NAME
Math::NumSeq::PlanePathTurn  turn sequence from PlanePath module
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
"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 "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, not straight or right. Similarly "Right" means to the right side of the N1 to N line, 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 andpred()
reflects that. $i = $seq>i_start()

Return the first index
$i
in the sequence. This is the positionrewind()
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
SEE ALSO
Math::NumSeq, Math::NumSeq::PlanePathCoord, Math::NumSeq::PlanePathDelta, Math::NumSeq::PlanePathN
Math::NumberCruncher has a Clockwise()
turn calculator
HOME PAGE
http://user42.tuxfamily.org/mathplanepath/index.html
LICENSE
Copyright 2011, 2012, 2013, 2014, 2015 Kevin Ryde
This 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/>.