Warp wrote:
>   There's no difference between those two. The gravity at any point in
> space is calculated in the same way regardless of where that point is.

I know that. But the technique and approach to taking shortcuts can differ.

>   Anyways, I'm not so interested in the end result as in the *process* of
> getting there by numerical approximation, which is the whole point. :)

Fair enough.

>> It also seems if you made *enough* test point masses, worrying about how to 
>> subdivide it wouldn't be worthwhile. If your torus has radius 1, and you 
>> slice it into 10,000 test masses, isn't that going to give you enough 
>> accuracy? Use the digitalness of your compuations to advantage. Put mass in 
>> a sphere if the center of the sphere is inside the torus, and calculate from 
>> there.
> 
>   The amount of points is not the problem. It's their distribution that is
> (either spatial or mass).

Then make each point the size of a grain of sand, and you have a really, 
really good approximation. That's what I mean.

>   You can't just put points of equal mass in whichever way you want inside
> the torus because you easily end up with uneven density. You have to either
> distribute the points evenly, or scale their masses according to the local
> point density. That's the problem I'm trying to figure out.

Right. Not knowing why you want the answer, I was suggesting that you 
distribute the points evenly and use lots and lots of points.

If it's just for personal interest in the puzzle of it, or you want to do it 
in real time or something, then sure, that's not the best solution. :-)

-- 
Darren New, San Diego CA, USA (PST)
  "How did he die?"   "He got shot in the hand."
     "That was fatal?"
          "He was holding a live grenade at the time."

Post a reply to this message