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Math-PlanePath-76
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.

                      *    line X=Y
\     anti-diag        \  /
 2    numbering         \/
\ \     X+Y             /
 1 2                   /  ^
\ \ \                 /  /
 0 1 2               o  distance X+Y
                       /

"SumAbs" is a similar projection, but onto the cross-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 any combination of up and down. If a path uses only the first quadrant, ie. X>=0,Y>=0, then of course Sum and SumAbs are identical.

"DiffXY" is similar, 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   diagonal              \/
  / / / /    numbering              \
-1 0 1 2       X-Y                ^  \
  / / /                            \  \
 0 1 2                    X-Y distance o
                                        \

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

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 either 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.

$str = $seq->oeis_anum()

Return the A-number (a string) for $seq in Sloane's Online Encyclopedia of Integer Sequences, or return undef if not in the OEIS or not known.

Known A-numbers are presented through Math::NumSeq::OEIS::Catalogue so PlanePath related sequences can be created with Math::NumSeq::OEIS by their A-number in the usual way.

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/>.