/// <summary>
/// Given a initial vertex and a new point, finds the face that is split by a new edge in this direction
/// </summary>
/// <param name="a_vertex"></param>
/// <param name="a_point"></param>
/// <returns></returns>
private Face GetSplittingFace(DCELVertex a_vertex, Vector2 a_point)
{
List <HalfEdge> outedges = OutgoingEdges(a_vertex).ToList();
if (outedges.Count == 0)
{
// a_Vertex1 leaving is null
throw new GeomException("Vertex should be connected to a face boundary");
}
outedges.Sort(EdgeAngleComparer);
foreach (var curEdge in outedges)
{
var angle = MathUtil.Angle(a_vertex.Pos, a_vertex.Pos + new Vector2(1f, 0f), curEdge.To.Pos);
var angle2 = MathUtil.Angle(a_vertex.Pos, a_vertex.Pos + new Vector2(1f, 0f), a_point);
if (angle >= angle2)
{
return(curEdge.Face);
}
}
return(outedges.FirstOrDefault().Face);
}
/// <summary>
/// Fix the edge chaining from the given vertex and insert the half edge.
/// Updates the next/prev data from the adjacent edges of a_Vertex
/// to include the new edge.
/// </summary>
/// <param name="a_Vertex"></param>
/// <param name="a_Edge"></param>
private void AddEdgeInVertexChain(DCELVertex a_Vertex, HalfEdge a_Edge)
{
List <HalfEdge> outedges = OutgoingEdges(a_Vertex).ToList();
if (outedges.Count == 0)
{
// Add initial edge to vertex
Chain(a_Edge.Twin, a_Edge);
a_Vertex.Leaving = a_Edge;
return;
}
outedges.Sort(EdgeAngleComparer);
// loop over edges in order of angle
for (int i = 0; i < outedges.Count; i++)
{
var curEdge = outedges[i];
var angle = MathUtil.Angle(curEdge.From.Pos, curEdge.From.Pos + new Vector2(1f, 0f), curEdge.To.Pos);
var angle2 = MathUtil.Angle(a_Edge.From.Pos, a_Edge.From.Pos + new Vector2(1f, 0f), a_Edge.To.Pos);
if (angle >= angle2)
{
// chain new edge correctly
var prevEdge = outedges[MathUtil.PositiveMod(i - 1, outedges.Count)];
Chain(a_Edge.Twin, curEdge);
Chain(prevEdge.Twin, a_Edge);
return;
}
}
// new edge between first and last edge
Chain(a_Edge.Twin, outedges.FirstOrDefault());
Chain(outedges.Last().Twin, a_Edge);
}
/// <summary>
///
/// </summary>
/// <param name="a_Edge"></param>
/// <param name="a_Vertex"></param>
/// <returns> The inserted Vertex.
/// If the requested insertion Vertex is on a endpoint we insert no vertex
/// and instead return said endpoint
///</returns>
public DCELVertex AddVertexInEdge(HalfEdge a_Edge, Vector2 a_Point)
{
if (!m_Edges.Contains(a_Edge))
{
throw new GeomException("Edge should already be part of DCEL");
}
if (!a_Edge.Segment.IsOnSegment(a_Point))
{
throw new GeomException("Point should lie on edge");
}
if (MathUtil.EqualsEpsVertex(a_Edge.From.Pos, a_Point))
{
return(a_Edge.From);
//throw new GeomException("Requested insertion in Edge on From.Pos");
}
if (MathUtil.EqualsEpsVertex(a_Edge.To.Pos, a_Point))
{
return(a_Edge.To);
//throw new GeomException("Requested insertion in Edge on To.Pos");
}
// create vertex with outgoing edge
var a_Vertex = new DCELVertex(a_Point, a_Edge.Twin);
m_Vertices.AddLast(a_Vertex);
// update old edge pointers
var oldTo = a_Edge.To;
a_Edge.To = a_Vertex;
a_Edge.Twin.From = a_Vertex;
// create new halfedges
var newedge = new HalfEdge(a_Vertex, oldTo);
var newtwinedge = new HalfEdge(oldTo, a_Vertex);
m_Edges.AddLast(newedge);
m_Edges.AddLast(newtwinedge);
Twin(newedge, newtwinedge);
// fix next/prev pointers in the original cycle
Chain(newedge, a_Edge.Next);
Chain(a_Edge, newedge);
// fix pointers in the twin cycle
Chain(a_Edge.Twin.Prev, newtwinedge);
Chain(newtwinedge, a_Edge.Twin);
// set faces
newedge.Face = a_Edge.Face;
newtwinedge.Face = a_Edge.Twin.Face;
// update old leaving edge as it may point to the wrong edge now
oldTo.Leaving = newtwinedge;
return(a_Vertex);
}
/// <summary>
/// Find all half edges adjacent to the given vertex, ingoing as well as outgoing.
/// </summary>
/// <param name="a_Vertex1"></param>
/// <returns></returns>
public List <HalfEdge> AdjacentEdges(DCELVertex a_Vertex1)
{
var edges = new List <HalfEdge>();
foreach (var e in OutgoingEdges(a_Vertex1))
{
edges.Add(e);
edges.Add(e.Twin);
}
return(edges);
}
/// <summary>
/// Adds a given DCELVertex to the DCEL.
/// </summary>
/// <param name="a_Vertex"></param>
/// <returns>The added vertex</returns>
public DCELVertex AddVertex(DCELVertex a_Vertex)
{
HalfEdge a_Edge;
if (OnEdge(a_Vertex, out a_Edge))
{
return(AddVertexInEdge(a_Edge, a_Vertex.Pos));
}
else
{
m_Vertices.AddLast(a_Vertex);
return(a_Vertex);
}
}
/// <summary>
/// Returns all edges that are outgoing from the given vertex.
/// </summary>
/// <param name="a_Vertex1"></param>
/// <returns></returns>
public List <HalfEdge> OutgoingEdges(DCELVertex a_Vertex1)
{
if (a_Vertex1.Leaving == null)
{
return(new List <HalfEdge>());
}
var edges = new List <HalfEdge>();
var e = a_Vertex1.Leaving;
do
{
edges.Add(e);
e = e.Twin.Next;
} while (e != a_Vertex1.Leaving);
return(edges);
}
/// <summary>
/// Checks whether the given vertex lies on the cycle
/// </summary>
/// <param name="a_Vertex"></param>
/// <param name="a_Edge"></param>
/// <returns></returns>
private bool OnEdge(DCELVertex a_Vertex, out HalfEdge a_Edge)
{
a_Edge = m_Edges.FirstOrDefault(e => e.Segment.IsOnSegment(a_Vertex.Pos));
return(a_Edge != null);
}
/// <summary>
/// Checks whether the given vertex lies on the edge cycle specified by the halfedge.
/// </summary>
/// <param name="a_startedge"></param>
/// <param name="a_Vertex"></param>
/// <returns></returns>
private static bool OnCycle(HalfEdge a_startedge, DCELVertex a_Vertex)
{
return(Cycle(a_startedge).ToList().Exists(e => e.To == a_Vertex));
}
/// <summary>
/// Finds a vertex with the given location, or null otherwise.
/// </summary>
/// <remarks>
/// Slow method O(n), not recommended.
/// </remarks>
/// <param name="a_Point"></param>
/// <param name="a_Vertex"></param>
/// <returns></returns>
public bool FindVertex(Vector2 a_Point, out DCELVertex a_Vertex)
{
a_Vertex = m_Vertices.FirstOrDefault(v => a_Point.Equals(v.Pos));
return(a_Vertex != null);
}
/// <summary>
/// Adds an edge, consisting of two halfedges, between existing vertices in the DCEL.
/// </summary>
/// <remarks>
/// Vertices should be adjacent to a common face.
/// </remarks>
/// <param name="a_vertex1"></param>
/// <param name="a_vertex2"></param>
/// <returns> One of the newly added edges </returns>
public HalfEdge AddEdge(DCELVertex a_Vertex1, DCELVertex a_Vertex2)
{
if (!m_Vertices.Contains(a_Vertex1) || !m_Vertices.Contains(a_Vertex2))
{
throw new GeomException("Vertices should already be part of the DCEL");
}
// create edges
var e1 = new HalfEdge(a_Vertex1, a_Vertex2);
var e2 = new HalfEdge(a_Vertex2, a_Vertex1);
m_Edges.AddLast(e1);
m_Edges.AddLast(e2);
bool newFace = false;
Face face1, face2;
// check if both vertices already part of face
// or disconnected inside a face
if (OutgoingEdges(a_Vertex1).Count() != 0 && OutgoingEdges(a_Vertex2).Count() != 0)
{
// get faces split by new edge from each vertex
face1 = GetSplittingFace(a_Vertex1, a_Vertex2.Pos);
face2 = GetSplittingFace(a_Vertex2, a_Vertex1.Pos);
// check if new edge will create additional face
var newInnerFace = face1.InnerComponents.Exists(e => OnCycle(e, a_Vertex1) && OnCycle(e, a_Vertex2));
var outerFaceSplit = !face1.IsOuter &&
OnCycle(face1.OuterComponent, a_Vertex1) &&
OnCycle(face1.OuterComponent, a_Vertex2);
newFace = newInnerFace || outerFaceSplit;
}
else if (OutgoingEdges(a_Vertex2).Count() != 0)
{
face1 = GetContainingFace(a_Vertex1.Pos);
face2 = GetSplittingFace(a_Vertex2, a_Vertex1.Pos);
}
else if (OutgoingEdges(a_Vertex1).Count() != 0)
{
face1 = GetSplittingFace(a_Vertex1, a_Vertex2.Pos);
face2 = GetContainingFace(a_Vertex2.Pos);
}
else
{
face1 = GetContainingFace(a_Vertex1.Pos);
face2 = GetContainingFace(a_Vertex2.Pos);
// new inner component inside face
face1.InnerComponents.Add(e1);
}
if (face1 != face2)
{
throw new GeomException("Vertices do not lie in the same face:\n"
+ a_Vertex1 + "\n" + a_Vertex2 + "\n" + face1 + "\n" + face2);
}
// fix edge pointers
e1.Face = face1;
e2.Face = face1;
Twin(e1, e2);
AddEdgeInVertexChain(a_Vertex1, e1);
AddEdgeInVertexChain(a_Vertex2, e2);
if (newFace)
{
face2 = SplitFace(e1, e2, face1);
}
else
{
face2 = null;
}
// check whether inner component has become part of outer component
// or inner components have merged
FixInnerComponents(e1, e2, face1, face2);
return(e1);
}