NAME

Math::NumSeq::PlanePathDelta -- sequence of changes and directions of PlanePath coordinates

SYNOPSIS

 use Math::NumSeq::PlanePathDelta;
 my $seq = Math::NumSeq::PlanePathDelta->new
             (planepath => 'SquareSpiral',
              delta_type => 'dX');
 my ($i, $value) = $seq->next;

DESCRIPTION

This is a tie-in to present coordinate changes and directions from a Math::PlanePath module in the form of a NumSeq sequence.

The delta_type choices are

    "dX"       change in X coordinate
    "dY"       change in Y coordinate
    "dSum"     change in X+Y
    "dDiffXY"  change in X-Y
    "dDiffYX"  change in Y-X
    "Dir4"     direction 0=East, 1=North, 2=West, 3=South
    "TDir6"    triangular 0=E, 1=NE, 2=NW, 3=W, 4=SW, 5=SE

In each case the value at i is per $path->n_to_dxdy($i), being the change from N=i to N=i+1, or from N=i to N=i+arms for paths with multiple "arms" (thus following a particular arm). i values start from the usual $path->n_start().

"dSum" is the change in X+Y and is also simply dX+dY since

    dSum = (Xnext+Ynext) - (X+Y)
         = (Xnext-X) + (Ynext-Y)
         = dX + dY

The sum X+Y counts anti-diagonals, as described in Math::NumSeq::PlanePathCoord. dSum is therefore a move between diagonals or 0 if a step stays within the same diagonal.

"dDiffXY" is the change in DiffXY = X-Y and is also simply dX-dY since

    dDiffXY = (Xnext-Ynext) - (X-Y)
            = (Xnext-X) - (Ynext-Y)
            = dX - dY

The difference X-Y counts diagonals, downwards to the south-east, as described in Math::NumSeq::PlanePathCoord. dDiffXY is therefore movement between those diagonals or 0 if a step stays within the same diagonal.

"dDiffYX" is the negative of dDiffXY. Which one is desired depends on which way you want to measure diagonals, or what sign to have the changes. dDiffYX is based on Y-X and so counts diagonals upwards (North-West).

"Dir4" is a fraction when a delta is in between the cardinal N,S,E,W directions. For example dX=-1,dY=+1 to the North-West would be direction=1.5.

    Dir4 = atan2 (dY, dX)       in range to 0 <= Dir4 < 4

"TDir6" is in triangular style per "Triangular Lattice" in Math::PlanePath. So dX=1,dY=1 is 60 degrees, dX=-1,dY=1 is 120 degrees, dX=-2,dY=0 is 180 degrees, etc and fractional values if in between. It behaves as if dY was scaled by a factor sqrt(3) to make equilateral triangles,

    TDir6 = atan2(dY*sqrt(3), dX)      in range 0 <= TDir6 < 6

FUNCTIONS

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

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

Create and return a new sequence object. The options are

    planepath          string, name of a PlanePath module
    planepath_object   PlanePath object
    delta_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 change at N=$i in the PlanePath.

$i = $seq->i_start()

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

This is $path->n_start() from the PlanePath.

SEE ALSO

Math::NumSeq, Math::NumSeq::PlanePathCoord, Math::NumSeq::PlanePathTurn, Math::NumSeq::PlanePathN

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/>.

cpanm Math::PlanePath

perl -MCPAN -e shell
install Math::PlanePath