🚀 go-pugleaf

In article <3zADx9AXVWd3EwJU@merlyn.demon.co.uk>,
  Dr John Stockton <jrs@merlyn.demon.co.uk> wrote:
> JRS:  In article <7l357k$4m6$1@nnrp1.deja.com> of Sat, 26 Jun 1999
> 18:13:14 in news:comp.lang.pascal.delphi.misc, David C. Ullrich
> <ullrich@math.okstate.edu> wrote:
> >In article <zZIi7jAzW8c3EwDD@merlyn.demon.co.uk>,
> >  Dr John Stockton <jrs@merlyn.demon.co.uk> wrote:
>
> >       I have no idea what a "subset-capability" is, but modulo
> >that of course there is. Set one endpoint P1 of the needle to a
> >random point in a large square. Then set the other endpoint
> >to another random point. Reject the second endpoint until you
> >get one with say 0.5 < |P1 - P2| < 2. Then rescale it so
> >|P1 - P2| = 1. There's your random needle, no trig and hence
> >no Pi required.
> >
> >   ("rescale": say P2 := P1 + (P2 - P1)/|P2 - P1| . No
> >angles, just a square root.)
>
> ISTM, seemingly confirmed by test, that your method does not give a
> uniform distribution of angles.

    If so then you're trying something other than what I suggested.
Did you read all of it or just a few sentences?

    Psuedocode (note these are all real variables, converting to
integers too soon would be bad):

//"Set [...] P1 [...] to a random
//point in a large square":

    N:= LargeNumber;
    P1.X:= N*random;
    P1.Y:= N*random;

//"Then set the other endpoint
//to another random point. Reject the second endpoint until you
//get one with say 0.5 < |P1 - P2| < 2":

    repeat
       X:= 1 - 2*random;
       Y:= 1 - 2*random;
    until 0.25 < X*X + Y*Y < 4;
//the actual numbers 0.25 and 4 don't matter

//"rescale" as suggested:

    r:= sqrt(X*X + Y*Y);
    P2.X:= P1.X + X/r;
    P2.Y:= P1.Y + Y/r;

     If you don't get a uniform distribution of angles from
lemme know and I'll make an actual compilable version (if the
RNG is worse than I thought it won't work, of course. But I
didn't think the RNG was _that_ bad.)

> >> It must be better still to glue large numbers, evenly distributed
in
> >> angle, together - centrally to get a disc, or endwise to get a
ring.
> >> Not too many, though; with an infinite number of needles, unless
> >> carefully treated, there's a risk of getting infinity/infinity as
the
> >> result.
> >
> >     Huh? The limit in question _is_ a limit "of the form
> >infinity/infinity". I don't think there's much danger of
> >the actual algorithm running infinitely many times.
>
> With an infinite number of needles glued together, the algorithm need
> only be run once - though this will take infinite time.

    Aha.

> --
>  � John Stockton, Surrey, UK.  jrs@merlyn.demon.co.uk   Turnpike v4.00
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