/// <summary>
/// Returns the convex hull from the given vertices..
/// </summary>
public static Vertices GetConvexHull(Vertices vertices)
{
if (vertices.Count <= 3)
{
return(vertices);
}
Vertices pointSet = new Vertices(vertices);
//Sort by X-axis
pointSet.Sort(_pointComparer);
FPVector2[] h = new FPVector2[pointSet.Count];
Vertices res;
int top = -1; // indices for bottom and top of the stack
int i; // array scan index
// Get the indices of points with min x-coord and min|max y-coord
const int minmin = 0;
FP xmin = pointSet[0].x;
for (i = 1; i < pointSet.Count; i++)
{
if (pointSet[i].x != xmin)
{
break;
}
}
// degenerate case: all x-coords == xmin
int minmax = i - 1;
if (minmax == pointSet.Count - 1)
{
h[++top] = pointSet[minmin];
if (pointSet[minmax].y != pointSet[minmin].y) // a nontrivial segment
{
h[++top] = pointSet[minmax];
}
h[++top] = pointSet[minmin]; // add polygon endpoint
res = new Vertices(top + 1);
for (int j = 0; j < top + 1; j++)
{
res.Add(h[j]);
}
return(res);
}
top = -1;
// Get the indices of points with max x-coord and min|max y-coord
int maxmax = pointSet.Count - 1;
FP xmax = pointSet[pointSet.Count - 1].x;
for (i = pointSet.Count - 2; i >= 0; i--)
{
if (pointSet[i].x != xmax)
{
break;
}
}
int maxmin = i + 1;
// Compute the lower hull on the stack H
h[++top] = pointSet[minmin]; // push minmin point onto stack
i = minmax;
while (++i <= maxmin)
{
// the lower line joins P[minmin] with P[maxmin]
if (MathUtils.Area(pointSet[minmin], pointSet[maxmin], pointSet[i]) >= 0 && i < maxmin)
{
continue; // ignore P[i] above or on the lower line
}
while (top > 0) // there are at least 2 points on the stack
{
// test if P[i] is left of the line at the stack top
if (MathUtils.Area(h[top - 1], h[top], pointSet[i]) > 0)
{
break; // P[i] is a new hull vertex
}
top--; // pop top point off stack
}
h[++top] = pointSet[i]; // push P[i] onto stack
}
// Next, compute the upper hull on the stack H above the bottom hull
if (maxmax != maxmin) // if distinct xmax points
{
h[++top] = pointSet[maxmax]; // push maxmax point onto stack
}
int bot = top;
i = maxmin;
while (--i >= minmax)
{
// the upper line joins P[maxmax] with P[minmax]
if (MathUtils.Area(pointSet[maxmax], pointSet[minmax], pointSet[i]) >= 0 && i > minmax)
{
continue; // ignore P[i] below or on the upper line
}
while (top > bot) // at least 2 points on the upper stack
{
// test if P[i] is left of the line at the stack top
if (MathUtils.Area(h[top - 1], h[top], pointSet[i]) > 0)
{
break; // P[i] is a new hull vertex
}
top--; // pop top point off stack
}
h[++top] = pointSet[i]; // push P[i] onto stack
}
if (minmax != minmin)
{
h[++top] = pointSet[minmin]; // push joining endpoint onto stack
}
res = new Vertices(top + 1);
for (int j = 0; j < top + 1; j++)
{
res.Add(h[j]);
}
return(res);
}
