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.
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
"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
planepathcan 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
$iin the sequence. This is the position
$path->n_start()from the PlanePath.
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/>.