arc Class Reference

Convex arc of a circle through the points p0 and p1 in 2D. More...

#include <arc.h>

Collaboration diagram for arc:

List of all members.

Public Member Functions
	arc ()
	Construct an arc in an undefined state.
	arc (doublec radius_, pt2c &p0_, pt2c &p1_)
	Construct an arc.
void	constructRadiusTwoPoints (doublec radius_, pt2c &p0_, pt2c &p1_)
	Construct the arc from two points and the signed radius.
void	constructPhi0TwoPoints (doublec phi0_, pt2c &p0_, pt2c &p1_)
	Construct the arc from two points and an initial angle(in radians).
boolc	isAntiClockwise () const
	Does the arc have an anticlockwise winding?
boolc	isStraightLine () const
	Is the arc a straight line?
boolc	valid () const
	Is the arc valid.
	operator string () const
	Output the arc uniquely as p0 p1 radius.
void	print () const
	Print info on this class to the console (for debugging).
doublec	length () const
	Find the length of the arc segment.
void	distance (double &val, pt2c &p) const
	Find the distance from the point to the arc.
void	distanceSquared (double &val, pt2c &p) const
	Find distance squared from the point to the arc.
Static Public Member Functions
static void	arcreader (vector< arc > &v, string const &filename)
	Read in a file or vector arcs.
Public Attributes
pt2	p0
	The starting point of the arc.
pt2	p1
	The end point of the arc.
double	radius
	The sign of the radius describes which side of line p01 the arc lies on.
double	phi0
	Angle from center to p0 in radians.
double	phi1
	Angle from center to p1 in radians.
pt2	center
	The center of the arc.
Static Public Attributes
static double	zero = 1e-12
	Used to detect the straight line case.

---

Detailed Description

Convex arc of a circle through the points p0 and p1 in 2D.

For a positive radius the arc is on the rhs of line p01. For a negative radius the arc is on the lhs of line p01.

<TODO> clarify For a radius less that distance(p0,p1)/2 a straight line is assumed. For r==0.0 the arc is a straight line (infinite radius).

Definition at line 24 of file arc.h.

---

Constructor & Destructor Documentation

arc::arc

(

)

Construct an arc in an undefined state.

Definition at line 10 of file arc.cpp.

  : radius(0.0), phi0(0.0), phi1(0.0)
{
}

arc::arc	(	doublec	radius_,
		pt2c &	p0_,
		pt2c &	p1_
	)

Construct an arc.

Definition at line 228 of file arc.cpp.

{
  constructRadiusTwoPoints(radius_,p0_,p1_);
}

---

Member Function Documentation

void arc::arcreader	(	vector< arc > &	v,
		string const &	filename
	)			[static]

Read in a file or vector arcs.

The format is as follows. Number of points, points,

number of arcs, arcs. The arc is defined by indexing the two points into the points array and then the signed radius.

Example

7
0.0 0.0
1.0 1.1
1.5 2.8
2.8 4.2
4.8 4.0
6.8 4.2
8.1 5.5
6
0 1 -2.5
1 2 -2.5 
2 3 -2.5
3 4 0.0
4 5 2.5
5 6 3.0

Definition at line 256 of file arc.cpp.

References pts.

Referenced by test03(), and writearcgeometry().

{
  v.clear();

  ifstream targ(filename.c_str());

  assert(targ.good()==true);
  if (targ.good()==false)
    return;
  
  vector< pt2 > pts;

  pt2 p;
  uint k;
  targ >> k;
  for ( uint i=0; i<k; ++i)
  {
    targ >> p;
    pts.push_back(p);
  }

  uint a;
  uint b;
  double radius;

  targ >> k;

  for ( uint i=0; i<k; ++i)
  {
    targ >> a;
    targ >> b;
    targ >> radius;

    assert(a<pts.size());
    assert(b<pts.size());

    v.push_back( arc(radius,pts[a],pts[b]) );
  }
}

void arc::constructPhi0TwoPoints	(	doublec	phi0_,
		pt2c &	p0_,
		pt2c &	p1_
	)

Construct the arc from two points and an initial angle(in radians).

Definition at line 128 of file arc.cpp.

References point2< T >::dot(), point2< T >::x, and point2< T >::y.

Referenced by arcsconnected::constructPhi0(), test04(), and test08().

{
  p0 = p0_;
  p1 = p1_;
  phi0 = phi0_;
/*
cout << endl << endl;

cout << SHOW(phi0*180.0/PI) << endl; 
cout << SHOW(p0) << endl;
cout << SHOW(p1) << endl;
*/

  pt2c f(cos(phi0),sin(phi0));
  pt2c dp(p0-p1);

  doublec fdotdp(f.dot(dp));
  if ( abs(fdotdp)<zero)
  {
    radius=0.0;
    return;
  }
  

if ( fdotdp< 0.0 )
{
#ifndef NDEBUG
cout << "error:  wrong initial angle" << endl;
#endif
  constructPhi0TwoPoints(phi0+PI,p0,p1);
  return;
}

  radius = dp.dot() / fdotdp * 0.5;
//cout << SHOW(radius) << endl;

#ifndef NDEBUG
if (radius<0.0)
  cout << "error: the radius should be positive." << endl;
#endif
  //center = p0 - f * abs(radius);
  center = p0 - f * radius;





/*
  pt2 c0 = p0 - f * radius;
  center = c0;


cout << SHOW(c0) << endl;
cout << SHOW(c0 + f * radius) << endl;
cout << SHOW(c0 - f * radius) << endl;
cout << SHOW( (p0-c0).distance() ) << endl;
cout << SHOW( (p1-c0).distance() ) << endl;
*/


  pt2 p4(p1-center);
  p4 *= 1.0 / radius;
  phi1 = atan2(p4.y,p4.x);

  if (isAntiClockwise2()==false)
  {

    if (radius<0)
    {
#ifndef NDEBUG
cout << "error:  radius already -ve, this message should not appear" << endl;
#endif
    }
    else
      radius *= -1;
  }

/*

cout << "Verify by finding p2 from phi1." << endl;
  pt2 p5(cos(phi1),sin(phi1));
  p5 *= radius;
  p5 += center;


cout << SHOW(p4) << endl;
cout << SHOW(p4.dot()) << endl;
cout << SHOW(phi1*180.0/PI) << endl;
cout << SHOW(p5) << endl;
*/


}

void arc::constructRadiusTwoPoints	(	doublec	radius_,
		pt2c &	p0_,
		pt2c &	p1_
	)

Construct the arc from two points and the signed radius.

Definition at line 95 of file arc.cpp.

References point2< T >::x, and point2< T >::y.

{
  radius = radius_;
  p0 = p0_;
  p1 = p1_;

  if (isStraightLine()==true)
    return;

  calculateCenter();

  pt2 g0(p0-center);
  //g0.normalize();
  phi0 = atan2(g0.y,g0.x);
  angleAdjusted(phi0);
  pt2 g1(p1-center);
  //g1.normalize();
  phi1 = atan2(g1.y,g1.x);
  angleAdjusted(phi1);

/*
cout << SHOW(g0) << " " << SHOW(phi0*180./PI) << endl;
cout << SHOW(g1) << " " << SHOW(phi1*180./PI) << endl;
cout << SHOW(phi1-phi0) << " " << SHOW(length()) << endl;
*/
  
}

void arc::distance	(	double &	val,
		pt2c &	p
	)			const

Find the distance from the point to the arc.

Definition at line 323 of file arc.cpp.

References center, point2< T >::distance(), point2< T >::dot(), isAntiClockwise(), p0, p1, radius, and point2< T >::rotate90().

Referenced by test06().

{
  pt2 p3(p-center);

  if (isAntiClockwise())
  {
    {
      pt2 z(center-p0);
      z.rotate90();
      if (z.dot(p3)>0.0)
      {
//cout << "greater than p0 arm." << endl;
        // Take the distance from the endpoint.
        val = (p-p0).distance();
        return;
      }
    }
    {
      pt2 z(p1-center);
      z.rotate90();
      if (z.dot(p3)>0.0)
      {
//cout << "greater than p1 arm." << endl;
        // Take the distance from the endpoint.
        val = (p-p1).distance();
        return;
      }
    }
  }
  else
  {
    {
      pt2 z(center-p1);
      z.rotate90();
      if (z.dot(p3)>0.0)
      {
        val = (p-p1).distance();
        return;
      }
    }
    {
      pt2 z(p0-center);
      z.rotate90();
      if (z.dot(p3)>0.0)
      {
        val = (p-p0).distance();
        return;
      }
    }
  }

  val = abs(p3.distance() - radius);
  return;
  
} 

void arc::distanceSquared	(	double &	val,
		pt2c &	p
	)			const

Find distance squared from the point to the arc.

Definition at line 379 of file arc.cpp.

References center, point2< T >::dot(), isAntiClockwise(), p0, p1, radius, and point2< T >::rotate90().

Referenced by arcsconnected::sumdisttoarc().

{
  pt2 p3(p-center);

  if (isAntiClockwise())
  {
    {
      pt2 z(center-p0);
      z.rotate90();
      if (z.dot(p3)>0.0)
      {
        //val = (p-p0).distanceSquared();
        val = (p-p0).dot();
        return;
      }
    }
    {
      pt2 z(p1-center);
      z.rotate90();
      if (z.dot(p3)>0.0)
      {
        //val = (p-p1).distanceSquared();
        val = (p-p1).dot();
        return;
      }
    }
  }
  else
  {
    {
      pt2 z(center-p1);
      z.rotate90();
      if (z.dot(p3)>0.0)
      {
        //val = (p-p1).distanceSquared();
        val = (p-p1).dot();
        return;
      }
    }
    {
      pt2 z(p0-center);
      z.rotate90();
      if (z.dot(p3)>0.0)
      {
        //val = (p-p0).distanceSquared();
        val = (p-p0).dot();
        return;
      }
    }
  }

  //val = abs(p3.distanceSquared() - radius*radius);
  val = abs(p3.dot() - radius*radius);
} 

boolc arc::isAntiClockwise

(

)

const [inline]

Does the arc have an anticlockwise winding?

Definition at line 79 of file arc.h.

References radius.

Referenced by distance(), distanceSquared(), print(), and arcdraw::update().

    { return radius > 0.0; }

boolc arc::isStraightLine

(

)

const [inline]

Is the arc a straight line?

Definition at line 83 of file arc.h.

References radius.

Referenced by length(), arcdraw::update(), and valid().

    { return radius == 0.0; }

doublec arc::length

(

)

const

Find the length of the arc segment.

Definition at line 237 of file arc.cpp.

References isStraightLine(), p0, p1, phi1, radius, and valid().

{
  assert(valid()==true);

  if (isStraightLine())
    return (p1-p0).distance();


  // Interpret the arc as convex between points p0 and p1.
  //  Find the acute angle between the points p0 and p1.
  double dphi = abs(phi1-phi0);
  if (dphi>PI)
    dphi = 2.0*PI - dphi;

  return abs(dphi*radius);
}

arc::operator string

(

)

const

Output the arc uniquely as p0 p1 radius.

Definition at line 86 of file arc.cpp.

References p0, p1, and radius.

{
  stringstream ss;
  ss << p0 << " " << p1 << " " << radius; 
  return ss.str();
}

void arc::print

(

)

const

Print info on this class to the console (for debugging).

Definition at line 300 of file arc.cpp.

References center, isAntiClockwise(), p0, p1, phi1, radius, and SHOW.

Referenced by test04(), test06(), and test08().

{
  cout << SHOW(radius) << endl;
  cout << SHOW(p0) << endl;
  cout << SHOW(p1) << endl;
  
  cout << SHOW(center) << endl;
  cout << SHOW(phi0*180.0/PI) << endl;
  cout << SHOW(phi1*180.0/PI) << endl;
  cout << SHOW(isAntiClockwise()) << endl;
  cout << SHOW(isAntiClockwise2()) << endl;
  cout << SHOW(center+pt2(cos(phi0),sin(phi0))*abs(radius) ) << endl;
  cout << SHOW(center+pt2(cos(phi1),sin(phi1))*abs(radius) ) << endl;
  cout << endl;
}

boolc arc::valid

(

)

const

Is the arc valid.

For example if the radius is less than the distance between the arc end points then there can be no arc connecting the two points.

Definition at line 15 of file arc.cpp.

References isStraightLine(), p0, and p1.

Referenced by length().

{
  
  if ((p0==p1)==true)
  {
    cout << "error:  " << *this << " has p0 and p1 equal.";
    cout << endl;
    return false;
  }

  if (isStraightLine())
    return true;

/*
  if ( ((p0-p1).dot() <= radius*radius*4.0) == false )
  {
    cout << *this << " failed radius condition." << endl;
    assert(false);
    return false;
  }
*/
  
  return true;
}

---

Member Data Documentation

pt2 arc::center

The center of the arc.

Definition at line 50 of file arc.h.

Referenced by distance(), distanceSquared(), print(), test02(), and arcdraw::update().

pt2 arc::p0

The starting point of the arc.

Definition at line 34 of file arc.h.

Referenced by distance(), distanceSquared(), length(), operator string(), print(), arcdraw::update(), and valid().

pt2 arc::p1

The end point of the arc.

Definition at line 36 of file arc.h.

Referenced by distance(), distanceSquared(), length(), operator string(), print(), arcdraw::update(), and valid().

double arc::phi0

Angle from center to p0 in radians.

Definition at line 46 of file arc.h.

Referenced by arcdraw::update().

double arc::phi1

Angle from center to p1 in radians.

Definition at line 48 of file arc.h.

Referenced by length(), print(), test04(), and arcdraw::update().

double arc::radius

The sign of the radius describes which side of line p01 the arc lies on.

Definition at line 40 of file arc.h.

Referenced by arcsconnected::constructPhi0(), distance(), distanceSquared(), isAntiClockwise(), isStraightLine(), length(), operator string(), print(), and arcdraw::update().

double arc::zero = 1e-12 [static]

Used to detect the straight line case.

Definition at line 141 of file arc.h.

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The documentation for this class was generated from the following files:

• arcs/arc.h
• arcs/arc.cpp