/ 
Math-PlanePath-90
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
"GCD"          greatest common divisor of X,Y
"Depth"        tree_n_to_depth()
"NumChildren"  tree_n_num_children()

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

"SumAbs"=abs(X)+abs(Y) is a similar projection, but onto the cross-diagonal of whichever quadrant contains the X,Y. It's also thought of as a "taxi-cab" or Manhatten distance, being how far to travel through a square-grid city to get to X,Y. If a path uses only the first quadrant, ie. X>=0,Y>=0, then of course Sum and SumAbs are identical.

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

                            X=-Y diagonal    * X,Y
    / / / /                              \  /
  -1 0 1 2   diagonal                     \/
  / / / /    numbering                     \
-1 0 1 2       X-Y                       ^  \
  / / /                                   \  \
 0 1 2                           distance X-Y o
                                               \

"DiffYX"=Y-X is simply the negative of DiffXY. Both forms are included for convenience to get positive values from paths which are above or below the X=Y leading diagonal. DiffXY is positive for paths such as CoprimeColumns which are below X=Y. DiffYX is positive for paths such as CellularRule which are above X=Y.

"TRadius" and "TRSquared" are designed 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 by factor sqrt(3). Most triangular paths use every second X,Y point which makes TRSquared even, but some such as KochPeaks have an offset 1 from the origin making it odd instead.

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::PlanePathTurn, 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/>.