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 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-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.

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 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

HOME PAGE

<http://user42.tuxfamily.org/math-planepath/index.html>

LICENSE

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/>.

2021-01-23

perl v5.32.0