/// <summary>
///
/// </summary>
/// <param name="centre"></param>
/// <param name="baseGraph"></param>
/// <param name="origin"></param>
/// <param name="destination"></param>
/// <param name="singleVertices"></param>
/// <param name="halfScan"></param>
/// <returns name="visibleVertices">List of Vertices visible from the analysed vertex</returns>
private static List <Vertex> VisibleVertices(
Vertex centre,
Graph baseGraph,
Vertex origin = null,
Vertex destination = null,
List <Vertex> singleVertices = null,
bool halfScan = true,
bool reducedGraph = true,
bool maxVisibility = false)
{
#region Initialize variables and sort vertices
List <Edge> edges = baseGraph.Edges;
List <Vertex> vertices = baseGraph.Vertices;
if (origin != null)
{
vertices.Add(origin);
}
if (destination != null)
{
vertices.Add(destination);
}
if (singleVertices != null)
{
vertices.AddRange(singleVertices);
}
vertices = Vertex.OrderByRadianAndDistance(vertices, centre);
#endregion
#region Initialize openEdges
//Initialize openEdges with any intersecting Edge with a XAxis Ray from the centre
List <EdgeKey> openEdges = new List <EdgeKey>();
Ray sweepRay = Ray.XAxis(centre);
foreach (Edge e in edges)
{
if (centre.OnEdge(e))
{
continue;
}
if (sweepRay.Intersects(e))
{
if (sweepRay.Contains(e.StartVertex))
{
continue;
}
if (sweepRay.Contains(e.EndVertex))
{
continue;
}
EdgeKey k = EdgeKey.ByRayAndEdge(sweepRay, e);
openEdges.AddItemSorted(k);
}
}
#endregion
List <Vertex> visibleVertices = new List <Vertex>();
Vertex prev = null;
bool prevVisible = false;
for (var i = 0; i < vertices.Count; i++)
{
Vertex vertex = vertices[i];
if (vertex.Equals(centre) || vertex.Equals(prev))
{
continue;
} // v == to centre or to previous when updating graph
//Check only half of Vertices as eventually they will become 'v'
if (halfScan && Vertex.RadAngle(centre, vertex) > Math.PI)
{
break;
}
// Update Ray to new vertex;
sweepRay = Ray.ByTwoVertices(centre, vertex);
//Removing clock wise Edges incident on v
if (openEdges.Count > 0 && baseGraph._vertexEdgesDict.ContainsKey(vertex))
{
foreach (Edge edge in baseGraph._vertexEdgesDict[vertex])
{
int orientation = Vertex.Orientation(centre, vertex, edge.GetVertexPair(vertex));
if (orientation == -1)
{
EdgeKey k = EdgeKey.ByRayAndEdge(sweepRay, edge);
int index = openEdges.BisectIndex(k) - 1;
index = (index < 0) ? openEdges.Count - 1 : index;
if (openEdges.Count > 0 && openEdges.ElementAt(index).Equals(k))
{
openEdges.RemoveAt(index);
}
}
}
}
//Checking if p is visible from p.
bool isVisible = false;
Polygon vertexPolygon = null;
if (vertex.Parent is Polygon)
{
baseGraph._polygonsDict.TryGetValue(vertex.Parent.Id, out vertexPolygon);
}
// If centre is on an edge of a inner polygon vertex belongs, check if the centre-vertex edge lies inside
// or if on one of vertex's Edges.
if (vertexPolygon != null && !vertexPolygon.isBoundary && vertexPolygon.ContainsVertex(centre))
{
Vertex mid = Vertex.MidVertex(centre, vertex);
// If mid is on any edge of vertex, is visible, otherwise not.
foreach (Edge edge in baseGraph._vertexEdgesDict[vertex])
{
if (mid.OnEdge(edge))
{
isVisible = true;
break;
}
}
}
//No collinear Vertices
else if (prev == null || !prev.OnEdge(centre, vertex))
{
if (openEdges.Count == 0)
{
if (vertexPolygon != null && vertexPolygon.isBoundary && vertexPolygon.ContainsVertex(centre))
{
isVisible = vertexPolygon.ContainsVertex(Vertex.MidVertex(centre, vertex));
}
else
{
isVisible = true;
}
}
else if (vertex.OnEdge(openEdges.First().Edge) || !openEdges.First().Edge.Intersects(Edge.ByStartVertexEndVertex(centre, vertex)))
{
isVisible = true;
}
}
//For collinear Vertices, if previous was not visible, vertex is not either
else if (!prevVisible)
{
isVisible = false;
}
//For collinear Vertices, if prev was visible need to check that
//the edge from prev to vertex does not intersect with any open edge
else
{
isVisible = true;
foreach (EdgeKey k in openEdges)
{
//if (!k.edge.Contains(prev) && EdgeIntersect(prev, vertex, k.edge))
if (EdgeIntersect(prev, vertex, k.Edge) && !k.Edge.Contains(prev))
{
isVisible = false;
break;
}
}
// If visible (doesn't intersect any open edge) and edge 'prev-vertex'
// is in any polygon, vertex is visible if it belongs to a external boundary
if (isVisible && EdgeInPolygon(prev, vertex, baseGraph))
{
isVisible = IsBoundaryVertex(vertex, baseGraph);
}
// If still visible (not inside polygon or is boundary vertex),
// if not on 'centre-prev' edge means there is a gap between prev and vertex
if (isVisible && !vertex.OnEdge(centre, prev))
{
isVisible = !IsBoundaryVertex(vertex, baseGraph);
}
}
//If vertex is visible and centre belongs to any polygon, checks
//if the visible edge is interior to its polygon
if (isVisible && centre.Parent is Polygon && !baseGraph.GetAdjecentVertices(centre).Contains(vertex))
{
if (IsBoundaryVertex(centre, baseGraph) && IsBoundaryVertex(vertex, baseGraph))
{
isVisible = EdgeInPolygon(centre, vertex, baseGraph);
}
else
{
isVisible = !EdgeInPolygon(centre, vertex, baseGraph);
}
}
prev = vertex;
prevVisible = isVisible;
if (isVisible)
{
// Check reducedGraph if Vertices belongs to different _polygonsDict
// TODO: If using ConvexHull, most of this could be removed.
if (reducedGraph && centre.Parent != vertex.Parent)
{
bool isOriginExtreme = true;
bool isTargetExtreme = true;
// For reduced graphs, it is checked if the edge is extrem or not.
// For an edge to be extreme, the Edges coincident at the start and end vertex
// will have the same orientation (both clock or counter-clock wise)
// Vertex belongs to a polygon
if (centre.Parent is Polygon && !IsBoundaryVertex(centre, baseGraph))
{
var orientationsOrigin = baseGraph.GetAdjecentVertices(centre).Select(otherVertex => Vertex.Orientation(vertex, centre, otherVertex)).ToList();
isOriginExtreme = orientationsOrigin.All(o => o == orientationsOrigin.First());
}
if (centre.Parent is Polygon && !IsBoundaryVertex(vertex, baseGraph))
{
var orientationsTarget = baseGraph.GetAdjecentVertices(vertex).Select(otherVertex => Vertex.Orientation(centre, vertex, otherVertex)).ToList();
isTargetExtreme = orientationsTarget.All(o => o == orientationsTarget.First());
}
if (isTargetExtreme || isOriginExtreme)
{
visibleVertices.Add(vertex);
}
}
else
{
visibleVertices.Add(vertex);
}
}
if (baseGraph.Contains(vertex))
{
foreach (Edge e in baseGraph._vertexEdgesDict[vertex])
{
if (!centre.OnEdge(e) && Vertex.Orientation(centre, vertex, e.GetVertexPair(vertex)) == 1)
{
EdgeKey k = EdgeKey.ByRayAndEdge(sweepRay, e);
openEdges.AddItemSorted(k);
}
}
}
if (isVisible && maxVisibility && vertex.Parent is Polygon)
{
List <Vertex> vertexPairs = baseGraph.GetAdjecentVertices(vertex);
int firstOrientation = Vertex.Orientation(centre, vertex, vertexPairs[0]);
int secondOrientation = Vertex.Orientation(centre, vertex, vertexPairs[1]);
bool isColinear = false;
//if both Edges lie on the same side of the centre-vertex edge or one of them is colinear or centre is contained on any of the Edges
if (firstOrientation == secondOrientation || firstOrientation == 0 || secondOrientation == 0)
{
Vertex projectionVertex = null;
// if both orientation are not on the same side, means that one of them is colinear
isColinear = firstOrientation != secondOrientation ? true : false;
foreach (EdgeKey ek in openEdges)
{
Vertex intersection = sweepRay.Intersection(ek.Edge) as Vertex;
if (intersection != null && !intersection.Equals(vertex))
{
projectionVertex = intersection;
Polygon polygon;
if (baseGraph._polygonsDict.TryGetValue(vertex.Parent.Id, out polygon))
{
// If polygon is internal, don't compute intersection if mid point lies inside the polygon but not on its Edges
Vertex mid = Vertex.MidVertex(vertex, intersection);
bool containsEdge = Vertex.Orientation(centre, vertex, mid) != 0 && polygon.ContainsVertex(mid);
if (!polygon.isBoundary && containsEdge)
{
projectionVertex = null;
}
}
break;
}
}
if (projectionVertex != null)
{
// if Edges are before rayEdge, projection Vertex goes after vertex
if (firstOrientation == -1 || secondOrientation == -1)
{
visibleVertices.Add(projectionVertex);
}
else
{
visibleVertices.Insert(visibleVertices.Count - 1, projectionVertex);
}
}
}
if (vertexPairs.Contains(centre) && !visibleVertices.Contains(centre))
{
visibleVertices.Add(centre);
}
}
}
return(visibleVertices);
}
