/// <summary>
/// Determines if a Vertex is inside the gPolygon using Fast Winding Number method
/// </summary>
/// <param name="vertex"></param>
/// <returns></returns>
public bool ContainsVertex(Vertex vertex)
{
// http://geomalgorithms.com/a03-_inclusion.html
Vertex maxVertex = vertices.OrderByDescending(v => v.DistanceTo(vertex)).First();
double maxDistance = vertex.DistanceTo(maxVertex) * 1.5;
Vertex v2 = Vertex.ByCoordinates(vertex.X + maxDistance, vertex.Y, vertex.Z);
Edge ray = Edge.ByStartVertexEndVertex(vertex, v2);
int windNumber = 0;
foreach (Edge edge in edges)
{
if (vertex.OnEdge(edge))
{
return(true);
}
Vertex intersection = ray.Intersection(edge) as Vertex;
if (intersection is Vertex)
{
if (edge.StartVertex.Y <= vertex.Y)
{
if (edge.EndVertex.Y > vertex.Y)
{
if (IsLeft(edge, vertex) > 0)
{
++windNumber;
}
}
}
else
{
if (edge.EndVertex.Y < vertex.Y)
{
if (IsLeft(edge, vertex) < 0)
{
--windNumber;
}
}
}
}
}
// If windNumber is different from 0, vertex is in polygon
return(windNumber != 0);
}
public GeometryBase Intersection(Edge other)
{
// http://mathworld.wolfram.com/Line-LineIntersection.html
if (!this.BoundingBox.Intersects(other.BoundingBox))
{
return(null);
}
if (!this.IsCoplanarTo(other))
{
return(null);
}
if (this.Equals(other))
{
return(this);
} // Issues if same polygon id???
var a = this.Direction;
var b = other.Direction;
if (a.IsParallelTo(b))
{
// Fully contains the test edge
if (other.StartVertex.OnEdge(this) && other.EndVertex.OnEdge(this))
{
return(other);
}
// Is fully contained by test edge
else if (this.StartVertex.OnEdge(other) && this.EndVertex.OnEdge(other))
{
return(this);
}
// Not fully inclusive but overlapping
else if (this.StartVertex.OnEdge(other) || this.EndVertex.OnEdge(other))
{
Vertex[] vertices = new Vertex[4]
{
this.StartVertex,
this.EndVertex,
other.StartVertex,
other.EndVertex
};
var sorted = vertices.OrderBy(v => v.Y).ThenBy(v => v.X).ThenBy(v => v.Z).ToList();
return(Edge.ByStartVertexEndVertex(sorted[1], sorted[2]));
}
// Not intersecting
else
{
return(null);
}
}
// No parallels but intersecting on one of the extreme vertices
if (other.Contains(this.StartVertex))
{
return(this.StartVertex);
}
else if (other.Contains(this.EndVertex))
{
return(this.EndVertex);
}
// No coincident nor same extremes
var c = Vector.ByTwoVertices(this.StartVertex, other.StartVertex);
var cxb = c.Cross(b);
var axb = a.Cross(b);
var dot = cxb.Dot(axb);
// If dot == 0 it means that other edge contains at least a vertex from this edge
// and they are parallel or perpendicular. Cannot be parallel as that was tested before.
// It might also mean they don't intersect but the would if extending the projections
double s = (dot) / Math.Pow(axb.Length, 2);
if (s.AlmostEqualTo(0))
{
if (this.StartVertex.OnEdge(other))
{
return(this.StartVertex);
}
else if (this.EndVertex.OnEdge(other))
{
return(this.EndVertex);
}
else if (other.StartVertex.OnEdge(this))
{
return(other.StartVertex);
}
else if (other.EndVertex.OnEdge(this))
{
return(other.EndVertex);
}
else
{
return(null);
}
}
// s > 1, means that "intersection" vertex is not on either edge
// s == NaN means they are parallels so never intersect
if (s < 0 || s > 1 || Double.IsNaN(s))
{
return(null);
}
Vertex intersection = this.StartVertex.Translate(a.Scale(s));
if (intersection.Equals(other.StartVertex))
{
return(other.StartVertex);
}
if (intersection.Equals(other.EndVertex))
{
return(other.EndVertex);
}
if (!intersection.OnEdge(other))
{
return(null);
}
return(intersection);
}