SYNOPSIS
use Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn>new (planepath => 'DragonCurve',
turn_type => 'Left');
my ($i, $value) = $seq>next;
DESCRIPTION
This is a tiein to present turns from a "Math::PlanePath" module in the form of a NumSeq sequence.The "turn_type" choices are
"Left" 1=left 0=right or straight "Right" 1=right 0=left or straight "Straight" 1=straight, 0=left or right "LSR" 1=left 0=straight 1=right "SLR" 0=straight 1=left 2=right "SRL" 0=straight 1=right 2=left
In each case the value at i is the turn which occurs at N=i,
i+1 ^   i1 > i turn at i first turn at i = n_start + 1
For multiple ``arms'' the turn follows that particular arm so it's iarms, i, i+arms. i values start "n_start()+arms_count()" so iarms is "n_start()", the first N on the path. A single arm path beginning N=0 has its first turn at i=1.
For ``Straight'', ``LSR'', ``SLR'' and ``SRL'', straight means either straight ahead or 180degree reversal, ie. the direction N to N+1 is along the same line as N1 to N was.
``Left'' means to the left side of the N1 to N line, so not straight or right. Similarly ``Right'' means to the right side of the N1 to N line, so not straight or left.
FUNCTIONS
See ``FUNCTIONS'' in Math::NumSeq for behaviour common to all sequence classes. "$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
"planepath" can 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 $value occurs as a turn. Often this is merely the possible turn values 1,0,1, etc, but some spiral paths for example only go left or straight in which case only 1 and 0 occur and "pred()" reflects that.
 "$i = $seq>i_start()"

Return the first index $i in the sequence. This is the position
"rewind()" returns to.
This is "$path>n_start()  $path>arms_count()" from the PlanePath object.
FORMULAS
Turn Left or Right
A turn left or right is identified by considering the dX,dY at N1 and at N.
N+1 *    dx2,dy2  N * / / / dx1,dy1 N1 *
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 crossproduct 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
So
dy2*dx1 > dx2*dy1 left dy2*dx1 < dx2*dy1 right dy2*dx1 = dx2*dy1 straight, including 180 degree reverse
LICENSE
Copyright 2011, 2012, 2013, 2014, 2015, 2016 Kevin RydeThis file is part of MathPlanePath.
MathPlanePath 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.
MathPlanePath 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 MathPlanePath. If not, see <http://www.gnu.org/licenses/>.