NAME

       Math::PlanePath::PixelRings -- pixellated concentric circles

SYNOPSIS

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

DESCRIPTION

       This path puts points on the pixels of concentric circles using the midpoint ellipse
       drawing algorithm.

                       63--62--61--60--59                     5
                     /                    \
                   64  .   40--39--38   .  58                 4
                 /       /            \       \
               65  .   41  23--22--21  37   .  57             3
             /       /   /            \   \       \
           66  .   42  24  10-- 9-- 8  20  36   .  56         2
            |    /   /   /            \   \   \     |
           67  43  25  11   .   3   .   7  19  35  55         1
            |   |   |   |     /   \     |   |   |   |
           67  44  26  12   4   1   2   6  18  34  54       Y=0
            |   |   |   |     \   /
           68  45  27  13   .   5   .  17  33  53  80        -1
            |    \   \   \            /   /   /     |
           69  .   46  28  14--15--16  32  52   .  79        -2
             \       \   \            /   /       /
               70  .   47  29--30--31  51   .  78            -3
                 \       \            /       /
                   71  .   48--49--50   .  77                -4
                     \                    /
                       72--73--74--75--76                    -5

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

       The way the algorithm works means the rings don't overlap.  Each is 4 or 8 pixels longer
       than the preceding.  If the ring follows the preceding tightly then it's 4 longer, for
       example N=18 to N=33.  If it goes wider then it's 8 longer, for example N=54 to N=80 ring.
       The average extra is approximately 4*sqrt(2).

       The rings can be thought of as part-way between the diagonals like "DiamondSpiral" and the
       corners like "SquareSpiral".

            *           **           *****
             *            *              *
              *            *             *
               *            *            *
                *           *            *

           diagonal     ring         corner
           5 points    6 points     9 points

       For example the N=54 to N=80 ring has a vertical part N=54,55,56 like a corner then a
       diagonal part N=56,57,58,59.  In bigger rings the verticals are intermingled with the
       diagonals but the principle is the same.  The number of vertical steps determines where it
       crosses the 45-degree line, which is at R*sqrt(2) but rounded according to the midpoint
       algorithm.

FUNCTIONS

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

       "$path = Math::PlanePath::PixelRings->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.

       "$n = $path->xy_to_n ($x,$y)"
           Return an integer point number for coordinates "$x,$y".  Each integer N is considered
           the centre of a unit square and an "$x,$y" within that square returns N.

           Not every point of the plane is covered (like those marked by a "." in the sample
           above).  If "$x,$y" is not reached then the return is "undef".

SEE ALSO

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

HOME PAGE

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

LICENSE

       Copyright 2010, 2011, 2012, 2013, 2014, 2015 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/>.