 Math::NumSeq::PlanePathTurn(3) 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
"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-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.

## 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.

## 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
```

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