/// <summary>
/// Function to join the 2 lines at the point where they do / would intersect. If they do then
/// the lines are clipped to remove the smallest part of the line. Returns false if they
/// cannot be joined.
/// </summary>
/// <param name="Other">The other line</param>
public bool Join(C2DLine Other)
{
var p1 = point;
var p2 = GetPointTo();
var p3 = Other.point;
var p4 = Other.GetPointTo();
var Ua = (p4.x - p3.x) * (p1.y - p3.y) - (p4.y - p3.y) * (p1.x - p3.x);
var Ub = (p2.x - p1.x) * (p1.y - p3.y) - (p2.y - p1.y) * (p1.x - p3.x);
var dDenominator = (p4.y - p3.y) * (p2.x - p1.x) - (p4.x - p3.x) * (p2.y - p1.y);
if (dDenominator == 0)
{
return(false);
}
Ua = Ua / dDenominator;
Ub = Ub / dDenominator;
var IntPt = new C2DPoint(p1.x + Ua * (p2.x - p1.x), p1.y + Ua * (p2.y - p1.y));
if (Ua >= 0.5)
{
this.SetPointTo(IntPt);
}
else
{
this.SetPointFrom(IntPt);
}
if (Ub >= 0.5)
{
Other.SetPointTo(IntPt);
}
else
{
Other.SetPointFrom(IntPt);
}
return(true);
}
/// <summary>
/// Gets the point half way along the curve as a new object.
/// </summary>
public C2DPoint GetMidPoint()
{
Debug.Assert(IsValid(), "Invalid arc defined, cannot calculate midpoint");
// Make a line from the circle centre to the middle of the line
C2DPoint ptCentre = new C2DPoint(GetCircleCentre());
C2DPoint ptLineCentre = new C2DPoint(Line.GetMidPoint());
C2DLine CenToMid = new C2DLine(ptCentre, ptLineCentre);
if (CenToMid.vector.i == 0 && CenToMid.vector.j == 0)
{
// The centre of the line is the same as the centre of the circle
// i.e. this arc is 180 degrees or half a circle.
CenToMid.Set(Line);
CenToMid.SetPointFrom(ptLineCentre);
if (ArcOnRight)
{
CenToMid.vector.TurnRight();
}
else
{
CenToMid.vector.TurnLeft();
}
}
else
{
// extend it to the edge of the arc
CenToMid.SetLength(Radius);
// if the arc on the opposite side to the centre then reverse the line.
if (ArcOnRight == CentreOnRight)
{
CenToMid.vector.Reverse();
}
}
return(CenToMid.GetPointTo());
}
/// <summary>
/// Function to join the 2 lines at the point where they do / would intersect. If they do then
/// the lines are clipped to remove the smallest part of the line. Returns false if they
/// cannot be joined.
/// </summary>
/// <param name="Other">The other line</param>
public bool Join(C2DLine Other)
{
C2DPoint p1 = point;
C2DPoint p2 = GetPointTo();
C2DPoint p3 = Other.point;
C2DPoint p4 = Other.GetPointTo();
double Ua = (p4.x - p3.x) * (p1.y - p3.y) - (p4.y - p3.y) * (p1.x - p3.x);
double Ub = (p2.x - p1.x) * (p1.y - p3.y) - (p2.y - p1.y) * (p1.x - p3.x);
double dDenominator = (p4.y - p3.y) * (p2.x - p1.x) - (p4.x - p3.x) * (p2.y - p1.y);
if (dDenominator == 0)
return false;
Ua = Ua / dDenominator;
Ub = Ub / dDenominator;
C2DPoint IntPt = new C2DPoint(p1.x + Ua * (p2.x - p1.x), p1.y + Ua * (p2.y - p1.y));
if ( Ua >=0.5)
this.SetPointTo( IntPt );
else
this.SetPointFrom( IntPt );
if ( Ub >=0.5)
Other.SetPointTo( IntPt );
else
Other.SetPointFrom( IntPt );
return true;
}
/// <summary>
/// Static version of Fermat point function.
/// </summary>
public static C2DPoint GetFermatPoint(C2DPoint pt1, C2DPoint pt2, C2DPoint pt3)
{
C2DLine Line12 = new C2DLine(pt1, pt2);
C2DLine Line23 = new C2DLine(pt2, pt3);
C2DLine Line31 = new C2DLine(pt3, pt1);
double dAng2 = Constants.conPI - Line12.vector.AngleBetween(Line23.vector);
if (dAng2 >= Constants.conTWOTHIRDPI) // greater than 120 degrees
{
return new C2DPoint(pt2);
}
else if (dAng2 < Constants.conTHIRDPI) // if less than 60 then 1 of the other 2 could be greater than 120
{
double dAng3 = Constants.conPI - Line23.vector.AngleBetween(Line31.vector);
if (dAng3 >= Constants.conTWOTHIRDPI) // greater than 120 degrees
{
return new C2DPoint(pt3);
}
else if ((Constants.conPI - dAng2 - dAng3) >= Constants.conTWOTHIRDPI) // if least angle is greater than 120
{
return new C2DPoint(pt1);
}
}
bool bClockwise = Line12.IsOnRight(pt3);
if (bClockwise)
{
Line12.vector.TurnLeft(Constants.conTHIRDPI); // 60 degrees
Line23.vector.TurnLeft(Constants.conTHIRDPI); // 60 degrees
}
else
{
Line12.vector.TurnRight(Constants.conTHIRDPI); // 60 degrees
Line23.vector.TurnRight(Constants.conTHIRDPI); // 60 degrees
}
Line12.SetPointFrom(pt3);
Line23.SetPointFrom(pt1);
List<C2DPoint> IntPt = new List<C2DPoint>();
bool B1 = true, B2 = true;
if (Line12.Crosses(Line23, IntPt, ref B1, ref B2, false))
{
return IntPt[0];
}
else
{
Debug.Assert(false);
}
return new C2DPoint(0, 0);
}
/// <summary>
/// Distance to a circle, returns the closest point on both circles.
/// </summary>
/// <param name="Other">Circle to calculate the distance to.</param>
/// <param name="ptOnThis">Closest point on this circle to recieve the result.</param>
/// <param name="ptOnOther">Closest point on the other circle to recieve the result.</param>
public double Distance(C2DCircle Other, C2DPoint ptOnThis, C2DPoint ptOnOther)
{
double dCenCenDist = _Centre.Distance(Other.Centre);
double dOtherRadius = Other.Radius;
// C2DPoint ptThis;
// C2DPoint ptOther;
double dDist = dCenCenDist - Radius - dOtherRadius;
if (dDist > 0)
{
// they do not interect and they are outside each other.
C2DLine Line = new C2DLine(_Centre, Other.Centre);
Line.vector.SetLength(Radius);
ptOnThis.Set(Line.GetPointTo());
Line.vector.Reverse();
Line.SetPointFrom(Other.Centre);
Line.vector.SetLength(Other.Radius);
ptOnOther.Set(Line.GetPointTo());
}
else
{
if ((dCenCenDist + Radius) < dOtherRadius)
{
// This is inside the other
dDist = dCenCenDist + Radius - dOtherRadius; // -ve if inside
C2DVector vec = new C2DVector(Other.Centre, Centre);
vec.Multiply(Radius / dCenCenDist); // set the vector to be the length of my radius.
ptOnThis.Set(_Centre.GetPointTo(vec));
vec.Multiply(dDist / Radius); // set the vector to be the distance.
ptOnOther.Set(ptOnThis.GetPointTo(vec));
}
else if ((dCenCenDist + dOtherRadius) < Radius)
{
// The other is inside this.
dDist = dCenCenDist + dOtherRadius - Radius; // -ve if inside
C2DVector vec = new C2DVector(_Centre, Other.Centre);
vec.Multiply(dOtherRadius / dCenCenDist); // set the vector to be the length of my radius.
ptOnOther.Set(Other.Centre.GetPointTo(vec));
vec.Multiply(dDist / dOtherRadius); // set the vector to be the distance.
ptOnThis.Set(ptOnOther.GetPointTo(vec));
}
else
{
// there is an intersection
dDist = 0;
List <C2DPoint> Ints = new List <C2DPoint>();
if (Crosses(Other, Ints))
{
ptOnThis.Set(Ints[0]);
ptOnOther.Set(ptOnThis);
}
else
{
Debug.Assert(false);
return(0);
}
}
}
// if (ptOnThis)
// *ptOnThis = ptThis;
// if (ptOnOther)
// *ptOnOther = ptOther;
return(dDist);
}
/// <summary>
/// Distance to a circle, returns the closest point on both circles.
/// </summary>
/// <param name="Other">Circle to calculate the distance to.</param>
/// <param name="ptOnThis">Closest point on this circle to recieve the result.</param>
/// <param name="ptOnOther">Closest point on the other circle to recieve the result.</param>
public double Distance(C2DCircle Other, C2DPoint ptOnThis, C2DPoint ptOnOther)
{
double dCenCenDist = _Centre.Distance(Other.Centre);
double dOtherRadius = Other.Radius;
// C2DPoint ptThis;
// C2DPoint ptOther;
double dDist = dCenCenDist - Radius - dOtherRadius;
if (dDist > 0 )
{
// they do not interect and they are outside each other.
C2DLine Line = new C2DLine(_Centre, Other.Centre);
Line.vector.SetLength( Radius);
ptOnThis.Set( Line.GetPointTo() );
Line.vector.Reverse();
Line.SetPointFrom(Other.Centre);
Line.vector.SetLength(Other.Radius);
ptOnOther.Set(Line.GetPointTo());
}
else
{
if ( (dCenCenDist + Radius) < dOtherRadius)
{
// This is inside the other
dDist = dCenCenDist + Radius - dOtherRadius ; // -ve if inside
C2DVector vec = new C2DVector( Other.Centre, Centre);
vec.Multiply( Radius /dCenCenDist ); // set the vector to be the length of my radius.
ptOnThis.Set( _Centre.GetPointTo( vec));
vec.Multiply( dDist /Radius ); // set the vector to be the distance.
ptOnOther.Set(ptOnThis.GetPointTo( vec));
}
else if ( (dCenCenDist + dOtherRadius) < Radius)
{
// The other is inside this.
dDist = dCenCenDist + dOtherRadius - Radius; // -ve if inside
C2DVector vec = new C2DVector( _Centre, Other.Centre);
vec.Multiply ( dOtherRadius /dCenCenDist ); // set the vector to be the length of my radius.
ptOnOther.Set( Other.Centre.GetPointTo( vec));
vec.Multiply( dDist / dOtherRadius ); // set the vector to be the distance.
ptOnThis.Set(ptOnOther.GetPointTo( vec));
}
else
{
// there is an intersection
dDist = 0;
List<C2DPoint> Ints = new List<C2DPoint>();
if (Crosses(Other, Ints))
{
ptOnThis.Set(Ints[0]);
ptOnOther.Set(ptOnThis);
}
else
{
Debug.Assert(false);
return 0;
}
}
}
// if (ptOnThis)
// *ptOnThis = ptThis;
// if (ptOnOther)
// *ptOnOther = ptOther;
return dDist;
}
/// <summary>
/// Gets the point half way along the curve as a new object.
/// </summary>
public C2DPoint GetMidPoint()
{
Debug.Assert(IsValid(), "Invalid arc defined, cannot calculate midpoint");
// Make a line from the circle centre to the middle of the line
C2DPoint ptCentre = new C2DPoint(GetCircleCentre());
C2DPoint ptLineCentre = new C2DPoint(Line.GetMidPoint());
C2DLine CenToMid = new C2DLine(ptCentre, ptLineCentre);
if ( CenToMid.vector.i == 0 && CenToMid.vector.j == 0)
{
// The centre of the line is the same as the centre of the circle
// i.e. this arc is 180 degrees or half a circle.
CenToMid.Set(Line);
CenToMid.SetPointFrom( ptLineCentre );
if ( ArcOnRight )
CenToMid.vector.TurnRight();
else
CenToMid.vector.TurnLeft();
}
else
{
// extend it to the edge of the arc
CenToMid.SetLength( Radius );
// if the arc on the opposite side to the centre then reverse the line.
if ( ArcOnRight == CentreOnRight)
{
CenToMid.vector.Reverse();
}
}
return CenToMid.GetPointTo();
}
