/// <summary>
/// Split an edge with <paramref name="vertexIndex"/>.
/// For each half edge two new triangles replace old one.
/// </summary>
/// <param name="vertexIndex">Vertex index.</param>
/// <param name="edge">Half edge.</param>
private void SplitEdge(int vertexIndex, HalfEdge edge)
{
var twin = edge.Twin;
var edgesToCheck = new List <HalfEdge>(12);
SplitHalfEdge(edge);
if (twin != null)
{
SplitHalfEdge(twin);
var twinSplitNext = twin.Next.Twin.Next;
twin.TwinWith(edge.Next.Twin.Next);
twinSplitNext.TwinWith(edge);
}
edge.Constrained = edge.Constrained;
edge.Next.Twin.Next.Constrained = edge.Constrained;
RestoreDelaunayProperty(edgesToCheck);
void SplitHalfEdge(HalfEdge e)
{
var next = e.Next;
var prev = next.Next;
// Form first triangle
var split = new HalfEdge(vertexIndex)
{
Next = prev,
};
e.Next = split;
// Form second triangle
var splitTwin = new HalfEdge(prev.Origin);
var splitTwinNext = new HalfEdge(vertexIndex)
{
Next = next,
};
splitTwin.Next = splitTwinNext;
next.Next = splitTwin;
splitTwin.TwinWith(split);
edgesToCheck.Add(e);
edgesToCheck.Add(split);
edgesToCheck.Add(prev);
edgesToCheck.Add(splitTwin);
edgesToCheck.Add(splitTwinNext);
edgesToCheck.Add(next);
}
}
private HalfEdge Flip(HalfEdge edge)
{
var twin = edge.Twin;
var edgeNext = edge.Next;
var twinNext = twin.Next;
edge.Prev.Next = twinNext;
twin.Prev.Next = edgeNext;
edge.Detach();
twin.Detach();
edge = new HalfEdge(edgeNext.Next.Origin)
{
Next = twinNext.Next
};
twin = new HalfEdge(twinNext.Next.Origin)
{
Next = edgeNext.Next
};
edge.TwinWith(twin);
edgeNext.Next = edge;
twinNext.Next = twin;
return(edge);
}
private void ToConvexHull(HalfEdge borderEdge = null)
{
var current = borderEdge;
if (current == null)
{
foreach (var halfEdge in HalfEdges)
{
if (halfEdge.Twin == null)
{
current = halfEdge;
break;
}
}
}
var edgesToCheck = new List <HalfEdge>();
var prev = PrevBorderEdge(current);
var start = current;
// Same as Ear clipping method but for 'outside' ears.
do
{
var o1 = prev.Origin;
var o2 = current.Origin;
var o3 = current.Next.Origin;
var p1 = InnerVertices[o1].Pos;
var p2 = InnerVertices[o2].Pos;
var p3 = InnerVertices[o3].Pos;
if (!AreClockwiseOrderedOrCollinear(p1, p2, p3))
{
var c = start;
var intersectAny = false;
do
{
if (c.Origin == o1 || c.Origin == o2 || c.Origin == o3 || c.Next.Origin == o1)
{
c = NextBorderEdge(c);
continue;
}
var s1 = InnerVertices[c.Origin].Pos;
var s2 = InnerVertices[c.Next.Origin].Pos;
if (RobustSegmentSegmentIntersection(p1, p3, s1, s2))
{
intersectAny = true;
break;
}
c = NextBorderEdge(c);
} while (start != c);
if (!intersectAny)
{
var t = new HalfEdge(current.Next.Origin)
{
Next = new HalfEdge(current.Origin)
{
Next = new HalfEdge(prev.Origin),
},
};
edgesToCheck.Add(t.Prev);
t.Prev.Next = t;
t.TwinWith(current);
t.Next.TwinWith(prev);
start = current = t.Prev;
prev = PrevBorderEdge(start);
continue;
}
}
prev = current;
current = NextBorderEdge(current);
if (current == start)
{
break;
}
} while (true);
RestoreDelaunayProperty(edgesToCheck);
}
private bool InnerInsertConstrainedEdge(int index0, int index1, bool destroyConstrained = false)
{
var location = LocateClosestTriangle(index0, out var start);
System.Diagnostics.Debug.Assert(location == LocationResult.SameVertex);
System.Diagnostics.Debug.Assert(start.Origin == index0);
// Check test cases for explanation
var upperUsed = new HashSet <int>();
var lowerUsed = new HashSet <int>();
var shouldBeReinserted = new HashSet <int>();
var shouldBeReconstrained = new List <(int, int)>();
var a = InnerVertices[index0].Pos;
var b = InnerVertices[index1].Pos;
var ab = b - a;
var signab = new IntVector2(Mathf.Sign(ab.X), Mathf.Sign(ab.Y));
// In order to insert a constrain edge we have to delete all
// triangles that (index0, index1) crosses. Thereafter we
// have 2 polygonal holes that should be triangulated.
List <HalfEdge> upperPolygon = null, lowerPolygon = null;
var current = start;
foreach (var incidentEdge in IncidentEdges(start))
{
var next = incidentEdge.Next;
var prev = next.Next;
// Special case: requested edge already exists.
if (next.Origin == index1)
{
return(incidentEdge.Constrained = true);
}
if (prev.Origin == index1)
{
return(prev.Constrained = true);
}
var c = InnerVertices[next.Origin].Pos;
var d = InnerVertices[prev.Origin].Pos;
var e = InnerVertices[incidentEdge.Origin].Pos;
// Special case: requested edge lies on the same line as [e, c] or [e, d].
// If true then mark edge as constrained and insert edge [next.Origin, index1] or [prev.Origin, index1].
if (IsVertexOnLine(a, e, c) && IsVertexOnLine(b, e, c))
{
var ec = c - e;
// Check for co-directionality in order to prevent looping
if (Mathf.Sign(ec.X) == signab.X && Mathf.Sign(ec.Y) == signab.Y)
{
return(incidentEdge.Constrained = InnerInsertConstrainedEdge(next.Origin, index1, destroyConstrained));
}
}
else if (IsVertexOnLine(a, e, d) && IsVertexOnLine(b, e, d))
{
var ed = d - e;
// Check for co-directionality in order to prevent looping
if (Mathf.Sign(ed.X) == signab.X && Mathf.Sign(ed.Y) == signab.Y)
{
return(prev.Constrained = InnerInsertConstrainedEdge(prev.Origin, index1, destroyConstrained));
}
}
else if (RobustSegmentSegmentIntersection(a, b, c, d))
{
// Should not delete existing constrain edges.
if (next.Constrained && !destroyConstrained)
{
return(false);
}
// Then we should start traversing
upperPolygon = new List <HalfEdge> {
incidentEdge
};
lowerPolygon = new List <HalfEdge> {
prev
};
lowerUsed.Add(prev.Origin);
upperUsed.Add(incidentEdge.Origin);
current = next;
break;
}
}
while (true)
{
if (current.Twin == null)
{
// Something horrible has happened..
// Something like trying to connect two vertices trough concavity.
// Should not happen at all in current implementation.
return(false);
}
current = current.Twin;
var next = current.Next;
var prev = next.Next;
if (prev.Origin == index1)
{
// We found the end of the requested edge.
// Stop traversing and triangulate both polygons.
AddLower(prev);
AddUpper(next);
Finish(index0, index1);
return(true);
}
var c = InnerVertices[next.Origin].Pos;
var d = InnerVertices[prev.Origin].Pos;
var e = InnerVertices[current.Origin].Pos;
if (IsVertexOnLine(d, a, b))
{
// Special case: [a, b] intersects triangle exactly in the
// vertex that is opposite to basis (`current` edge).
// Should finish traversing and insert constrain edge
// between prev.Origin and index1.
AddLower(prev);
AddUpper(next);
var edge = Finish(index0, prev.Origin);
edge.Constrained = InnerInsertConstrainedEdge(prev.Origin, index1, destroyConstrained);
RestoreDelaunayProperty(upperPolygon);
RestoreDelaunayProperty(lowerPolygon);
return(edge.Constrained);
}
if (RobustSegmentSegmentIntersection(a, b, c, d))
{
if (next.Constrained && !destroyConstrained)
{
return(false);
}
AddLower(prev);
current = next;
}
else if (RobustSegmentSegmentIntersection(a, b, d, e))
{
if (prev.Constrained && !destroyConstrained)
{
return(false);
}
AddUpper(next);
current = prev;
}
else
{
System.Diagnostics.Debug.Fail("This is impossible case.");
}
}
void AddUpper(HalfEdge e)
{
if (upperUsed.Add(e.Origin))
{
upperPolygon.Add(e);
}
else
{
// It means that triangles from i to polygon.Count should be removed.
// Removing those triangles makes some vertices isolated and
// also may remove previously inserted constrained edges.
// So we keep that in mind in order to reinsert missing elements later.
var i = upperPolygon.FindIndex(edge => edge.Origin == e.Origin);
for (int j = upperPolygon.Count - 1; j >= i; j--)
{
var t = upperPolygon[j];
shouldBeReinserted.Add(t.Origin);
shouldBeReinserted.Add(t.Next.Origin);
if (t.Constrained)
{
shouldBeReconstrained.Add((t.Origin, t.Next.Origin));
}
upperPolygon.RemoveAt(j);
}
upperPolygon.Add(e);
}
}
void AddLower(HalfEdge e)
{
if (lowerUsed.Add(e.Origin))
{
lowerPolygon.Add(e);
}
else
{
// Same as for upper polygon except that it is filled in reverse order.
var i = lowerPolygon.FindIndex(edge => edge.Origin == e.Origin);
for (int j = lowerPolygon.Count - 1; j > i; j--)
{
var t = lowerPolygon[j];
shouldBeReinserted.Add(t.Origin);
shouldBeReinserted.Add(t.Next.Origin);
if (t.Constrained)
{
shouldBeReconstrained.Add((t.Origin, t.Next.Origin));
}
lowerPolygon.RemoveAt(j);
}
shouldBeReinserted.Add(e.Next.Origin);
}
}
HalfEdge Finish(int i0, int i1)
{
// Create (i0, i1) half edges.
var e1 = new HalfEdge(i1);
var e2 = new HalfEdge(i0);
e1.TwinWith(e2);
e1.Constrained = true;
AddUpper(e1);
AddLower(e2);
lowerPolygon.Reverse();
// Triangulate both polygonal holes.
TriangulatePolygonByEarClipping(upperPolygon, false);
TriangulatePolygonByEarClipping(lowerPolygon, false);
RestoreDelaunayProperty(upperPolygon);
// Reinsert missing elements.
foreach (var vertexIndex in shouldBeReinserted)
{
AddVertex(vertexIndex);
}
foreach (var edge in shouldBeReconstrained)
{
InnerInsertConstrainedEdge(edge.Item1, edge.Item2);
}
return(e2);
}
}