/// <summary>
/// Return the Delaunay triangulation of the supplied points
/// Optionally check for duplicate points
/// </summary>
/// <param name="points">List of 2D vertices</param>
/// <param name="rejectDuplicatePoints">Whether to omit duplicated points</param>
/// <returns></returns>
public List <Triad> Triangulation(List <Vertex> points, bool rejectDuplicatePoints)
{
List <Triad> triads = new List <Triad>();
Hull hull = new Hull();
Analyse(points, hull, triads, rejectDuplicatePoints, false);
// Now, need to flip any pairs of adjacent triangles not satisfying
// the Delaunay criterion
int numt = triads.Count;
bool[] idsA = new bool[numt];
bool[] idsB = new bool[numt];
// We maintain a "list" of the triangles we've flipped in order to propogate any
// consequent changes
// When the number of changes is large, this is best maintained as a vector of bools
// When the number becomes small, it's best maintained as a set
// We switch between these regimes as the number flipped decreases
//
// the iteration cycle limit is included to prevent degenerate cases 'oscillating'
// and the algorithm failing to stop.
int flipped = FlipTriangles(triads, idsA);
int iterations = 1;
while (flipped > (int)(fraction * (float)numt) && iterations < 1000)
{
if ((iterations & 1) == 1)
{
flipped = FlipTriangles(triads, idsA, idsB);
}
else
{
flipped = FlipTriangles(triads, idsB, idsA);
}
iterations++;
}
Set <int> idSetA = new Set <int>(), idSetB = new Set <int>();
flipped = FlipTriangles(triads,
((iterations & 1) == 1) ? idsA : idsB, idSetA);
iterations = 1;
while (flipped > 0 && iterations < 2000)
{
if ((iterations & 1) == 1)
{
flipped = FlipTriangles(triads, idSetA, idSetB);
}
else
{
flipped = FlipTriangles(triads, idSetB, idSetA);
}
iterations++;
}
return(triads);
}
private void Analyse(List <Vertex> suppliedPoints, Hull hull, List <Triad> triads, bool rejectDuplicatePoints, bool hullOnly)
{
if (suppliedPoints.Count < 3)
{
throw new ArgumentException("Number of points supplied must be >= 3");
}
this.points = suppliedPoints;
int nump = points.Count;
float[] distance2ToCentre = new float[nump];
int[] sortedIndices = new int[nump];
// Choose first point as the seed
for (int k = 0; k < nump; k++)
{
distance2ToCentre[k] = points[0].distance2To(points[k]);
sortedIndices[k] = k;
}
// Sort by distance to seed point
Array.Sort(distance2ToCentre, sortedIndices);
// Duplicates are more efficiently rejected now we have sorted the vertices
if (rejectDuplicatePoints)
{
// Search backwards so each removal is independent of any other
for (int k = nump - 2; k >= 0; k--)
{
// If the points are identical then their distances will be the same,
// so they will be adjacent in the sorted list
if ((points[sortedIndices[k]].x == points[sortedIndices[k + 1]].x) &&
(points[sortedIndices[k]].y == points[sortedIndices[k + 1]].y))
{
// Duplicates are expected to be rare, so this is not particularly efficient
Array.Copy(sortedIndices, k + 2, sortedIndices, k + 1, nump - k - 2);
Array.Copy(distance2ToCentre, k + 2, distance2ToCentre, k + 1, nump - k - 2);
nump--;
}
}
}
Debug.WriteLine((points.Count - nump).ToString() + " duplicate points rejected");
if (nump < 3)
{
throw new ArgumentException("Number of unique points supplied must be >= 3");
}
int mid = -1;
float romin2 = float.MaxValue, circumCentreX = 0, circumCentreY = 0;
// Find the point which, with the first two points, creates the triangle with the smallest circumcircle
Triad tri = new Triad(sortedIndices[0], sortedIndices[1], 2);
for (int kc = 2; kc < nump; kc++)
{
tri.c = sortedIndices[kc];
if (tri.FindCircumcirclePrecisely(points) && tri.circumcircleR2 < romin2)
{
mid = kc;
// Centre of the circumcentre of the seed triangle
romin2 = tri.circumcircleR2;
circumCentreX = tri.circumcircleX;
circumCentreY = tri.circumcircleY;
}
else if (romin2 * 4 < distance2ToCentre[kc])
{
break;
}
}
// Change the indices, if necessary, to make the 2th point produce the smallest circumcircle with the 0th and 1th
if (mid != 2)
{
int indexMid = sortedIndices[mid];
float distance2Mid = distance2ToCentre[mid];
Array.Copy(sortedIndices, 2, sortedIndices, 3, mid - 2);
Array.Copy(distance2ToCentre, 2, distance2ToCentre, 3, mid - 2);
sortedIndices[2] = indexMid;
distance2ToCentre[2] = distance2Mid;
}
// These three points are our seed triangle
tri.c = sortedIndices[2];
tri.MakeClockwise(points);
tri.FindCircumcirclePrecisely(points);
// Add tri as the first triad, and the three points to the convex hull
triads.Add(tri);
hull.Add(new HullVertex(points, tri.a));
hull.Add(new HullVertex(points, tri.b));
hull.Add(new HullVertex(points, tri.c));
// Sort the remainder according to their distance from its centroid
// Re-measure the points' distances from the centre of the circumcircle
Vertex centre = new Vertex(circumCentreX, circumCentreY);
for (int k = 3; k < nump; k++)
{
distance2ToCentre[k] = points[sortedIndices[k]].distance2To(centre);
}
// Sort the _other_ points in order of distance to circumcentre
Array.Sort(distance2ToCentre, sortedIndices, 3, nump - 3);
// Add new points into hull (removing obscured ones from the chain)
// and creating triangles....
int numt = 0;
for (int k = 3; k < nump; k++)
{
int pointsIndex = sortedIndices[k];
HullVertex ptx = new HullVertex(points, pointsIndex);
float dx = ptx.x - hull[0].x, dy = ptx.y - hull[0].y; // outwards pointing from hull[0] to pt.
int numh = hull.Count, numh_old = numh;
List <int> pidx = new List <int>(), tridx = new List <int>();
int hidx; // new hull point location within hull.....
if (hull.EdgeVisibleFrom(0, dx, dy))
{
// starting with a visible hull facet !!!
int e2 = numh;
hidx = 0;
// check to see if segment numh is also visible
if (hull.EdgeVisibleFrom(numh - 1, dx, dy))
{
// visible.
pidx.Add(hull[numh - 1].pointsIndex);
tridx.Add(hull[numh - 1].triadIndex);
for (int h = 0; h < numh - 1; h++)
{
// if segment h is visible delete h
pidx.Add(hull[h].pointsIndex);
tridx.Add(hull[h].triadIndex);
if (hull.EdgeVisibleFrom(h, ptx))
{
hull.RemoveAt(h);
h--;
numh--;
}
else
{
// quit on invisibility
hull.Insert(0, ptx);
numh++;
break;
}
}
// look backwards through the hull structure
for (int h = numh - 2; h > 0; h--)
{
// if segment h is visible delete h + 1
if (hull.EdgeVisibleFrom(h, ptx))
{
pidx.Insert(0, hull[h].pointsIndex);
tridx.Insert(0, hull[h].triadIndex);
hull.RemoveAt(h + 1); // erase end of chain
}
else
{
break; // quit on invisibility
}
}
}
else
{
hidx = 1; // keep pt hull[0]
tridx.Add(hull[0].triadIndex);
pidx.Add(hull[0].pointsIndex);
for (int h = 1; h < numh; h++)
{
// if segment h is visible delete h
pidx.Add(hull[h].pointsIndex);
tridx.Add(hull[h].triadIndex);
if (hull.EdgeVisibleFrom(h, ptx))
{ // visible
hull.RemoveAt(h);
h--;
numh--;
}
else
{
// quit on invisibility
hull.Insert(h, ptx);
break;
}
}
}
}
else
{
int e1 = -1, e2 = numh;
for (int h = 1; h < numh; h++)
{
if (hull.EdgeVisibleFrom(h, ptx))
{
if (e1 < 0)
{
e1 = h; // first visible
}
}
else
{
if (e1 > 0)
{
// first invisible segment.
e2 = h;
break;
}
}
}
// triangle pidx starts at e1 and ends at e2 (inclusive).
if (e2 < numh)
{
for (int e = e1; e <= e2; e++)
{
pidx.Add(hull[e].pointsIndex);
tridx.Add(hull[e].triadIndex);
}
}
else
{
for (int e = e1; e < e2; e++)
{
pidx.Add(hull[e].pointsIndex);
tridx.Add(hull[e].triadIndex); // there are only n-1 triangles from n hull pts.
}
pidx.Add(hull[0].pointsIndex);
}
// erase elements e1+1 : e2-1 inclusive.
if (e1 < e2 - 1)
{
hull.RemoveRange(e1 + 1, e2 - e1 - 1);
}
// insert ptx at location e1+1.
hull.Insert(e1 + 1, ptx);
hidx = e1 + 1;
}
// If we're only computing the hull, we're done with this point
if (hullOnly)
{
continue;
}
int a = pointsIndex, T0;
int npx = pidx.Count - 1;
numt = triads.Count;
T0 = numt;
for (int p = 0; p < npx; p++)
{
Triad trx = new Triad(a, pidx[p], pidx[p + 1]);
trx.FindCircumcirclePrecisely(points);
trx.bc = tridx[p];
if (p > 0)
{
trx.ab = numt - 1;
}
trx.ac = numt + 1;
// index back into the triads.
Triad txx = triads[tridx[p]];
if ((trx.b == txx.a && trx.c == txx.b) | (trx.b == txx.b && trx.c == txx.a))
{
txx.ab = numt;
}
else if ((trx.b == txx.a && trx.c == txx.c) | (trx.b == txx.c && trx.c == txx.a))
{
txx.ac = numt;
}
else if ((trx.b == txx.b && trx.c == txx.c) | (trx.b == txx.c && trx.c == txx.b))
{
txx.bc = numt;
}
triads.Add(trx);
numt++;
}
// Last edge is on the outside
triads[numt - 1].ac = -1;
hull[hidx].triadIndex = numt - 1;
if (hidx > 0)
{
hull[hidx - 1].triadIndex = T0;
}
else
{
numh = hull.Count;
hull[numh - 1].triadIndex = T0;
}
}
}