public static void GrahamScanSortingTest(List <Vector3> points, List <Vector3> ccwPolygonPoints)
{
if (points.Count < 3)
{
return;
}
if (points.Count == 3)
{
for (int i = 0; i < points.Count; i++)
{
ccwPolygonPoints.Add(points[i]);
}
return;
}
//find the point having the lowest y coordinate (use x for euqual cases if any)
//put it at the end of the list and remove it (this will be point P)
Vector3 tmp = Vector3.zero;
for (int i = points.Count - 1; i >= 0; i--)
{
if (points[points.Count - 1].z > points[i].z)
{
//swap
tmp = points[points.Count - 1];
points[points.Count - 1] = points[i];
points[i] = tmp;
}
else if (points[points.Count - 1].z == points[i].z)
{
if (points[points.Count - 1].x < points[i].x)
{
tmp = points[points.Count - 1];
points[points.Count - 1] = points[i];
points[i] = tmp;
}
}
}
//sort the remaining point according the angle they form with the point P
Vector3 P = points[points.Count - 1];
points.RemoveAt(points.Count - 1);
SortAlgorithms.HeapSortGrahamScan(points, ref P);
points.Add(P); //just a test
}
/// <summary>
/// Performs the computation of the convex hull of the passed points
/// through Graham scan http://en.wikipedia.org/wiki/Graham_scan
/// the returned points are the vertices of the polygon sorted
/// counter clockwise
/// </summary>
/// <param name="points"> The points of which to find the convex hull that contains them
/// A <see cref="List<Vector3>"/>
/// </param>
/// <returns>
/// A <see cref="List<Vector3>"/> The list of counter clockwise sorted vertices of the convex hull polygon
/// </returns>
public static List <Vector3> GrahamScan(List <Vector3> points)
{
List <Vector3> ccwPolygonPoints = new List <Vector3> ();
/*
* if(points.Count < 3)
* {
* return ;
* }
* if(points.Count == 3)
* {
* for(int i=0; i < points.Count; i++)
* {
* ccwPolygonPoints.Add(points[i]);
* }
* return ;
* }
*/
if (points.Count > 3)
{
//find the point having the lowest y coordinate (use x for euqual cases if any)
//put it at the end of the list and remove it (this will be point P)
Vector3 tmp = Vector3.zero;
for (int i = points.Count - 1; i >= 0; i--)
{
if (points[points.Count - 1].z > points[i].z)
{
//swap
tmp = points[points.Count - 1];
points[points.Count - 1] = points[i];
points[i] = tmp;
}
else if (points[points.Count - 1].z == points[i].z)
{
if (points[points.Count - 1].x < points[i].x)
{
tmp = points[points.Count - 1];
points[points.Count - 1] = points[i];
points[i] = tmp;
}
}
}
//sort the remaining point according the angle they form with the point P
Vector3 P = points[points.Count - 1];
points.RemoveAt(points.Count - 1);
SortAlgorithms.HeapSortGrahamScan(points, ref P);
ccwPolygonPoints.Add(P);
ccwPolygonPoints.Add(points[0]);
//points.Add(P);
int k = 1;
while (k < points.Count)
{
//Debug.Log("while graham scan");
if (Vector3.Cross(ccwPolygonPoints[ccwPolygonPoints.Count - 1] - ccwPolygonPoints[ccwPolygonPoints.Count - 2],
points[k] - ccwPolygonPoints[ccwPolygonPoints.Count - 2]).y < -SCAN_EPSILON) //Left turn, it should be > 0 but I am using 3D coordinate using z as y axis reported in the algorithm
{
ccwPolygonPoints.Add(points[k]);
k++;
}
else
{
ccwPolygonPoints.RemoveAt(ccwPolygonPoints.Count - 1);
if (ccwPolygonPoints.Count == 1) //in order to make the algorithm more robust
{
ccwPolygonPoints.Add(points[k]);
k++;
}
}
}
}
else if (points.Count == 3)
{
for (int i = 0; i < points.Count; i++)
{
ccwPolygonPoints.Add(points[i]);
}
}
return(ccwPolygonPoints);
}