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, like the 18 to 33 ring. If it goes wider then it's 8 longer, like the 54 to 80 ring. The average extra is 4*sqrt(2) or thereabouts.

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

     *           **           *****
      *            *              *
       *            *             *
        *            *            *
         *           *            *
   
    diagonal     ring         corner
    5 points    6 points     9 points

For example the 54 to 80 has a vertical corner-type part 54,55,56 then a diagonal part 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 determine where it crosses the 45-degree line, at R*sqrt(2) but rounded according to the midpoint algorithm.

FUNCTIONS

See "FUNCTIONS" in Math::PlanePath for the 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 not settled yet. A position on the line segment between the integer N's might make sense, but perhaps pointing 17.99 towards the "6" position to make a ring instead of towards the "18".

$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 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/>.