Math::NumSeq::PlanePathTurn -- turn sequence from PlanePath module
use Math::NumSeq::PlanePathTurn; my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'DragonCurve', turn_type => 'Left'); my ($i, $value) = $seq->next;
This is a tie-in to present turns from a
Math::PlanePath module in the form of a NumSeq sequence.
turn_type choices are
"Left" 1=left 0=right or straight "Right" 1=right 0=left or straight "LSR" 1=left 0=straight -1=right "SLR" 0=straight 1=left 2=right "SRL" 0=straight 1=right 2=left
In each case the value at i is the turn which occurs at N=i,
i+1 ^ | | i-1 ---> i turn at i first turn at i = n_start + 1
For multiple "arms" the turn follows that particular arm so it's i-arms, i, i+arms. i values start
n_start()+arms_count() so i-arms is
n_start(), the first N on the path. A single arm path beginning N=0 has its first turn at i=1.
For "LSR", "SLR" and "SRL", straight means either straight ahead or 180-degree reversal, ie. the direction N to N+1 is along the same line as N-1 to N was.
"Left" means to the left side of the N-1 to N line, not straight or right. Similarly "Right" means to the right side of the N-1 to N line, not straight or left.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::PlanePathTurn->new (key=>value,...)
Create and return a new sequence object. The options are
planepath string, name of a PlanePath module planepath_object PlanePath object turn_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 turn at N=$i in the PlanePath.
$bool = $seq->pred($value)
Return true if
$valueoccurs as a turn. Often this is merely the possible turn values 1,0,-1, etc, but some spiral paths for example only go left or straight in which case only 1 and 0 occur and
$i = $seq->i_start()
Return the first index
$iin the sequence. This is the position
$path->n_start() - $path->arms_count()from the PlanePath object.
Turn Left or Right
A turn left or right is identified by considering the dX,dY at N-1 and at N.
N+1 * | | | dx2,dy2 | N * / / / dx1,dy1 N-1 *
With the two vectors dx1,dy1 and dx2,dy2 at a common origin, if the dx2,dy2 is above the dx1,dy1 line then it's a turn to the left, or below is a turn to the right
dx2,dy2 * | * dx1,dy1 | / | / |/ o
At dx2 the Y value of the dx1,dy1 vector is
cmpY = dx2 * dy1/dx1 if dx1 != 0 left if dy2 > cmpY dy2 > dx2 * dy1/dx1 so dy2 * dx1 > dx2 * dy1
This cross-product comparison dy2*dx1 > dx2*dy1 works when dx1=0 too, ie. when dx1,dy1 is vertical
left if dy2 * 0 > dx2 * dy1 0 > dx2*dy1 good, left if dx2 and dy1 opposite signs
dy2*dx1 > dx2*dy1 left dy2*dx1 < dx2*dy1 right dy2*dx1 = dx2*dy1 straight, including 180 degree reverse
Math::NumberCruncher has a
Clockwise() turn calculator
Copyright 2011, 2012, 2013, 2014 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.
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