/// <summary>
/// Checks if the other group's outer perimeter is inside this group's perimeter. Inclusive of the two groups
/// sharing vertices.
/// </summary>
/// <param name="otherGroup"></param>
/// <returns>True if the other group is inside this group, false otherwise.</returns>
public bool IsOtherGroupInThisGroup(ConnectedNodeGroup otherGroup)
{
HashSet <Vector2> sharedVertices = this.GetSharedVertices(otherGroup);
if (sharedVertices.Count == 0)
{
return(GeometryFuncs.IsPolyInPoly(otherGroup.outerPerimSimplified, this.outerPerimSimplified));
}
else
{
bool isInside = true;
foreach (PolygonSplittingGraphNode node in otherGroup.nodes.Values)
{
var nodeCoord = new Vector2(node.x, node.y);
if (sharedVertices.Contains(nodeCoord))
{
continue;
}
if (!GeometryFuncs.IsPointInPoly(nodeCoord, this.outerPerimSimplified))
{
isInside = false;
break;
}
}
return(isInside);
}
}
/// <summary>
/// Checks if another ConnectedNodeGroup shares a vertex (or vertices) with this group, IFF the shared vertex nodes
/// have different IDs.
/// </summary>
/// <param name="otherGroup"></param>
/// <returns>A HashSet of Vector2s of the vertices that appear in both groups but with different IDs.</returns>
public HashSet <Vector2> GetSharedVertices(ConnectedNodeGroup otherGroup)
{
if (otherGroup is null)
{
throw new ArgumentNullException(nameof(otherGroup));
}
var sharedVertices = new HashSet <Vector2>();
foreach (PolygonSplittingGraphNode thisNode in this.outerPerimNodes)
{
foreach (PolygonSplittingGraphNode otherNode in otherGroup.outerPerimNodes)
{
if (thisNode.x == otherNode.x && thisNode.y == otherNode.y)
{
if (thisNode.id == otherNode.id)
{
continue;
}
sharedVertices.Add(new Vector2(thisNode.x, thisNode.y));
}
}
}
return(sharedVertices);
}
/// <summary>
/// Given the input <param>connectedGroup</param>, gets all faces by running the following algorithm for EACH
/// CONNECTION for EVERY NODE:
/// 1. Ensure that all nodes have their connections ordered counter-clockwise (already done in ConnectedNodeGroup
/// constructor)
/// 2. Given some starting node S, travel any of its connections, which we will define as C
/// 3. From C, pick its connection that is next in order from the previous node (in this case, S)
/// 4. Repeat until we get back to S, and now we have a face.
/// This method gets all faces, many of which will be duplicates.
/// A better explanation is from here: https://math.stackexchange.com/questions/8140/find-all-cycles-faces-in-a-graph
/// </summary>
/// <param name="connectedGroup"></param>
/// <returns></returns>
private static List <List <PolygonSplittingGraphNode> > _GetAllFaces(ConnectedNodeGroup connectedGroup)
{
var allFaces = new List <List <PolygonSplittingGraphNode> >();
foreach (PolygonSplittingGraphNode node in connectedGroup.nodes.Values)
{
foreach (int connID in node.connectedNodeIDs)
{
if (!connectedGroup.nodes.ContainsKey(connID))
{
continue; //thanks to bridges a node may have a connection to a node that is not present in its node group (bridges split node groups)
}
var face = new List <PolygonSplittingGraphNode>
{
node
};
int prevID = node.id;
int currentID = connID;
do
{
face.Add(connectedGroup.nodes[currentID]);
int nextID;
do
{ //in case of bridge, keep getting nextID if it does not exist in connectedGroup
nextID = connectedGroup.GetCCWNextNodeID(prevID, currentID);
} while (!connectedGroup.nodes.ContainsKey(nextID));
prevID = currentID;
currentID = nextID;
} while (prevID != node.id);
allFaces.Add(face);
}
}
return(allFaces);
}
/// <summary>
/// Final step in partitioning a ConnectedNodeGroup, by converting it into a RectangularPolygon and checking if
/// the partition contains any holes (AKA the outerPerim of any ConnectedNodeGroups its parent ConnectedNodeGroup
/// contains).
/// </summary>
/// <param name="cycle">Cycle discovered from BFS, AKA partition of ConnectedNodeGroup.></param>
/// <param name="connectedGroup">The ConnectedNodeGroup <param>cycle</param> was derived from.</param>
/// <param name="connectedGroups">A list of all ConnectedNodeGroups.</param>
/// <param name="idsContainedInGroup">The IDs of the ConnectedNodeGroups contained within <param>connectedGroup</param></param>
/// <param name="nodes"></param>
/// <param name="innerHoles">Holes extracted from the same ConnectedNodeGroup.</param>
/// <returns></returns>
private static ChordlessPolygon _FinalisePartition(List <PolygonSplittingGraphNode> cycle, ConnectedNodeGroup connectedGroup,
SortedList <int, ConnectedNodeGroup> connectedGroups,
SortedDictionary <int, HashSet <int> > idsContainedInGroup,
SortedList <int, PolygonSplittingGraphNode> nodes,
List <ChordlessPolygon> innerHoles)
{
var cycleAsVectorArray = new Vector2[cycle.Count];
for (int i = 0; i < cycle.Count; i++)
{
PolygonSplittingGraphNode node = cycle[i];
cycleAsVectorArray[i] = new Vector2(node.x, node.y);
}
var potentialHoles = new List <List <Vector2> >();
potentialHoles.AddRange(innerHoles.Select(innerHole => innerHole.outerPerim.ToList()));
var bridges = new Dictionary <Vector2, HashSet <Vector2> >();
foreach (int connectedGroupID in idsContainedInGroup[connectedGroup.id])
{
ConnectedNodeGroup groupInside = connectedGroups[connectedGroupID];
potentialHoles.Add(groupInside.outerPerimSimplified.ToList());
foreach (int nodeID in groupInside.bridges.Keys)
{
if (!cycle.Exists(x => x.id == nodeID))
{
continue;
}
var nodeCoord = new Vector2(nodes[nodeID].x, nodes[nodeID].y);
foreach (int neighbourID in groupInside.bridges[nodeID])
{
if (!cycle.Exists(x => x.id == neighbourID))
{
continue;
}
var neighbourCoord = new Vector2(nodes[neighbourID].x, nodes[neighbourID].y);
if (!bridges.ContainsKey(nodeCoord))
{
bridges[nodeCoord] = new HashSet <Vector2>();
}
bridges[nodeCoord].Add(neighbourCoord);
}
}
}
return(new ChordlessPolygon(cycleAsVectorArray, potentialHoles.ToArray(), bridges, false));
}
/// <summary>
/// Creates a dictionary that stores IDs of ConnectedNodeGroups contained within each ConnectedNodeGroup.
/// </summary>
/// <param name="connectedGroups">List of ConnectedNodeGroups, sorted in order of area size, descending.</param>
/// <returns></returns>
public static SortedDictionary <int, HashSet <int> > StoreNestedGroups(SortedList <int, ConnectedNodeGroup> connectedGroups)
{
if (connectedGroups is null)
{
throw new ArgumentNullException(nameof(connectedGroups));
}
var idsContainedInGroup = new SortedDictionary <int, HashSet <int> >();
for (int i = 0; i < connectedGroups.Count; i++)
{
ConnectedNodeGroup thisGroup = connectedGroups[i];
idsContainedInGroup.Add(thisGroup.id, new HashSet <int>());
for (int j = 0; j < connectedGroups.Count; j++)
{
ConnectedNodeGroup otherGroup = connectedGroups[j];
if (i != j && thisGroup.IsOtherGroupInThisGroup(otherGroup))
{
idsContainedInGroup[thisGroup.id].Add(otherGroup.id);
}
}
}
return(_SimplifyNestedGroups(idsContainedInGroup));
}
private bool _Equals(ConnectedNodeGroup other)
{
return(this.id == other.id && this.nodes.Equals(other.nodes) && this.outerPerimNodes.Equals(other.outerPerimNodes));
}
/// <summary>
/// Partitions a connected node group by:
/// 1. Repeatedly running BFS on its nodes to find cycles and removing edges for the next BFS until no more
/// cycles can be found.
/// 1.1 Note that the BFS only runs on nodes with two or less VALID EDGES. Edges are only removed IFF either
/// of its vertices has two or less valid edges. This ensures we do not remove an edge that could be used
/// twice, for example two adjacent cycles that share an edge.
/// 2. The cycle is added to a list of perimeters (AKA a list of nodes) IFF it is NOT a hole.
/// </summary>
/// <param name="connectedGroup">ConnectedNodeGroup that is being partitioned.</param>
/// <param name="idsContainedInGroup">The IDs of the ConnectedNodeGroups contained within <param>connectedGroup</param></param>
/// <param name="connectedGroups">List of all ConnectedNodeGroups.</param>
/// <param name="nodes">List of all nodes.</param>
/// <param name="holes">Holes of the polygon that was made into a PolygonSplittingGraph.</param>
/// <returns></returns>
public static List <ChordlessPolygon> PartitionConnectedNodeGroup(ConnectedNodeGroup connectedGroup,
SortedDictionary <int, HashSet <int> > idsContainedInGroup,
SortedList <int, ConnectedNodeGroup> connectedGroups,
SortedList <int, PolygonSplittingGraphNode> nodes,
List <Vector2>[] holes)
{
if (connectedGroup is null)
{
throw new ArgumentNullException(nameof(connectedGroup));
}
if (idsContainedInGroup is null)
{
throw new ArgumentNullException(nameof(idsContainedInGroup));
}
if (connectedGroups is null)
{
throw new ArgumentNullException(nameof(connectedGroups));
}
if (nodes is null)
{
throw new ArgumentNullException(nameof(nodes));
}
if (holes is null)
{
throw new ArgumentNullException(nameof(holes));
}
var outerPerimCycle = new List <PolygonSplittingGraphNode>();
var polyCycles = new List <List <PolygonSplittingGraphNode> >();
var holeCycles = new List <List <PolygonSplittingGraphNode> >();
List <List <PolygonSplittingGraphNode> > allFaces = _GetAllFaces(connectedGroup);
var uniqueFaces = new List <List <Vector2> >();
foreach (List <PolygonSplittingGraphNode> newFace in allFaces)
{
//construct Vector2[] or List<Vector2> describing face perim in Vector2s
var newFacePerim = new Vector2[newFace.Count];
for (int i = 0; i < newFace.Count; i++)
{
PolygonSplittingGraphNode node = newFace[i];
newFacePerim[i] = new Vector2(node.x, node.y);
}
bool newFaceUnique = true;
foreach (List <Vector2> uniqueFace in uniqueFaces)
{
if (GeometryFuncs.ArePolysIdentical(uniqueFace.ToArray(), newFacePerim))
{
newFaceUnique = false;
break;
}
}
if (newFaceUnique)
{
uniqueFaces.Add(newFacePerim.ToList());
if (IsCycleHole(newFacePerim, holes))
{
holeCycles.Add(newFace);
}
else if (IsCycleOuterPerim(newFacePerim, connectedGroup.outerPerimNodes))
{
outerPerimCycle.AddRange(newFace);
}
else if (IsCycleComplex(newFacePerim))
{
continue;
}
else
{
polyCycles.Add(newFace);
}
}
}
var innerHoles = holeCycles.Select(_FinaliseInnerHole).ToList();
var partitions = new List <ChordlessPolygon>();
foreach (List <PolygonSplittingGraphNode> polyCycle in polyCycles)
{
partitions.Add(_FinalisePartition(polyCycle, connectedGroup, connectedGroups,
idsContainedInGroup, nodes, innerHoles));
}
if (partitions.Count == 0 && outerPerimCycle.Count > 0) //planar face that represents the outer perim is only relevant IFF there are no other (non-hole) faces
{
partitions.Add(_FinalisePartition(outerPerimCycle, connectedGroup, connectedGroups,
idsContainedInGroup, nodes, innerHoles));
}
return(partitions);
}