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


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


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
    "AbsdX"    abs(dX)
    "AbsdY"    abs(dY)
    "dSum"     change in X+Y, equals dX+dY
    "dDiffXY"  change in X-Y, equals dX-dY
    "dDiffYX"  change in Y-X, equals dY-dX
    "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. Whether X-Y or Y-X is desired depends on which way you want to measure diagonals, or what sign to have for the changes. dDiffYX is based on Y-X and so counts diagonals upwards to the North-West.

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

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

"TDir6" direction 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


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.


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





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/>.