---
name: "Math::NumSeq::PlanePathTurn"
section: "3pm"
platform: "linux"
package: "libmath-planepath-perl"
version: "129-1"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/Math::NumSeq::PlanePathTurn"
---

# Math::NumSeq::PlanePathTurn(3pm)

## 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
```

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/math-planepath/index.html\>

## LICENSE

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/\>.