private async Task <Partition> Subdivide(int lidx, int ridx)
{
Debug.Assert(lidx != ridx);
if (ridx - lidx == 1) //2 points
{
QuadEdge edge = QuadEdge.MakeEdge(this._points[lidx], this._points[lidx + 1]);
return(new Partition
{
Left = edge,
Right = edge.Inverse
});
}
if (ridx - lidx == 2) //3 points
{
QuadEdge a = QuadEdge.MakeEdge(this._points[lidx], this._points[lidx + 1]);
QuadEdge b = QuadEdge.MakeEdge(this._points[lidx + 1], this._points[lidx + 2]);
QuadEdge.Splice(a.Inverse, b);
if (Point.IsCounterClockWise(this._points[lidx], this._points[lidx + 1], this._points[lidx + 2]))
{
QuadEdge c = QuadEdge.ConnectLeft(b, a);
return(new Partition
{
Left = a,
Right = b.Inverse
});
}
if (Point.IsCounterClockWise(this._points[lidx], this._points[lidx + 2], this._points[lidx + 1]))
{
QuadEdge c = QuadEdge.ConnectLeft(b, a);
return(new Partition
{
Left = c.Inverse,
Right = c
});
}
return(new Partition
{
Left = a,
Right = b.Inverse
});
}
int midx = (lidx + ridx) / 2;
Task <Partition> leftTask = Subdivide(lidx, midx);
Task <Partition> rightTask = Subdivide(midx + 1, ridx);
return(Merge(await leftTask, await rightTask));
}
/// <summary>
/// Triangulate the set of points using a divide and conquer approach.
/// </summary>
private QuadEdge <T>[] Triangulate(Vec3[] pts)
{
QuadEdge <T> a, b, c, nextCand;
// Only two points -> One edge
if (pts.Length == 2)
{
a = QuadEdge <T> .MakeEdge(pts[0], pts[1]);
return(new QuadEdge <T>[] { a, a.Sym });
}
// Only tree points
else if (pts.Length == 3)
{
a = QuadEdge <T> .MakeEdge(pts[0], pts[1]);
b = QuadEdge <T> .MakeEdge(pts[1], pts[2]);
QuadEdge <T> .Splice(a.Sym, b);
// Closing triangle
if (Geometry.Ccw(pts[0], pts[1], pts[2]))
{
c = QuadEdge <T> .Connect(b, a);
return(new QuadEdge <T>[] { a, b.Sym });
}
else if (Geometry.Ccw(pts[0], pts[2], pts[1]))
{
c = QuadEdge <T> .Connect(b, a);
return(new QuadEdge <T>[] { c.Sym, c });
}
else
{
// Points are collinear
return(new QuadEdge <T>[] { a, b.Sym });
}
}
// SPLITTING
// Divide them halfsize recursively
int halfLength = (pts.Length + 1) / 2;
QuadEdge <T>[] left = Triangulate(pts.Take(halfLength).ToArray());
QuadEdge <T>[] right = Triangulate(pts.Skip(halfLength).ToArray());
// MERGING
// From left to right
QuadEdge <T> ldo = left[0];
QuadEdge <T> ldi = left[1];
QuadEdge <T> rdi = right[0];
QuadEdge <T> rdo = right[1];
// Compute lower common tangent to be able to merge both triangulations
bool crossEdgeNotFound = true;
while (crossEdgeNotFound)
{
if (Geometry.LeftOf(rdi.Origin, ldi))
{
ldi = ldi.Lnext;
}
else if (Geometry.RightOf(ldi.Origin, rdi))
{
rdi = rdi.Rprev;
}
else
{
crossEdgeNotFound = false;
}
}
// Start merging
// 1) Creation of the baseEdge quad edge (See Fig.21)
QuadEdge <T> baseEdge = QuadEdge <T> .Connect(rdi.Sym, ldi);
if (ldi.Origin == ldo.Origin)
{
ldo = baseEdge.Sym;
}
if (rdi.Origin == rdo.Origin)
{
rdo = baseEdge;
}
// 2) Rising bubble (See Fig. 22)
bool upperCommonTangentNotFound = true;
while (upperCommonTangentNotFound)
{
// Locate the first L site (lCand.Destination) to be encountered
// by the rising bubble, and delete L edges out of baseEdge.Destination
// that fail the circle test.
QuadEdge <T> lCand = baseEdge.Sym.Onext;
if (IsValid(lCand, baseEdge))
{
while (Geometry.InCircumCercle2D(lCand.Onext.Destination,
baseEdge.Destination, baseEdge.Origin, lCand.Destination))
{
nextCand = lCand.Onext;
QuadEdge <T> .Delete(lCand);
lCand = nextCand;
}
}
// Same for the right part (Symetrically)
QuadEdge <T> rCand = baseEdge.Oprev;
if (IsValid(rCand, baseEdge))
{
while (Geometry.InCircumCercle2D(rCand.Oprev.Destination,
baseEdge.Destination, baseEdge.Origin, rCand.Destination))
{
nextCand = rCand.Oprev;
QuadEdge <T> .Delete(rCand);
rCand = nextCand;
}
}
// Upper common tangent is baseEdge
if (!IsValid(lCand, baseEdge) && !IsValid(rCand, baseEdge))
{
upperCommonTangentNotFound = false;
}
// Construct new cross edge between left and right
// The next cross edge is to be connected to either lcand.Dest or rCand.Dest
// If both are valid, then choose the appropriate one using the
// Geometry.InCircumCercle2D test
else if (!IsValid(lCand, baseEdge) ||
(
IsValid(rCand, baseEdge) &&
Geometry.InCircumCercle2D(rCand.Destination,
lCand.Destination,
lCand.Origin,
rCand.Origin)
)
)
{
// Cross edge baseEdge added from rCand.Destination to basel.Destination
baseEdge = QuadEdge <T> .Connect(rCand, baseEdge.Sym);
}
else
{
// Cross edge baseEdge added from baseEdge.Origin to lCand.Destination
baseEdge = QuadEdge <T> .Connect(baseEdge.Sym, lCand.Sym);
}
}
return(new QuadEdge <T>[] { ldo, rdo });
}
/// <summary>
/// Insert a new site inside an existing delaunay triangulation. New site
/// must be inside the convex hull of previoulsy added sites.
/// Set <paramref name="safe"/> to true to first test if new site is correct.
/// </summary>
/// <param name="newPos">The position to of new site</param>
/// <param name="edge">Edge used to start locate process. Can be used to speed up search.</param>
/// <param name="safe">If true, check if <paramref name="newPos"/> inside the convex hull.</param>
public bool Insert(Vec3 newPos, QuadEdge <T> edge = null, bool safe = false)
{
if (safe)
{
bool result = InsideConvexHull(newPos);
if (!result)
{
// Cannot add site not already inside the convex hull
return(false);
}
}
// Start somewhere if no hint
if (edge == null)
{
edge = _leftRightEdges[1];
}
// Locate edge (must be inside the boundary)
QuadEdge <T> foundE = Locate(newPos, edge, safe: false);
// Site already triangulated
if (Geometry.AlmostEquals(foundE.Origin, newPos) ||
Geometry.AlmostEquals(foundE.Destination, newPos))
{
return(false);
}
// On an edge ?
if (Geometry.AlmostColinear(foundE.Origin, foundE.Destination, newPos))
{
var temp = foundE.Oprev;
QuadEdge <T> .Delete(foundE);
foundE = temp;
}
// Create new edge to connect new site to neighbors
QuadEdge <T> baseE = QuadEdge <T> .MakeEdge(foundE.Origin, newPos);
Vec3 first = baseE.Origin;
QuadEdge <T> .Splice(baseE, foundE);
// Up to 4 vertices if new site on an edge
do
{
baseE = QuadEdge <T> .Connect(foundE, baseE.Sym);
foundE = baseE.Oprev;
} while (foundE.Destination != first);
// Fill star shaped polygon and swap suspect edges
// Adding a new point can break old condition about InCircle test
foundE = baseE.Oprev;
bool shouldExit = false;
do
{
var tempE = foundE.Oprev;
if (Geometry.RightOf(tempE.Destination, foundE) &&
Geometry.InCircumCercle2D(newPos, foundE.Origin, tempE.Destination, foundE.Destination))
{
QuadEdge <T> .Swap(foundE);
// tempE != foundE.Oprev after swap
foundE = foundE.Oprev;
}
else if (foundE.Origin == first)
{
// No more suspect edge ... exit
shouldExit = true;
}
else
{
// Get next suspect edge from top to bottom
foundE = foundE.Onext.Lprev;
}
} while (!shouldExit);
return(true);
}