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# 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`.

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