private List <Geometry> IntersectionNaive(Edge edge)
{
List <Geometry> intersections = new List <Geometry>();
if (this.BoundingBox.Intersects(edge.BoundingBox))
{
for (int i = 0; i < this.Edges.Count; i++)
{
var side = this.Edges[i];
var intersection = edge.Intersection(side);
if (intersection != null)
{
if (!intersections.Any() && !intersections.Last().Equals(intersection))
{
intersections.Add(intersection);
}
}
}
}
return(intersections);
}
public List <Geometry> Intersection(Edge edge)
{
// No fast algorithm yet to calculate intersection on concave polygons
if (!this.IsConvex())
{
return(this.IntersectionNaive(edge));
}
//https://stackoverflow.com/questions/4497841/asymptotically-optimal-algorithm-to-compute-if-a-line-intersects-a-convex-polygo
List <Geometry> intersections = new List <Geometry>();
if (!this.BoundingBox.Intersects(edge.BoundingBox))
{
return(intersections);
}
var vertexCount = this.Vertices.Count;
int midIndex = (int)(vertexCount / 2);
Edge diagonal = this.DiagonalByVertexIndex(0, midIndex);
int polygonDirection = this.Vertices[1].IsLeftFrom(diagonal);
Geometry intersection = diagonal.Intersection(edge);
while (intersection == null)
{
// If midIndex is any neighbour from the start vertex
// means the whole line is to one side or the other and doesn't intersect.
if (midIndex == 1 || midIndex == vertexCount - 1)
{
return(intersections);
}
int startSide = edge.StartVertex.IsLeftFrom(diagonal);
int endSide = edge.EndVertex.IsLeftFrom(diagonal);
// If same side, don't intersect
if (startSide == polygonDirection && endSide == polygonDirection)
{
return(intersections);
}
// Is on other side from the polygonDirection (Vertices[1])
else if (startSide != polygonDirection)
{
midIndex += (int)((vertexCount - midIndex) / 2);
}
else
{
midIndex = (int)(midIndex / 2);
}
diagonal = this.DiagonalByVertexIndex(0, midIndex);
intersection = edge.Intersection(diagonal);
}
// If intersection is an Edge
if (intersection is Edge edgeIntersection)
{
// If diagonal other edge is any neighbour, intersection is on one of the sides
if (midIndex == 1 || midIndex == vertexCount - 1)
{
intersections.Add(edgeIntersection);
return(intersections);
}
// If not, the intersection can pass through both diagonal extremes, so its external.
// Through just on, so only one intersection, or non and endge is inside polygon.
if (this.Vertices.First().OnEdge(edgeIntersection))
{
intersections.Add(this.Vertices.First());
}
if (this.Vertices[midIndex].OnEdge(edgeIntersection))
{
intersections.Add(this.Vertices[midIndex]);
}
return(intersections);
}
// If intersection is a Vertex
if (intersection is Vertex vertexIntersection)
{
if (vertexIntersection.Equals(this.Vertices.First()))
{
throw new NotImplementedException();
}
if (vertexIntersection.Equals(this.Vertices[midIndex]))
{
throw new NotImplementedException();
}
// Else the intersection is between the diagonal's extremes
// find intersection at each side of the mid vertex
// Going from midVertex to 0
for (int i = midIndex; i > 0; i--)
{
var side = DiagonalByVertexIndex(i, i - 1);
Vertex sideIntersection = edge.Intersection(side) as Vertex;
if (sideIntersection != null)
{
intersections.Add(sideIntersection);
break;
}
}
for (int j = midIndex; j < vertexCount; j++)
{
int next = (j + 1) % vertexCount;
var side = DiagonalByVertexIndex(j, next);
Vertex sideIntersection = edge.Intersection(side) as Vertex;
if (sideIntersection != null)
{
intersections.Add(sideIntersection);
break;
}
}
return(intersections);
}
return(intersections);
}