Math::NumSeq::PlanePathTurn -- turn sequence from PlanePath module
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.
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
"NotStraight" 0=straight, 1=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 sequence index i is the turn at N=i,
i-1 ---> i turn at i
first turn at i = n_start + 1
For multiple "arms" in the path, the turn follows that particular arm so locations of N = i-arms to i to i+arms. i values start n_start()+arms_count() so that i-arms is n_start() which is 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 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, so not straight or right. Similarly "Right" means to the right side of the N-1 to N line, so 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
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.
$path->n_start() - $path->arms_count()
A turn left or right is identified by considering the dX,dY at N-1 and at N.
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
^ * dx1,dy1
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::NumSeq, Math::NumSeq::PlanePathCoord, Math::NumSeq::PlanePathDelta, Math::NumSeq::PlanePathN
Math::NumberCruncher has a Clockwise() turn calculator
Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021 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/>.
To install Math::PlanePath, copy and paste the appropriate command in to your terminal.
perl -MCPAN -e shell
For more information on module installation, please visit the detailed CPAN module installation guide.