NAME

       Math::NumSeq::PlanePathN -- sequence of N values from PlanePath module

SYNOPSIS

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

DESCRIPTION

       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.

SEE ALSO

       Math::NumSeq, Math::NumSeq::PlanePathCoord, Math::NumSeq::PlanePathDelta

HOME PAGE

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

LICENSE

       Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021 Kevin Ryde

       This file is part of Math-PlanePath.

       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/>.