++ed by:
Kevin Ryde
and 1 contributors

# NAME

Math::PlanePath::Corner -- points shaped in a corner

# SYNOPSIS

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

# DESCRIPTION

This path puts points in layers working outwards from the corner of the first quadrant.

``````    ...
5  |  26 ................
4  |  17  18  19  20  21 .
3  |  10  11  12  13  22 .
2  |   5   6   7  14  23 .
1  |   2   3   8  15  24 .
y=0  |   1   4   9  16  25 .
----------------------
x=0,  1   2   3   4 ...``````

The horizontal 1,4,9,16,etc at y=0 is the perfect squares. The diagonal 2,6,12,20,etc starting x=0,y=1 is the pronic numbers s*(s+1), half way between those squares.

Each stripe across then down is 2 longer than the previous and in that respect the corner is the same as the Pyramid and SacksSpiral paths. The Corner and the PyramidSides are the same thing, just with a stretch from a single quadrant to two.

# FUNCTIONS

`\$path = Math::PlanePath::Corner->new ()`

Create and return a new path object.

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

Return the x,y coordinates of point number `\$n` on the path.

For `\$n < 0.5` the return is an empty list, it being considered there are no points before 1 in the corner.

`\$n = \$path->xy_to_n (\$x,\$y)`

Return the point number for coordinates `\$x,\$y`. `\$x` and `\$y` are each rounded to the nearest integer, which has the effect of treating each point as a square of side 1, so the quadrant x>=-0.5 and y>=-0.5 is entirely covered.