Math::NumSeq::PlanePathTurn(3) 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.

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 ---> 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 ``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.


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

       |   * 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


Copyright 2011, 2012, 2013, 2014, 2015, 2016 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 <>.