/// <summary>
/// This method uses a different method to the Monotone Chain convex hull
/// Instead of storing the vertices of the polygon in lists
/// The vertices are stored as doubly linked lists
/// </summary>
private static Polygon RecursiveSolve(Polygon points, bool stepThrough = false)
{
//If there are few enough points to warrant the Graham Scan algorithm
if (points.Count() <= MinimumSize)
{
return Polygon.Get(ConvexHull.Solve(points.Convert()));
}
//Sort the points by x value and then by y value
var sortedPoints = PolygonManipulation.SortLexographically(points.Convert());
//Split points into two sets
var a = new List<Point2D>();
var b = new List<Point2D>();
a.AddRange(sortedPoints.Take(sortedPoints.Count()/2));
b.AddRange(sortedPoints.Skip(sortedPoints.Count()/2).Take(sortedPoints.Count() - sortedPoints.Count()/2));
//Compute the convex hulls of a and b recursively
var polyA = RecursiveSolve(Polygon.Get(a), stepThrough);
var polyB = RecursiveSolve(Polygon.Get(b), stepThrough);
//Merge the convex hulls together
return Merge(polyA, polyB, stepThrough);
}
/// <summary>
/// Merges two convex hulls into one convex hull
/// Finds upper and lower tangents and removes the points in between
/// </summary>
private static Polygon Merge(Polygon polygonA, Polygon polygonB, Boolean stepThrough)
{
//Since a lot of functions require polygons of type List<Point2D>
//Convert them here to save time converting lots later on
var newPolygonA = PolygonManipulation.SortLexographically(polygonA.Convert());
var newPolygonB = PolygonManipulation.SortLexographically(polygonB.Convert());
//Get the rightmost point of polygon A and the leftmost point of polygon B
var tangentPointA = GetRightmostPoint(newPolygonA);
var tangentPointB = GetLeftmostPoint(newPolygonB);
//Find lower tangent
//While Tangent = tangentPointA -> tangentPointB is not a lower tangent to both A and B
while (!(IsLowerTangent(newPolygonA, tangentPointA, tangentPointB) && IsLowerTangent(newPolygonB, tangentPointB,tangentPointA)))
{
//While Tangent = tangentPointA -> tangentPointB is not a lower tangent to A
while (!IsLowerTangent(newPolygonA, tangentPointA,tangentPointB))
{
//Move counter clockwise
tangentPointA = PolygonManipulation.GetNextPoint(newPolygonA, tangentPointA);
}
//While Tangent = tangentPointA -> tangentPointB is not a lower tangent to B
while (!IsLowerTangent(newPolygonB, tangentPointB,tangentPointA))
{
//Move clockwise
tangentPointB = PolygonManipulation.GetPreviousPoint(newPolygonB, tangentPointB);
}
}
//Get the lower tangent
Vector2D lowerTangent = new Vector2D(tangentPointA, tangentPointB);
//Reset the tangent points
tangentPointA = GetRightmostPoint(newPolygonA);
tangentPointB = GetLeftmostPoint(newPolygonB);
//While Tangent = tangentPointA -> tangentPointB is not an upper tangent to both A and B
while (!IsUpperTangent(newPolygonA, tangentPointA, tangentPointB) || !(IsUpperTangent(newPolygonB, tangentPointB, tangentPointA)))
{
//While Tangent = tangentPointA -> tangentPointB is not an upper tangent to A
while (!IsUpperTangent(newPolygonA, tangentPointA, tangentPointB))
{
//Move counter clockwise
tangentPointA = PolygonManipulation.GetPreviousPoint(newPolygonA, tangentPointA);
}
//While Tangent = tangentPointA -> tangentPointB is not an upper tangent to B
while (!IsUpperTangent(newPolygonB, tangentPointB, tangentPointA))
{
//Move clockwise
tangentPointB = PolygonManipulation.GetNextPoint(newPolygonB, tangentPointB);
}
}
//Get the upper tangent
Vector2D upperTangent = new Vector2D(tangentPointA, tangentPointB);
//Draw tangents if in step through mode
if (stepThrough)
{
//Convert the polygons into a format for drawing
var listPolygonA = polygonA.Convert();
var listPolygonB = polygonB.Convert();
//If the polygons have more than two points, fill them in
if (listPolygonA.Count > 2)
{
GraphicalUserInterface.DrawPolygon(listPolygonA, true, XOffset, YOffset, new System.Drawing.SolidBrush(System.Drawing.Color.Coral));
GraphicalUserInterface.DrawPolygon(polygonB.Convert(), true, XOffset, YOffset);
}
GraphicalUserInterface.DrawPolygon(listPolygonA, false, XOffset, YOffset, new System.Drawing.SolidBrush(System.Drawing.Color.Coral));
GraphicalUserInterface.DrawPolygon(polygonB.Convert(), false, XOffset, YOffset);
GraphicalUserInterface.GraphicsObject.DrawLine(new System.Drawing.Pen(System.Drawing.Color.Blue) { Width = 4 },
lowerTangent.Start.Convert(XOffset, YOffset, GraphicalUserInterface.SizeMultiplier),
lowerTangent.Target.Convert(XOffset, YOffset, GraphicalUserInterface.SizeMultiplier));
GraphicalUserInterface.GraphicsObject.DrawLine(new System.Drawing.Pen(System.Drawing.Color.Black) { Width = 4 },
upperTangent.Start.Convert(XOffset, YOffset, GraphicalUserInterface.SizeMultiplier),
upperTangent.Target.Convert(XOffset, YOffset, GraphicalUserInterface.SizeMultiplier));
//Wait for the user to enter a key into the console to continue
Console.ReadKey();
}
//Wire together the polygons by tangent
return Wire(polygonA, polygonB, lowerTangent, upperTangent);
}
