/// <summary>
/// Returns the lines that go to make this up based on the set of points
/// provided which are assumed to be on the line.
/// </summary>
/// <param name="PtsOnLine">The points defining how the line is to be split.</param>
/// <param name="LineSet">The line set to recieve the result.</param>
public override void GetSubLines(List <C2DPoint> PtsOnLine, List <C2DLineBase> LineSet)
{
// if there are no points on the line to split on then add a copy of this and return.
int usPointsCount = PtsOnLine.Count;
if (usPointsCount == 0)
{
LineSet.Add(new C2DArc(this));
return;
}
else
{
// Make a copy of the points for sorting.
C2DPointSet TempPts = new C2DPointSet();
TempPts.MakeCopy(PtsOnLine);
if (usPointsCount > 1) // They need sorting
{
// Make a line from the mid point of my line to the start
C2DLine CenToStart = new C2DLine(Line.GetMidPoint(), Line.point);
// Now sort the points according to the order in which they will be encountered
if (ArcOnRight)
{
TempPts.SortByAngleToLeft(CenToStart);
}
else
{
TempPts.SortByAngleToRight(CenToStart);
}
}
C2DPoint ptCentre = new C2DPoint(GetCircleCentre());
// Add the line from the start of this to the first.
C2DLine NewLine = new C2DLine(Line.point, TempPts[0]);
LineSet.Add(new C2DArc(NewLine, Radius,
NewLine.IsOnRight(ptCentre), ArcOnRight));
// Add all the sub lines.
for (int i = 1; i < usPointsCount; i++)
{
NewLine.Set(TempPts[i - 1], TempPts[i]);
LineSet.Add(new C2DArc(NewLine, Radius,
NewLine.IsOnRight(ptCentre), ArcOnRight));
}
// Add the line from the last point on this to the end of this.
NewLine.Set(TempPts[TempPts.Count - 1], Line.GetPointTo());
LineSet.Add(new C2DArc(NewLine, Radius,
NewLine.IsOnRight(ptCentre), ArcOnRight));
}
}
/// <summary>
/// Static version of Fermat point function.
/// </summary>
public static C2DPoint GetFermatPoint(C2DPoint pt1, C2DPoint pt2, C2DPoint pt3)
{
var Line12 = new C2DLine(pt1, pt2);
var Line23 = new C2DLine(pt2, pt3);
var Line31 = new C2DLine(pt3, pt1);
var 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
{
var 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));
}
}
var 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);
var 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 between this and another straight line.
/// </summary>
/// <param name="TestLine">The test line.</param>
/// <param name="ptOnThis">The closest point on this to the other as a returned value.</param>
/// <param name="ptOnOther">The closest point on the other to this as a returned value.</param>
public double Distance(C2DLine TestLine, C2DPoint ptOnThis, C2DPoint ptOnOther)
{
C2DCircle Circle = new C2DCircle(GetCircleCentre(), Radius);
double dCircDist = Circle.Distance(TestLine, ptOnThis, ptOnOther);
double dDist = 0;
if (TestLine.IsOnRight(ptOnThis) ^ ArcOnRight)
{
// The point found isn't on this.
// This means the 2 closest points cannot be ON both lines, we must have a end point as one.
ptOnThis.Set(Line.point);
dDist = TestLine.Distance(ptOnThis, ptOnOther);
C2DPoint ptThisTemp = new C2DPoint(Line.GetPointTo());
C2DPoint ptOtherTemp = new C2DPoint();
double d2 = TestLine.Distance(ptThisTemp, ptOtherTemp);
if (d2 < dDist)
{
dDist = d2;
ptOnThis.Set(ptThisTemp);
ptOnOther.Set(ptOtherTemp);
}
// If the line was outside the circle then stop here as no need to go any further.
// This is because the closest point on this must be one of the end points.
if (dCircDist < 0)
{
double d3 = Distance(TestLine.point, ptThisTemp);
if (d3 < dDist)
{
dDist = d3;
ptOnThis.Set(ptThisTemp);
ptOnOther.Set(Line.point);
}
double d4 = Distance(TestLine.GetPointTo(), ptThisTemp);
if (d4 < dDist)
{
dDist = d4;
ptOnThis.Set(ptThisTemp);
ptOnOther.Set(Line.GetPointTo());
}
}
}
else
{
dDist = Math.Abs(dCircDist);
}
// ptOnThis.Set(ptThis);
// ptOnOther.Set(ptOther);
return(dDist);
}
/// <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 point.
/// </summary>
/// <param name="ptTest">The test point.</param>
/// <param name="ptOnThis">Output. The closest point on the triangle.</param>
public double Distance(C2DPoint ptTest, C2DPoint ptOnThis)
{
double dArea = GetAreaSigned();
bool BTemp = true;
// Construct the lines.
C2DLine Line12 = new C2DLine(P1, P2);
C2DLine Line23 = new C2DLine(P2, P3);
C2DLine Line31 = new C2DLine(P3, P1);
if (dArea == 0)
{
// Colinear so find the biggest line and return the distance from that
double d1 = Line12.GetLength();
double d2 = Line23.GetLength();
double d3 = Line31.GetLength();
if (d1 > d2 && d1 > d3)
return Line12.Distance(ptTest, ptOnThis);
else if (d2 > d3)
return Line23.Distance(ptTest, ptOnThis);
else
return Line31.Distance(ptTest, ptOnThis);
}
// Find out it the triangle is clockwise or not.
bool bClockwise = dArea < 0;
// Set up some pointers to record the lines that the point is "above", "above" meaning that the
// point is on the opposite side of the line to the rest of the triangle
C2DLine LineAbove1 = null;
C2DLine LineAbove2 = null;
// Find out which Lines have the point above.
if ( Line12.IsOnRight( ptTest ) ^ bClockwise ) // if the pt is on the opposite side to the triangle
LineAbove1 = Line12;
if ( Line23.IsOnRight( ptTest ) ^ bClockwise)
{
if (LineAbove1 != null)
LineAbove2 = Line23;
else
LineAbove1 = Line23;
}
if ( Line31.IsOnRight( ptTest ) ^ bClockwise)
{
if (LineAbove1 != null)
{
// We can't have all the lines with the point above.
Debug.Assert(LineAbove2 != null);
LineAbove2 = Line31;
}
else
LineAbove1 = Line31;
}
// Check for containment (if there isn't a single line that its above then it must be inside)
if (LineAbove1 == null)
{
// Pt inside so project onto all the lines and find the closest projection (there must be one).
// Set up a record of the point projection on the lines.
C2DPoint ptOnLine = new C2DPoint();
bool bSet = false;
double dMinDist = 0;
if (ptTest.ProjectsOnLine(Line12, ptOnLine, ref BTemp))
{
dMinDist = ptTest.Distance(ptOnLine);
ptOnThis.Set(ptOnLine);
bSet = true;
}
if (ptTest.ProjectsOnLine(Line23, ptOnLine, ref BTemp))
{
double dDist = ptTest.Distance(ptOnLine);
if (!bSet || dDist < dMinDist)
{
dMinDist = dDist;
ptOnThis.Set(ptOnLine);
bSet = true;
}
}
if (ptTest.ProjectsOnLine(Line31, ptOnLine, ref BTemp))
{
double dDist = ptTest.Distance(ptOnLine);
if (!bSet || dDist < dMinDist)
{
dMinDist = dDist;
ptOnThis.Set(ptOnLine);
bSet = true;
}
}
Debug.Assert(bSet);
return -dMinDist; //-ve if inside
}
else if (LineAbove2 == null)
{
// it is only above 1 of the lines so simply return the distance to that line
return LineAbove1.Distance(ptTest, ptOnThis);
}
else
{
// It's above 2 lines so first check them both for projection. Can only be projected on 1.
// If the point can be projected onto the line then that's the closest point.
C2DPoint ptOnLine = new C2DPoint();
if (ptTest.ProjectsOnLine(LineAbove1, ptOnLine, ref BTemp))
{
ptOnThis = ptOnLine;
return ptOnLine.Distance(ptTest);
}
else if (ptTest.ProjectsOnLine(LineAbove2, ptOnLine, ref BTemp))
{
ptOnThis = ptOnLine;
return ptOnLine.Distance(ptTest);
}
else
{
// The point doesn't project onto either line so find the closest point
if (LineAbove1 == Line12)
{
if (LineAbove2 == Line23)
{
ptOnThis = P2;
return ptTest.Distance(P2);
}
else
{
ptOnThis = P1;
return ptTest.Distance(P1);
}
}
else
{
ptOnThis = P3;
return ptTest.Distance(P3);
}
}
}
}
/// <summary>
/// Distance to a point.
/// </summary>
/// <param name="ptTest">The test point.</param>
/// <param name="ptOnThis">Output. The closest point on the triangle.</param>
public double Distance(C2DPoint ptTest, C2DPoint ptOnThis)
{
var dArea = GetAreaSigned();
var BTemp = true;
// Construct the lines.
var Line12 = new C2DLine(P1, P2);
var Line23 = new C2DLine(P2, P3);
var Line31 = new C2DLine(P3, P1);
if (dArea == 0)
{
// Colinear so find the biggest line and return the distance from that
var d1 = Line12.GetLength();
var d2 = Line23.GetLength();
var d3 = Line31.GetLength();
if (d1 > d2 && d1 > d3)
{
return(Line12.Distance(ptTest, ptOnThis));
}
else if (d2 > d3)
{
return(Line23.Distance(ptTest, ptOnThis));
}
else
{
return(Line31.Distance(ptTest, ptOnThis));
}
}
// Find out it the triangle is clockwise or not.
var bClockwise = dArea < 0;
// Set up some pointers to record the lines that the point is "above", "above" meaning that the
// point is on the opposite side of the line to the rest of the triangle
C2DLine LineAbove1 = null;
C2DLine LineAbove2 = null;
// Find out which Lines have the point above.
if (Line12.IsOnRight(ptTest) ^ bClockwise) // if the pt is on the opposite side to the triangle
{
LineAbove1 = Line12;
}
if (Line23.IsOnRight(ptTest) ^ bClockwise)
{
if (LineAbove1 != null)
{
LineAbove2 = Line23;
}
else
{
LineAbove1 = Line23;
}
}
if (Line31.IsOnRight(ptTest) ^ bClockwise)
{
if (LineAbove1 != null)
{
// We can't have all the lines with the point above.
Debug.Assert(LineAbove2 != null);
LineAbove2 = Line31;
}
else
{
LineAbove1 = Line31;
}
}
// Check for containment (if there isn't a single line that its above then it must be inside)
if (LineAbove1 == null)
{
// Pt inside so project onto all the lines and find the closest projection (there must be one).
// Set up a record of the point projection on the lines.
var ptOnLine = new C2DPoint();
var bSet = false;
double dMinDist = 0;
if (ptTest.ProjectsOnLine(Line12, ptOnLine, ref BTemp))
{
dMinDist = ptTest.Distance(ptOnLine);
ptOnThis.Set(ptOnLine);
bSet = true;
}
if (ptTest.ProjectsOnLine(Line23, ptOnLine, ref BTemp))
{
var dDist = ptTest.Distance(ptOnLine);
if (!bSet || dDist < dMinDist)
{
dMinDist = dDist;
ptOnThis.Set(ptOnLine);
bSet = true;
}
}
if (ptTest.ProjectsOnLine(Line31, ptOnLine, ref BTemp))
{
var dDist = ptTest.Distance(ptOnLine);
if (!bSet || dDist < dMinDist)
{
dMinDist = dDist;
ptOnThis.Set(ptOnLine);
bSet = true;
}
}
Debug.Assert(bSet);
return(-dMinDist); //-ve if inside
}
else if (LineAbove2 == null)
{
// it is only above 1 of the lines so simply return the distance to that line
return(LineAbove1.Distance(ptTest, ptOnThis));
}
else
{
// It's above 2 lines so first check them both for projection. Can only be projected on 1.
// If the point can be projected onto the line then that's the closest point.
var ptOnLine = new C2DPoint();
if (ptTest.ProjectsOnLine(LineAbove1, ptOnLine, ref BTemp))
{
ptOnThis = ptOnLine;
return(ptOnLine.Distance(ptTest));
}
else if (ptTest.ProjectsOnLine(LineAbove2, ptOnLine, ref BTemp))
{
ptOnThis = ptOnLine;
return(ptOnLine.Distance(ptTest));
}
else
{
// The point doesn't project onto either line so find the closest point
if (LineAbove1 == Line12)
{
if (LineAbove2 == Line23)
{
ptOnThis = P2;
return(ptTest.Distance(P2));
}
else
{
ptOnThis = P1;
return(ptTest.Distance(P1));
}
}
else
{
ptOnThis = P3;
return(ptTest.Distance(P3));
}
}
}
}
/// <summary>
/// Returns the lines that go to make this up based on the set of points
/// provided which are assumed to be on the line.
/// </summary>
/// <param name="PtsOnLine">The points defining how the line is to be split.</param>
/// <param name="LineSet">The line set to recieve the result.</param>
public override void GetSubLines(List<C2DPoint> PtsOnLine, List<C2DLineBase> LineSet)
{
// if there are no points on the line to split on then add a copy of this and return.
int usPointsCount = PtsOnLine.Count;
if (usPointsCount == 0 )
{
LineSet.Add(new C2DArc(this));
return;
}
else
{
// Make a copy of the points for sorting.
C2DPointSet TempPts = new C2DPointSet();
TempPts.MakeCopy(PtsOnLine);
if (usPointsCount > 1) // They need sorting
{
// Make a line from the mid point of my line to the start
C2DLine CenToStart = new C2DLine( Line.GetMidPoint(), Line.point );
// Now sort the points according to the order in which they will be encountered
if (ArcOnRight)
TempPts.SortByAngleToLeft( CenToStart );
else
TempPts.SortByAngleToRight( CenToStart );
}
C2DPoint ptCentre = new C2DPoint(GetCircleCentre());
// Add the line from the start of this to the first.
C2DLine NewLine = new C2DLine( Line.point, TempPts[0] );
LineSet.Add(new C2DArc(NewLine, Radius,
NewLine.IsOnRight(ptCentre), ArcOnRight));
// Add all the sub lines.
for (int i = 1; i < usPointsCount; i++)
{
NewLine.Set(TempPts[i - 1], TempPts[i]);
LineSet.Add(new C2DArc(NewLine, Radius,
NewLine.IsOnRight(ptCentre), ArcOnRight));
}
// Add the line from the last point on this to the end of this.
NewLine.Set(TempPts[TempPts.Count - 1], Line.GetPointTo());
LineSet.Add(new C2DArc(NewLine, Radius,
NewLine.IsOnRight(ptCentre), ArcOnRight));
}
}
/// <summary>
/// Distance between this and another straight line.
/// </summary>
/// <param name="TestLine">The test line.</param>
/// <param name="ptOnThis">The closest point on this to the other as a returned value.</param>
/// <param name="ptOnOther">The closest point on the other to this as a returned value.</param>
public double Distance(C2DLine TestLine, C2DPoint ptOnThis, C2DPoint ptOnOther)
{
C2DCircle Circle = new C2DCircle( GetCircleCentre(), Radius);
double dCircDist = Circle.Distance(TestLine, ptOnThis, ptOnOther);
double dDist = 0;
if (TestLine.IsOnRight(ptOnThis) ^ ArcOnRight)
{
// The point found isn't on this.
// This means the 2 closest points cannot be ON both lines, we must have a end point as one.
ptOnThis.Set(Line.point);
dDist = TestLine.Distance(ptOnThis, ptOnOther);
C2DPoint ptThisTemp = new C2DPoint(Line.GetPointTo());
C2DPoint ptOtherTemp = new C2DPoint();
double d2 = TestLine.Distance(ptThisTemp, ptOtherTemp);
if (d2 < dDist)
{
dDist = d2;
ptOnThis.Set(ptThisTemp);
ptOnOther.Set(ptOtherTemp);
}
// If the line was outside the circle then stop here as no need to go any further.
// This is because the closest point on this must be one of the end points.
if (dCircDist < 0)
{
double d3 = Distance(TestLine.point, ptThisTemp);
if (d3 < dDist)
{
dDist = d3;
ptOnThis.Set(ptThisTemp);
ptOnOther.Set(Line.point);
}
double d4 = Distance(TestLine.GetPointTo(), ptThisTemp);
if (d4 < dDist)
{
dDist = d4;
ptOnThis.Set(ptThisTemp);
ptOnOther.Set(Line.GetPointTo());
}
}
}
else
{
dDist = Math.Abs(dCircDist);
}
// ptOnThis.Set(ptThis);
// ptOnOther.Set(ptOther);
return dDist;
}