Math::PlanePath 88

Math::PlanePath is the Perl class for some mathematical paths which turn an integer position $n into coordinates $x,$y in the plane. The current classes include

 SquareSpiral four-sided spiral
 PyramidSpiral square base pyramid
 TriangleSpiral equilateral triangle
 TriangleSpiralSkewed equilateral skewed for compactness
 DiamondSpiral four-sided spiral, looping faster
 PentSpiralSkewed five-sided spiral, compact
 HexSpiral six-sided spiral
 HexSpiralSkewed six-sided spiral skewed for compactness
 HeptSpiralSkewed seven-sided spiral, compact
 OctagramSpiral eight pointed star
 KnightSpiral an infinite knight's tour
 GreekKeySpiral spiral with Greek key motif

 SacksSpiral quadratic on an Archimedean spiral
 VogelFloret seeds in a sunflower
 TheodorusSpiral unit steps at right angles
 ArchimedeanChords chords on an Archimedean spiral
 MultipleRings concentric circles
 PixelRings concentric circles by pixels
 Hypot points by distance
 HypotOctant first octant points by distance
 TriangularHypot points by triangular lattice distance
 PythagoreanTree primitive triples by tree

 PeanoCurve self-similar base-3 quadrant traversal
 HilbertCurve self-similar base-2 quadrant traversal
 ZOrderCurve replicating Z shapes
 KochCurve replicating triangular notches
 KochPeaks stacked replicating notches
 KochSnowflakes concentric snowflake rings

 Rows fixed-width rows
 Columns fixed-height columns
 Diagonals diagonals down from the Y to X axes
 Staircase stairs down from the Y to X 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 only a few subclasses have any parameters. See examples/numbers.pl for a cute way to print samples of all the paths.

The classes are generally based on integer $n positions and those designed for a square grid turn an integer $n into integer $x,$y. Usually they give in-between positions for fractional $n too. Classes not on a square grid, like SacksSpiral and VogelFloret, are designed 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 reflection up or down. Those things are thought better done by a general coordinate transformer that might expand or invert for display. Even clockwise instead of counter-clockwise spiralling can be had just by negating $x (or negate $y to stay starting at the right), or a quarter turn with -$y,$x. Try Transform::Canvas for scaling/shifting, and Geometry::AffineTransform for rotating too.

SYNOPSIS

 use Math::PlanePath;
 # only a base class, see the subclasses for actual operation


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Requirements:

· Perl