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Arc.php
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Arc.php
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<?php
namespace fw;
require_once("Path.php");
require_once("Point.php");
require_once("Vector.php");
///
/// A general circular curved path between two points.
///
class Arc extends Path
{
//__________________________________________________________________
// Properties
/// Point at arc's centre
private $centre;
/// Vector from centre to start
private $c2s;
/// Vector from centre to end
private $c2e;
/// Boolean indicating whether the arc is clockwise (true) or anti-clockwise (false)
private $cw;
/// Boolean indicating whether the arc is large (true) or small (flase)
private $large;
/// Radius of the arc
private $r;
//__________________________________________________________________
// Constructor
public function __construct(Point $start_, Point $end_, $radius_, $clockwise_ = true, $large_ = false)
{
$this->setArc($start_, $end_, $radius_, $clockwise_, $large_);
}
//__________________________________________________________________
// Methods
/// Return Point at centre
public function centre()
{
return $this->centre;
}
/// Returns Point at end
public function end()
{
$end = new Point( ($this->centre->x() + $this->c2e->x()), ($this->centre->y() + $this->c2e->y()) );
return $end;
}
/// Returns node at mid-point between start and end
public function getMidPoint(Point $start_, Point $end_)
{
$x = ($start_->x() + $end_->x()) / 2.0;
$y = ($start_->y() + $end_->y()) / 2.0;
$n = new Point($x, $y);
return $n;
}
/// Returns true, indicating that this is an arc
public function isArc()
{
return true;
}
/// Returns true if clockwise, false if anti-clockwise
public function isClockwise()
{
return $this->cw;
}
/// Returns true if large, false if small
public function isLarge()
{
return $this->large;
}
/// Returns false, because this is an arc
public function isLine()
{
return false;
}
/// Returns the length along the arc
public function length()
{
$theta = $this->c2s->theta($this->c2e);
if(!$this->cw) $theta = 2.0*pi() - $theta;
$l = $this->r * $theta;
return $l;
}
/// Return s a vector normal to the arc at a distance $length_ along
/// the arc
public function normalAt($length_)
{
$n = $this->c2s;
$n = $n->unit();
$theta = $length_ / $this->r;
if(!$this->cw) $theta *= -1.0;
$n->rotate($theta);
return $n;
}
/// Returns a Point corresponding to a position at distance $length_
/// along the arc
public function positionAt($length_)
{
$n = $this->normalAt($length_);
$n->scale($this->r);
$p = new Point( ($this->centre->x() + $n->x()), ($this->centre->y() + $n->y()) );
return $p;
}
/// Returns the arc's radius
public function radius()
{
return $this->r;
}
/// Used to calculate the arc's properties
private function setArc(Point $start_, Point $end_, $radius_, $clockwise_ = true, $large_ = false)
{
if( $start_ == $end_)
{
trigger_error("Start and end points are the same. Not currently supported", E_USER_ERROR);
}
if( $radius_ < ($start_->dist($end_)/2.0) )
{
trigger_error("Radius is too small.", E_USER_ERROR);
}
$this->cw = $clockwise_;
$this->large = $large_;
$this->r = $radius_;
$this->centre = $this->setCentre($start_, $end_);
$this->c2s = new Vector( ($start_->x() - $this->centre->x()), ($start_->y() - $this->centre->y()) );
$this->c2e = new Vector( ($end_->x() - $this->centre->x()), ($end_->y() - $this->centre->y()) );
}
/// Determines the centre Point
private function setCentre(Point $start_, Point $end_)
{
// Get mid-point
$mid = $this->getMidPoint($start_, $end_);
// Determine distance from mid-point to centre
$s2m = $start_->dist($mid);
$m2c = sqrt( $this->r*$this->r - $s2m*$s2m );
// Get vector from midpoint to one of the centres
$start_to_end = new Vector( ($end_->x()-$start_->x()), ($end_->y()-$start_->y()) );
$start_to_end = $start_to_end->unit();
$mid_to_centre = $start_to_end->norm();
$mid_to_centre->scale($m2c);
// Get two candidate centres
$c1 = new Point( ($mid->x() + $mid_to_centre->x()), ($mid->y() + $mid_to_centre->y()) );
$c2 = new Point( ($mid->x() - $mid_to_centre->x()), ($mid->y() - $mid_to_centre->y()) );
// get vectors from c1 to start/end points
$c1s = new Vector( ($start_->x() - $c1->x()), ($start_->y() - $c1->y()));
$c1e = new Vector( ($end_->x() - $c1->x()), ($end_->y() - $c1->y()));
// determine if small arc is clockwise or not
$c1cw = ( $c1s->cross($c1e) > 0.0 );
// determine if arc is small or large
$c1l = ( $c1s->theta($c1e) > pi() );
// return appropriate centre point
if( $c1cw == $this->isClockwise())
{
if( $c1l == $this->isLarge() )
{
return $c1;
}
else
{
return $c2;
}
}
else
{
if( $c1l == $this->isLarge())
{
return $c2;
}
else
{
return $c1;
}
}
}
public function setClockwise($clockwise_)
{
$this->setArc($this->start(), $this->end(), $this->radius(), $clockwise_, $this->isLarge());
}
/// Changes the end point to $end_
public function setEnd(Point $end_)
{
$this->setArc($this->start(), $end_, $this->radius(), $this->isClockwise, $this->isLarge());
}
public function setLarge($large_)
{
$this->setArc($this->start(), $this->end(), $this->radius(), $this->isClockwise(), $large_);
}
/// Changes the start point to $start_
public function setStart(Point $start_)
{
$this->setArc($start_, $this->end(), $this->radius(), $this->isClockwise, $this->isLarge());
}
/// Returns Point at the start
public function start()
{
$start = new Point( ($this->centre->x() + $this->c2s->x()), ($this->centre->y() + $this->c2s->y()) );
return $start;
}
/// Returns a Vector along the arc's direction at distance $length_
/// along it
public function vectorAt($length_)
{
$v = $this->normalAt($length_);
if($this->cw)
{
$v->rotate(pi()/2.0);
}
else
{
$v->rotate(-pi()/2.0);
}
return $v;
}
}

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