Math::NumSeq::PlanePathN3pm

Usage

 use Math::NumSeq::PlanePathN;
 my $seq = Math::NumSeq::PlanePathN->new (planepath => 'SquareSpiral',
                                          line_type => 'X_axis');
 my ($i, $value) = $seq->next;

Overview

This module presents N values from a "Math::PlanePath" as a sequence. The default is the X axis, or the "line_type" parameter (a string) can choose among

    "X_axis"        X axis (positive part)
    "Y_axis"        Y axis (positive part)
    "X_neg"         X negative axis
    "Y_neg"         Y negative axis
    "Diagonal"      leading diagonal X=i, Y=i
    "Diagonal_NW"   north-west diagonal X=-i, Y=i
    "Diagonal_SW"   south-west diagonal X=-i, Y=-i
    "Diagonal_SE"   south-east diagonal X=i, Y=-i
    "Depth_start"   first N at depth=i
    "Depth_end"     last N at depth=i

For example the "SquareSpiral" X axis starts i=0 with values 1, 2, 11, 28, 53, 86, etc.

"X_neg", "Y_neg", "Diagonal_NW", etc, on paths which don't traverse negative X or Y have just a single value from X=0,Y=0.

The behaviour on paths which visit only some of the points on the respective axis is unspecified as yet, as is behaviour on paths with repeat points, such as the "DragonCurve".

Functions

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

"$seq = Math::NumSeq::PlanePathN->new (key=>value,...)"

Create and return a new sequence object. The options are

    planepath          string, name of a PlanePath module
    planepath_object   PlanePath object
    line_type          string, as described above

"planepath" can be either the module part such as "SquareSpiral" or a full class name "Math::PlanePath::SquareSpiral".

"$value = $seq->ith($i)"

Return the N value at $i in the PlanePath. $i gives a position on the respective "line_type", so the X,Y to lookup a "$value=N" is

     X,Y       line_type
    -----      ---------
    $i, 0      "X_axis"
    0, $i      "Y_axis"
    -$i, 0     "X_neg"
    0, -$i     "Y_neg"
    $i, $i     "Diagonal"
    $i, -$i    "Diagonal_NW"
    -$i, -$i   "Diagonal_SW"
    $i, -$i    "Diagonal_SE"

"$bool = $seq->pred($value)"

Return true if $value occurs in the sequence.

This means $value is an integer N which is on the respective "line_type", ie. that "($path->n_to_xy($value)" is on the line type.

Home page

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