/// <summary>
/// Static version of InCentre function.
/// </summary>
public static C2DPoint GetInCentre(C2DPoint pt1, C2DPoint pt2, C2DPoint pt3)
{
// Set up a line to bisect the lines from 1 to 2 and 1 to 3
var Line1 = new C2DLine(pt1, pt2);
var Line2 = new C2DLine(pt1, pt3);
Line1.SetLength(Line2.GetLength());
var Line12Bisect = new C2DLine(pt1, pt3.GetMidPoint(Line1.GetPointTo()));
// Set up a line to bisect the lines from 2 to 1 and 2 to 3
var Line3 = new C2DLine(pt2, pt1);
var Line4 = new C2DLine(pt2, pt3);
Line3.SetLength(Line4.GetLength());
var Line34Bisect = new C2DLine(pt2, pt3.GetMidPoint(Line3.GetPointTo()));
// Now intersect the 2 lines and find the point.
var Int = new List <C2DPoint>();
// Add the intersection even if there isn't one (i.e. infinite lines)
bool B1 = true, B2 = true;
Line12Bisect.Crosses(Line34Bisect, Int, ref B1, ref B2, true);
Debug.Assert(Int.Count == 1);
return(Int[0]);
}
/// <summary>
/// Static version of circumcentre function.
/// </summary>
public static C2DPoint GetCircumCentre(C2DPoint pt1, C2DPoint pt2, C2DPoint pt3)
{
var Line12 = new C2DLine(pt1, pt2);
var Line23 = new C2DLine(pt2, pt3);
// Move the lines to start from the midpoint on them
Line12.point.Set(Line12.GetMidPoint());
Line23.point.Set(Line23.GetMidPoint());
// Turn them right (left would work as well)
Line12.vector.TurnRight();
Line23.vector.TurnRight();
// Find the intersection between them taking the intersect point even if they don't
// intersect directly (i.e. where they would intersect because we may have turned them
// the wrong way).
var IntPt = new List <C2DPoint>();
bool B1 = true, B2 = true;
Line12.Crosses(Line23, IntPt, ref B1, ref B2, true);
var ptResult = new C2DPoint(0, 0);
if (IntPt.Count == 1)
{
ptResult = IntPt[0];
}
else
{
// co-linear so fail.
Debug.Assert(false, "Colinnear triangle. Cannot calculate Circum Centre");
}
return(ptResult);
}
/// <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>
/// Static version of InCentre function.
/// </summary>
public static C2DPoint GetInCentre(C2DPoint pt1, C2DPoint pt2, C2DPoint pt3)
{
// Set up a line to bisect the lines from 1 to 2 and 1 to 3
C2DLine Line1 = new C2DLine(pt1, pt2);
C2DLine Line2 = new C2DLine(pt1, pt3);
Line1.SetLength( Line2.GetLength() );
C2DLine Line12Bisect = new C2DLine( pt1, pt3.GetMidPoint( Line1.GetPointTo()));
// Set up a line to bisect the lines from 2 to 1 and 2 to 3
C2DLine Line3 = new C2DLine(pt2, pt1);
C2DLine Line4 = new C2DLine(pt2, pt3);
Line3.SetLength( Line4.GetLength() );
C2DLine Line34Bisect = new C2DLine(pt2, pt3.GetMidPoint(Line3.GetPointTo()));
// Now intersect the 2 lines and find the point.
List<C2DPoint> Int = new List<C2DPoint>();
// Add the intersection even if there isn't one (i.e. infinite lines)
bool B1 = true, B2 = true;
Line12Bisect.Crosses(Line34Bisect, Int, ref B1, ref B2, true);
Debug.Assert (Int.Count == 1);
return Int[0];
}
/// <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>
/// Static version of circumcentre function.
/// </summary>
public static C2DPoint GetCircumCentre(C2DPoint pt1, C2DPoint pt2, C2DPoint pt3)
{
C2DLine Line12 = new C2DLine (pt1, pt2);
C2DLine Line23 = new C2DLine (pt2, pt3);
// Move the lines to start from the midpoint on them
Line12.point.Set( Line12.GetMidPoint());
Line23.point.Set( Line23.GetMidPoint());
// Turn them right (left would work as well)
Line12.vector.TurnRight();
Line23.vector.TurnRight();
// Find the intersection between them taking the intersect point even if they don't
// intersect directly (i.e. where they would intersect because we may have turned them
// the wrong way).
List<C2DPoint> IntPt = new List<C2DPoint>();
bool B1 = true , B2 = true;
Line12.Crosses(Line23, IntPt,ref B1, ref B2, true);
C2DPoint ptResult = new C2DPoint(0, 0);
if (IntPt.Count == 1)
{
ptResult = IntPt[0];
}
else
{
// co-linear so fail.
Debug.Assert(false, "Colinnear triangle. Cannot calculate Circum Centre");
}
return ptResult;
}
/// <summary>
/// Splits an edge on a convex polygon into two edges by adding a vertex on a random position
/// While keeping the Convex constraint.
/// </summary>
/// <param name="gm"></param>
/// <param name="e"></param>
/// <param name="maxOffset"></param>
/// <param name="index"></param>
/// <returns></returns>
public static List<Edge> SplitConvexEdge(GraphManager gm, Edge e, int maxOffset, int index)
{
var edgeLine = e.CreateLine();
List<Edge> result = new List<Edge>();
//Create random point on the edge
var offset = Convert.ToDouble(RandomGenerator.Next(0, 100)) / 122 + 0.1;
var point = edgeLine.GetPointOn(offset);
//Calculate offsets
var dx = e.v2.Point.x - e.v1.Point.x;
var dy = e.v2.Point.y - e.v1.Point.y;
//Note swapping offsets for X and Y.
var offsetX = Math.Abs(dx) / (dy);
var offsetY = Math.Abs(dy) / (dx * -1);
//Calculate the maximum endpoint for the new node.
var endPoint = new C2DPoint(offsetX * maxOffset + point.x, offsetY * maxOffset + point.y);
var newLine = new C2DLine(point, endPoint);
var otherVertex1 = e.v1;
var otherVertex2 = e.v2;
var otherEdge1 = otherVertex1.GetOther(e).CreateLine();
var otherEdge2 = otherVertex2.GetOther(e).CreateLine();
//Compare with both other edges, to check if the new vertex would still result in a convex polygon.
//If not, update the maximum offset for the new vertex
if (otherVertex1.GetOther(e) != otherVertex2.GetOther(e))
{
var intersections = new List<C2DPoint>();
otherEdge1.GrowFromCentre(100000000);//Hack: to check if they intersect. The library does not support rays in this case
if (newLine.Crosses(otherEdge1, intersections))
{
var newEndpoint = intersections.Single();
newLine = new C2DLine(point, newEndpoint);
}
intersections = new List<C2DPoint>();
otherEdge2.GrowFromCentre(100000000); //Hack: to check if they intersect. The library does not support rays in this case
if (newLine.Crosses(otherEdge2, intersections))
{
var newEndpoint = intersections.Single();
newLine = new C2DLine(point, newEndpoint);
}
}
//Select a random point on the line (which is bound)
var newlineOffset = Convert.ToDouble(RandomGenerator.Next(0, 100)) / 122+0.1;
var newPoint = newLine.GetPointOn(offset);
var newVertex = new Vertex() { Point = newPoint };
//Indexof might be very slow? Note this is just used for the creation of a testvertex
gm.AddVertexAt(newVertex, gm.Vertices.IndexOf(otherVertex2));
gm.DestroyEdge(e);//Unregister the old edge
result.Add(gm.CreateEdge(otherVertex1, newVertex)); //Add the two new ones
result.Add(gm.CreateEdge(newVertex, otherVertex2)); // :)
return result;
}
