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, 2016, 2017 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/>.