NAME

Math::PlanePath::FilledRings -- concentric filled lattice rings

SYNOPSIS

 use Math::PlanePath::FilledRings;
 my $path = Math::PlanePath::FilledRings->new;
 my ($x, $y) = $path->n_to_xy (123);

DESCRIPTION

This path puts points on integer X,Y pixels of filled rings of radius 1 unit.

                    110-109-108-107-106                        6
                   /                   \
            112-111  79--78--77--76--75 105-104                5
              |    /                   \      |
        114-113  80  48--47--46--45--44  74 103-102            4
          |    /      |               |    \      |
        115  81  50--49  27--26--25  43--42  73 101            3
       /   /      |    /           \      |    \   \
    116  82  52--51  28  14--13--12  24  41--40  72 100        2
      |   |   |    /   /           \   \      |   |   |
    117  83  53  29  15   5-- 4-- 3  11  23  39  71  99        1
      |   |   |   |   |   |       |   |   |   |   |   |
    118  84  54  30  16   6   1-- 2  10  22  38  70  98   <- Y=0
      |   |   |   |   |   |
    119  85  55  31  17   7-- 8-- 9  21  37  69  97 137       -1
      |   |   |    \   \           /   /      |   |   |
    120  86  56--57  32  18--19--20  36  67--68  96 136       -2
       \   \      |    \           /      |    /   /
        121  87  58--59  33--34--35  65--66  95 135           -3
          |    \      |               |    /      |
        122-123  88  60--61--62--63--64  94 133-134           -4
              |    \                   /      |
            124-125  89--90--91--92--93 131-132               -5
                   \                   /
                    126-127-128-129-130

                              ^
     -6  -5  -4  -3  -2  -1  X=0  1   2   3   4   5   6

For example the ring N=22 to N=37 is all the points

    2.5 < hypot(X,Y) < 3.5
    with hypot(X,Y) = sqrt(X^2+Y^2)

FUNCTIONS

See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.

$path = Math::PlanePath::FilledRings->new ()

Create and return a new path object.

($x,$y) = $path->n_to_xy ($n)

For $n < 1 the return is an empty list, it being considered there are no negative points.

The behaviour for fractional $n is unspecified as yet.

OEIS

Entries in Sloane's Online Encyclopedia of Integer Sequences related to this path include,

    http://oeis.org/A036705

    A036705  first diffs of N on X axis,
             being count of X,Y points n-1/2 < X^2+Y^2 <= n+1/2

SEE ALSO

Math::PlanePath, Math::PlanePath::PixelRings, Math::PlanePath::Hypot, Math::PlanePath::MultipleRings

HOME PAGE

http://user42.tuxfamily.org/math-planepath/index.html

LICENSE

Copyright 2012 Kevin Ryde

This file is part of Math-PlanePath.

Math-PlanePath is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-PlanePath is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.