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Math-PlanePath-73
River stage one • 3 direct dependents • 4 total dependents
/ Math::NumSeq::PlanePathCoord

NAME

Math::NumSeq::PlanePathCoord -- sequence of coordinate values from a PlanePath module

SYNOPSIS

use Math::NumSeq::PlanePathCoord;
my $seq = Math::NumSeq::PlanePathCoord->new
            (planepath => 'SquareSpiral',
             coordinate_type => 'X');
my ($i, $value) = $seq->next;

DESCRIPTION

This is a tie-in to present coordinates from a Math::PlanePath module as a NumSeq sequence. The NumSeq "i" index is the PlanePath "N" value.

The coordinate_type choices are

"X"          X coordinate
"Y"          Y coordinate
"Sum"        X+Y sum
"SumAbs"     abs(X)+abs(Y)
"Product"    X*Y product
"DiffXY"     X-Y difference
"DiffYX"     Y-X difference (negative of DiffXY)
"AbsDiff"    abs(Y-X) difference
"Radius"     sqrt(X^2+Y^2) radius
"RSquared"   X^2+Y^2 radius squared
"TRadius"    sqrt(X^2+3*Y^2) triangular radius
"TRSquared"  X^2+3*Y^2 triangular radius squared

"Sum" can be interpreted geometrically as a projection onto the X=Y leading diagonal, or equivalently as a measure of which anti-diagonal stripe contains the X,Y.

                  *    X=Y
\                  \  /
 2                  \/
\ \                 /  .
 1 2               /  /
\ \ \             / sum distance
 0 1 2           o  /
                   /

"SumAbs" is a similar projection, but onto the diagonal of whichever quadrant contains the X,Y. It's sometimes thought of as a taxi-cab or Manhatten distance, being how far be travelled through a square-grid city, by whatever combination of up and down. For paths using only the first quadrant, so X>=0,Y>=0 of course Sum and SumAbs are identical.

"DiffXY" similarly, but a projection onto the X=-Y opposite diagonal, or a measure of which leading diagonal stripe has the X,Y.

                    X=-Y  *
    / / / /           \  /
  -1 0 1 2             \/
  / / / /            .  \
-1 0 1 2              \  \
  / / /         diff dist \
 0 1 2                  \  o
                         \

The triangular "TRadius" and "TRSquared" are meant for use with points on a triangular lattice such as HexSpiral. TRSquared is the same as RSquared on the X axis but the Y axis is scaled up. The triangular paths generally use every second X,Y point which makes TRSquared always even, or for KochPeaks and similar offset 1 from the origin then always odd.

OEIS

Some path coordinates are in Sloane's Online Encyclopedia of Integer Sequences. See each PlanePath module for details.

$seq->oeis_anum() returns the A-number in the usual way, if there's one known. This includes things like A000004 all-zeros for cases where a coordinate is simple or even trivial.

Known A-numbers are presented through Math::NumSeq::OEIS::Catalogue so path related sequences can be created with Math::NumSeq::OEIS in the usual way. A-numbers specific to the paths are catalogued, plus a few of the simpler things not otherwise covered by NumSeq modules yet (such as A002262 successive 0 to k runs 0, 0,1, 0,1,2, 0,1,2,3, which arises in the Diagonals).

FUNCTIONS

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

$seq = Math::NumSeq::PlanePathCoord->new (planepath => $name, coordinate_type => 'X')

Create and return a new sequence object. The options are

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

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

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

Return the coordinate at N=$i in the PlanePath.

$i = $seq->i_start()

Return the first index $i in the sequence. This is the position rewind() returns to.

This is $path->n_start() from the PlanePath, since the i numbering is the N numbering of the underlying path. For some of the Math::NumSeq::OEIS generated sequences there may be a higher i_start() corresponding to a higher starting point in the OEIS, though this is slightly experimental.

SEE ALSO

Math::NumSeq, Math::NumSeq::PlanePathDelta, Math::NumSeq::PlanePathN, Math::NumSeq::OEIS

Math::PlanePath

HOME PAGE

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

LICENSE

Copyright 2011, 2012 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/>.