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# 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", the turn follows that particular arm so it's i-arms, i, i+arms. i values start `n_start()+arms_count()` so that 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.

# 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``````

Math::NumberCruncher has a `Clockwise()` turn calculator

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