turning in my brain.
> Just a few comments.
>
> Previously I was think of using a "reverse" lookup table like Zonn
> suggested, and I might go that route now after he suggested doing a binary
> search on it. (binary search had slipped my mind and I was planning on
> starting at one end and just moving through the table, which would have
> averaged 128 loops) I'm actually currently doing lots of calculations with
> data from lookup tables. I.E.- collision detection.
>
> I had considered using gravity in something like 16 steps, but I still
need
> the straight line distance to determine which ring I'm in. (as well as to
> normalize the vectors)
>
> The problem with doing equations like this
> if (distanceX < 10)
> scaleX = 1;
> if (distanceX < 20)
> scaleX = 2;
> if (distanceX < 30)
> scaleX = 4;
> ...etc...
> speed.x += gravity_constant/scaleX;
> is that it doesn't take into consideration the actual distance from the
sun.
> You could be 500 y units away and 10 x units and it will end up pulling
> harder in the x direction. Both vectors must first be normalized to
properly
> divide the gravitational pull between them.
>
> Rodger, I also couldn't get this to properly work, but if you do find the
> proper equation, it might be worth a try.
> Take the smaller of xlength or ylength, multiply it time 3, divide
> by 2, and add the result to the larger of xlength or ylength. The
> result is a close approximation of the square root of the sum of
> the squares.
>
> I have also toyed with the idea of doing linear gravity, I'm just afraid
> that you won't be able to orbit properly. (I get upset in gravitar because
> you can't quite orbit the planet that you can fly in circles around)
>
> Clay, I threw a few numbers into these equations
> "real dist" = sqrt(x^2+y^2), "fake dist" = ((X*2)+(Y*2))/4
> and in a circular obit, the gravity gets stronger when you have only an x
or
> y offset and weaker when your at one of the 45 degree angles from the sun.
> (making the gravity rings a square turned 45 degrees). But this might be
ok
> consider how little time it takes to calculate.
>
>
> thanks
> -jeff
>
>
Received on Fri Oct 29 08:04:17 1999