public static double ComputeSignedArea(Polygon polygon)
{
int i;
double area = 0;
Vertices vertices = polygon.Vertices;
for (i = 0; i < vertices.Count; i++)
{
int j = (i + 1)%vertices.Count;
area += vertices[i].X*vertices[j].Y;
area -= vertices[i].Y*vertices[j].X;
}
area /= 2.0;
return area;
}
/// <summary>
/// Winding number test for a point in a polygon.
/// </summary>
/// See more info about the algorithm here: http://softsurfer.com/Archive/algorithm_0103/algorithm_0103.htm
/// <param name="point">The point to be tested.</param>
/// <returns>-1 if the winding number is zero and the point is outside
/// the polygon, 1 if the point is inside the polygon, and 0 if the point
/// is on the polygons edge.</returns>
public static int PointInPolygon(Polygon polygon, Vector2D point)
{
// Winding number
int wn = 0;
Vertices polyVertices = polygon.Vertices;
// Iterate through polygon's edges
for (int i = 0; i < polyVertices.Count; i++)
{
// Get points
Vector2D p1 = polyVertices[i];
Vector2D p2 = polyVertices[polyVertices.NextIndex(i)];
// Test if a point is directly on the edge
Vector2D edge = p2 - p1;
double area = MathHelper.Area(ref p1, ref p2, ref point);
if (Math.Abs(area - 0f) < MathHelper.EpsilonD && Vector2D.Dot(point - p1, edge) >= 0 && Vector2D.Dot(point - p2, edge) <= 0)
{
return 0;
}
// Test edge for intersection with ray from point
if (p1.Y <= point.Y)
{
if (p2.Y > point.Y && area > 0)
{
++wn;
}
}
else
{
if (p2.Y <= point.Y && area < 0)
{
--wn;
}
}
}
return wn;
}
public static bool PolygonHitTest(Polygon polygon, Vector2D p)
{
double angle = 0;
Vector2D p1 = new Vector2D();
Vector2D p2 = new Vector2D();
for (int i = 0; i < polygon.Vertices.Count; i++)
{
p1.X = polygon.Vertices[i].X - p.X;
p1.Y = polygon.Vertices[i].Y - p.Y;
p2.X = polygon.Vertices[(i + 1)%polygon.Vertices.Count].X - p.X;
p2.Y = polygon.Vertices[(i + 1)%polygon.Vertices.Count].Y - p.Y;
angle += Angle2D(p1.X, p1.Y, p2.X, p2.Y);
}
if (Math.Abs(angle) < Math.PI)
return false;
else
return true;
}
public static Vector2D ComputeCentroid(Polygon polygon)
{
Vector2D centroid = new Vector2D(0, 0);
double signedArea = 0.0f;
double x0; // Current vertex X
double y0; // Current vertex Y
double x1; // Next vertex X
double y1; // Next vertex Y
double a; // Partial signed area
Vector2D[] vertices = polygon.Vertices.ToArray();
// For all vertices except last
int i;
for (i = 0; i < polygon.Vertices.Count - 1; ++i)
{
x0 = vertices[i].X;
y0 = vertices[i].Y;
x1 = vertices[i + 1].X;
y1 = vertices[i + 1].Y;
a = x0*y1 - x1*y0;
signedArea += a;
centroid.X += (x0 + x1)*a;
centroid.Y += (y0 + y1)*a;
}
// Do last vertex
x0 = vertices[i].X;
y0 = vertices[i].Y;
x1 = vertices[0].X;
y1 = vertices[0].Y;
a = x0*y1 - x1*y0;
signedArea += a;
centroid.X += (x0 + x1)*a;
centroid.Y += (y0 + y1)*a;
signedArea *= 0.5f;
centroid.X /= (6*signedArea);
centroid.Y /= (6*signedArea);
return centroid;
}
public static bool ConvexityTest(Polygon polygon)
{
if (polygon.Vertices.Count < 3) return false;
int xCh = 0, yCh = 0;
Vector2D a = polygon.Vertices[0] - polygon.Vertices[polygon.Vertices.Count - 1];
for (int i = 0; i < polygon.Vertices.Count - 1; ++i)
{
Vector2D b = polygon.Vertices[i] - polygon.Vertices[i + 1];
if (Math.Sign(a.X) != Math.Sign(b.X)) ++xCh;
if (Math.Sign(a.Y) != Math.Sign(b.Y)) ++yCh;
a = b;
}
return (xCh <= 2 && yCh <= 2);
}
public static ushort[] TriangulateBrute(IList<Vector2D> vertex)
{
int n = vertex.Count;
bool pointValid;
List<ushort> indices = new List<ushort>();
for (int i = 0;i < n - 2; i++)
{
for (int j = i + 1; j < n - 1; j++)
{
for (int k = j + 1; k < n; k++)
{
Circle circle = Circle.CircumCircle(vertex[i], vertex[j], vertex[k]);
pointValid = true;
for (int l = 0; l < n; l++)
{
if(l == i || l == j || l == k) continue;
if(!circle.IsInside(vertex[l])) continue;
pointValid = false;
break;
}
if(pointValid)
{
// Add triangle as graph links
Polygon t = new Polygon(new[] {vertex[i],vertex[j], vertex[k]} );
double a = Polygon.ComputeSignedArea(t);
if (a > 0)
indices.AddRange(new[] { (ushort)k, (ushort)j, (ushort)i });
else
indices.AddRange(new[] { (ushort)i, (ushort)j, (ushort)k });
}
}
}
}
return indices.ToArray();
}