public static bool checkCore(Point u, Point v, int[] gi, List <Point> vertices, out bool uRedundant, out bool vRedundant)
{
List <Point> corePoints = new List <Point>();
string index;
corePoints.AddRange(vertices);
for (int i = 0; i < Globals.d; i++)
{
index = (Globals.d - 1).ToString() + Globals.k.ToString() + gi[i].ToString();
if (Globals.coreSet.ContainsKey(index))
{
foreach (Point p in Globals.coreSet[index])
{
Point q = p.clone();
q.increaseDimensionality(i / 2, (i % 2 == 0));
corePoints.Add(q);
}
}
}
//todo -- this should check that the vertices remain vertices after chull.
return(CDD.convexHullVertex(corePoints, u, v, out uRedundant, out vRedundant));
}
//returns true if points are vertices of the convex core
private static bool checkConvexCore(Point u, Point v, int[] gap, out bool uRedundant, out bool vRedundant)
{
List <Point> corePoints = new List <Point>();
string index0, indexk;
Point q;
corePoints.Add(u);
corePoints.Add(v);
for (int i = 0; i < Globals.d; i++)
{
index0 = (Globals.d - 1).ToString() + Globals.k.ToString() + gap[i].ToString();
indexk = (Globals.d - 1).ToString() + Globals.k.ToString() + (((2 * Globals.gap - gap[i]) > Globals.gap) ? (Globals.gap) : (2 * Globals.gap - gap[i])).ToString();
//List<Point> corePoints0 = FileIO.readPointsFromFile(Globals.directory + "/" + index0 + "/coreSet");
//List<Point> corePointsk = FileIO.readPointsFromFile(Globals.directory + "/" + indexk + "/coreSet");
List <Point> corePoints0 = (Globals.coreSet.ContainsKey(index0)) ? Globals.coreSet[index0] : new List <Point>();
List <Point> corePointsk = (Globals.coreSet.ContainsKey(indexk)) ? Globals.coreSet[indexk] : new List <Point>();
foreach (Point p in corePoints0)
{
q = p.clone();
q.increaseDimensionality(i, true);
corePoints.Add(q);
}
foreach (Point p in corePointsk)
{
q = p.clone();
q.increaseDimensionality(i, false);
corePoints.Add(q);
}
}
return(CDD.convexHullVertex(corePoints, u, v, out uRedundant, out vRedundant));
}
private static List <Graph> shellHelper(Graph currFacets, List <Point> vertexSet, List <Point> nonVertexSet, List <Point> coreSet, bool[] facetsUsed, Point u, Point v, int[] facetDiameter)
{
List <Graph> result = new List <Graph>();
int sp;
bool uRedundant, vRedundant; //track if either u or v is redundant. For message output.
bool[] _facetsUsed = new bool[facetsUsed.Length];
List <Point> _nonVertexSet = new List <Point>(), _corePointSet = new List <Point>(), _vertexSet = new List <Point>();
//creating copies of reference data
for (int i = 0; i < facetsUsed.Length; i++)
{
_facetsUsed[i] = facetsUsed[i];
}
foreach (Point p in nonVertexSet)
{
_nonVertexSet.Add(p.clone());
}
foreach (Point p in coreSet)
{
_corePointSet.Add(p.clone());
}
foreach (Point p in vertexSet)
{
_vertexSet.Add(p.clone());
}
//calculates gi values
int[] gi = updateGi(currFacets, u, v);
//calculates next facet to add
int nextFacet = calculateNextFacet(u, v, currFacets, facetsUsed, gi);
List <Point> facetPoints = currFacets.getAllContainedPoints(nextFacet);
List <Point> dMinus1FacetPoints = new List <Point>();
foreach (Point p in facetPoints)
{
if (Convert.ToInt32(p.Coordinates[nextFacet / 2].ToString()) == ((nextFacet % 2 == 0) ? 0 : Globals.k))
{
dMinus1FacetPoints.Add(p.decreaseDimensionality(nextFacet / 2));
}
}
//generate all valid d-1 polytopes that can be considered as a facet.
List <Graph> possibleFacets = Generate.dMinus1Polytopes(dMinus1FacetPoints, gi[nextFacet]);
_facetsUsed[nextFacet] = true;
if (possibleFacets != null && possibleFacets.Count > 0)
{
if (Globals.messageOn)
{
Console.WriteLine("Number of possible facets: " + possibleFacets.Count);
}
//try every possible facet as a shell
foreach (Graph f in possibleFacets)
{
//todo -- test if .clone() is actually required
Graph temp = currFacets.clone();
Graph h = f.clone();
//set values for current selected facet to shell
facetDiameter[nextFacet] = f.Points.Count / 2;
//increase dimensionality of facet
h.addDimensionality(nextFacet / 2, (nextFacet % 2 == 0) ? true : false);
//add facet to gamma
temp.AddFacet(h);
//check 1 - looks for sp from u to v
sp = ShortestPath.BFS(temp, u, v);
if (sp >= 0 && sp < Globals.maxDiameter[Globals.k] + Globals.k - Globals.gap)
{
if (Globals.messageOn)
{
Console.WriteLine("SP < " + Globals.maxLength);
}
continue;
}
//check 2 - gamma check
int gamma = calculateGamma(u, v, temp, gi, facetDiameter);
if (gamma > 0)
{
if (Globals.messageOn)
{
Console.WriteLine("Gamma > 0.");
}
continue;
}
//check 3 - convex core check -- u and v must be vertices of the convex hull generated by the current subgraph.
if (!checkCore(u, v, gi, temp.getAllContainedPoints(), out uRedundant, out vRedundant))
{
if (Globals.messageOn)
{
Console.WriteLine("Convex Core Check. {0}", ((uRedundant && vRedundant) ? "u and v are not vertices." : (uRedundant ? "u is not a vertex." : "v is not a vertex.")));
}
continue;
}
//if shelling is incomplete
if (checkUnshelledFacet(_facetsUsed))
{
result.AddRange(shellHelper(temp, _vertexSet, _nonVertexSet, _corePointSet, _facetsUsed, u, v, facetDiameter));
}
else
{
if (!CDD.compareAlToPoints(temp.Points)) //convex hull call
{
continue;
}
totalShelling++;
if (Globals.messageOn)
{
Console.WriteLine("***** FULL SHELLING FOUND *****");
Console.WriteLine(temp);
}
result.Add(temp);
}
}
facetDiameter[nextFacet] = Globals.maxDiameter[Globals.k];
if (Globals.messageOn)
{
Console.WriteLine("All facets checked.");
}
return(result);
}
else
{
if (Globals.messageOn)
{
Console.WriteLine("No possible facets.");
}
return(new List <Graph>());
}
}
//todo -- generalize this function to any d, currently using iVal and jVal.
//This function currently generates just delta(d-1,k) - gap polytopes, should also generate delta(d-1,k) polytopes
public static List <Graph> dMinus1PolytopesHelper(List <Point> vertices, List <Point> nonVertices, List <Point> corePoints, int iVal, int jVal, int gap)
{
List <Graph> result = new List <Graph>();
List <Point> currVertices = new List <Point>();
List <Point> currNonVertices = new List <Point>();
Graph facet;
if (vertices.Count > (Globals.maxDiameter[Globals.k] * 2 + 1))
{
return(result);
}
if (vertices.Count == (Globals.maxDiameter[Globals.k] * 2 + 1) || vertices.Count == (Globals.maxDiameter[Globals.k] * 2))
{
Graph tempGraph;
if (CDD.convexHullAdjList(vertices, new List <Point>(), out tempGraph))
{
totalCount++;
result.Add(tempGraph.clone());
}
}
foreach (Point p in vertices)
{
currVertices.Add(p.clone());
}
foreach (Point p in nonVertices)
{
currNonVertices.Add(p.clone());
}
for (int i = iVal; i <= Globals.k; i++)
{
int vCount = vertexCount(vertices, i);
bool _found;
//find max number of potential vertices (e.g. terminate if not enough vertices can exist)
if (vCount + (2 * (Globals.k - (iVal - 1))) < 2 * (Globals.maxDiameter[Globals.k] - gap))
{
return(result);
}
for (int j = (i == iVal ? jVal + 1 : 0); j <= Globals.k; j++)
{
_found = false;
foreach (Point p in nonVertices)
{
if (i == (int)Char.GetNumericValue(p.Coordinates[0]) && j == (int)Char.GetNumericValue(p.Coordinates[1]))
{
_found = true;
break;
}
}
if (!_found)
{
foreach (Point p in vertices)
{
if (i == (int)Char.GetNumericValue(p.Coordinates[0]) && j == (int)Char.GetNumericValue(p.Coordinates[1]))
{
_found = true;
break;
}
}
}
if (_found)
{
continue;
}
Point tempVertex = new Point(new int[2] {
i, j
});
currVertices.Add(tempVertex);
if (!check2PointsInRow(currVertices, i))
{
currVertices.Remove(tempVertex);
jVal = 0;
break;
}
else if (!check2PointsInCol(currVertices, j))
{
currVertices.Remove(tempVertex);
continue;
}
else if (!checkDiagonals(currVertices))
{
currVertices.Remove(tempVertex);
continue;
}
else
{
if (CDD.convexHullAdjList(currVertices, corePoints, out facet))
{
if (currVertices.Count >= (Globals.maxDiameter[Globals.k] - gap) * 2)
{
totalCount++;
result.Add(facet.clone());
result.AddRange(dMinus1PolytopesHelper(currVertices, currNonVertices, corePoints, i, j, gap));
}
else
{
result.AddRange(dMinus1PolytopesHelper(currVertices, currNonVertices, corePoints, i, j, gap));
}
}
}
currVertices.Remove(tempVertex);
currNonVertices.Add(tempVertex.clone());
}
}
return(result);
}
