NAME
Math::PlanePath -- points on a path through a 2-D plane
SYNOPSIS
use Math::PlanePath;
# only a base class, see the subclasses for actual operation
DESCRIPTION
This is a base class for some mathematical paths which turn an integer position $n
into coordinates $x
,$y
. The current classes include
SquareSpiral four-sided spiral
DiamondSpiral four-sided spiral, looping faster
HexSpiral six-sided spiral
HexSpiralSkewed six-sided spiral skewed for compactness
SacksSpiral quadratic on an Archimedean spiral
VogelFloret seeds in a sunflower
KnightSpiral an infinite knight's tour
Rows fixed-width rows
Columns fixed-height columns
Diagonals diagonals between X and Y axes
Corner expanding stripes around a corner
PyramidRows expanding rows pyramid
PyramidSides along the sides of a 45-degree pyramid
The paths are object oriented to allow parameters, though currently only a few subclasses actually have any parameters.
The classes are generally oriented towards integer $n
positions and those designed for a square grid turn an integer $n
into integer $x
,$y
. Usually they can give in-between positions for fractional $n
too though. Classes not on a square grid, like SacksSpiral and VogelFloret, are scaled for a unit circle at each $n
but they too can give in-between positions on request.
In general there's no parameters for scaling, or an offset for the 0,0 origin, or a reflection up or down. Those things are thought better done by a general coordinate transformer if expanding or inverting for display. Even clockwise instead of counter-clockwise spiralling can be done just by negating $x
(or negate $y
to stay starting at the right).
FUNCTIONS
$path = Math::PlanePath::Foo->new (key=>value, ...)
-
Create and return a new path object. Optional key/value parameters may control aspects of the object.
Foo
here is one of the various subclasses, see the list under "SEE ALSO". ($x,$y) = $path->n_to_xy ($n)
-
Return x,y coordinates of point
$n
on the path. If there's no point$n
then the return is an empty list, so for examplemy ($x,$y) = $path->n_to_xy (-123) or next; # likely no negatives in $path
Currently all paths start from N=1, though some will give a position for N=0 or N=0.5 too.
$n = $path->xy_to_n ($x,$y)
-
Return the point number for coordinates
$x
,$y
. If there's nothing at$x
,$y
then returnundef
.my $n = $path->xy_to_n(20,20); if (! defined $n) { next; # nothing at this x,y }
$x
and$y
can be fractional and the path classes will give an integer$n
which contains$x
,$y
within a unit square, circle, or intended figure centred on that$n
.For paths which completely tile the plane there's always an
$n
to return, but for the spread-out paths an$x
,$y
position may fall in between (no$n
close enough). ($n_lo, $n_hi) = $path->rect_to_n_range ($x1,$y1, $x2,$y2)
-
Return a range of N values which occur in a rectangle with corners at
$x1
,$y1
and$x2
,$y2
. The range is inclusive, so for instancemy ($n_lo, $n_hi) = $path->rect_to_n_range (-5,-5, 5,5); foreach my $n ($n_lo .. $n_hi) { my ($x, $y) = $path->n_to_xy ($n) or next; print "$n $x,$y"; }
Note the return may be an over-estimate and there may be points between
$n_lo
and$n_hi
which are outside the rectangle.$n_hi
is usually no more than an extra partial row or revolution.$n_lo
is often just the starting point 1, which is correct if you always want the origin 0,0, but a rectangle away from the origin could start higher.$x1
,$y1
and$x2
,$y2
can be fractional and if they partly overlap some N figures then those N values are included in the return. If there's no points in the rectangle then the return is a "crossed" range like$n_lo=1
,$n_hi=0
(which can make aforeach
do no loops). $bool = $path->x_negative
$bool = $path->y_negative
-
Return true if the path extends into negative X coordinate and/or negative Y coordinates respectively.
$str = $path->figure
-
Return the name of the figure (shape) intended to be drawn at each
$n
position. Currently this is one ofsquare side 1 centred on $x,$y circle diameter 1 centred on $x,$y
Of course this is only a suggestion as PlanePath doesn't draw anything itself. A figure like a diamond for instance would work well too.
SEE ALSO
Math::PlanePath::SquareSpiral, Math::PlanePath::DiamondSpiral, Math::PlanePath::HexSpiral, Math::PlanePath::HexSpiralSkewed, Math::PlanePath::SacksSpiral, Math::PlanePath::VogelFloret, Math::PlanePath::KnightSpiral
Math::PlanePath::Rows, Math::PlanePath::Columns, Math::PlanePath::Diagonals, Math::PlanePath::Corner, Math::PlanePath::PyramidRows, Math::PlanePath::PyramidSides
HOME PAGE
http://user42.tuxfamily.org/math-planepath/index.html
LICENSE
Math-PlanePath is Copyright 2010 Kevin Ryde
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/>.