/// <summary>
/// Determination of the co-ordinates of point B
///
/// Point B can be characterized as having the same perpendicular distance to the straight line carrying
/// the "opposite" line segment to the vertex V and from both straight lines containing the line segments
/// starting at the vertex V. We have to find such an "opposite" line segment.
///
/// We traverse all line segments e of the original polygon [polyline] and test them whether they can be
/// "opposite" line segments. Unfortunately, a simple test of the intersection between a bisector starting
/// at V and the currently tested line segment cannot be used. We have to test the intersection with the
/// line holding the edge ei and by the bisectors bi and bi+1 leading from vertices at both ends of this
/// line segment.
/// </summary>
/// <param name="lav"></param>
/// <param name="vertex"></param>
/// <returns></returns>
private static Point2D?OppositeIntersection(CircularLinkedList <Vertex> lav, Vertex vertex)
{
double minDistance2 = Double.MaxValue;
Point2D?minIncenter = null;
// Project the supporting the edges starting at V (node) as rays
Ray2D inRay = new Ray2D(vertex.inEdge.target.Position, new Direction2D(vertex.inEdge.Vector));
Ray2D outRay = new Ray2D(vertex.outEdge.source.Position, new Direction2D(-vertex.outEdge.Vector));
// Ignore cases where the in and out edges are collinear.
if (!inRay.SupportingLine.IsParallelTo(outRay.SupportingLine))
{
lav.ForEachPair(delegate(Vertex oppA, Vertex oppB)
{
// Ignore testing againt the in and out edges of V
if (oppA == vertex || oppB == vertex)
{
return;
}
// Simple intersection test between the bisector starting at V and the (whole) line containing the
// currently tested line segment ei rejects the line segments laying "behind" the vertex V. We then compute
// the co-ordinates of the candidate point Bi as the intersection between the bisector at V and the axis [bisector]
// of the angle between of the edges starting at V and the tested line segment ei. Simple check should be performed
// to exclude the case where one of the line segments starting at V us parallel to ei. The resulting point B
// is selected from all the candidates Bi as the nearest point to the vertex V
// TODO: Performance: How much code can be factored out of this loop?
// TODO: Do we need to prevent testing against the in and out edges of V?
// and the candiate "opposite" line
Line2D oppositeLine = new Line2D(oppA.outEdge.source.Position, oppA.outEdge.target.Position);
// TODO: Need to use a ray-line intersection here, where inLine and outLine are
// replaced by rays which start at V and project in alignment with the two incident edges
Point2D?inOppIntersection = Intersector.Intersect(inRay, oppositeLine);
Point2D?outOppIntersection = Intersector.Intersect(outRay, oppositeLine);
if (inOppIntersection.HasValue && outOppIntersection.HasValue)
{
Triangle2D triangle = new Triangle2D(vertex.Position, inOppIntersection.Value, outOppIntersection.Value);
if (!triangle.IsDegenerate)
{
Point2D incenter = triangle.Incenter;
// Is the incenter in the zone bounded by the oppositeLine and bisectors at the beginning
// and end of the segment embedded within it?
// TODO: Check which way round these lines are - so the the positive side defines our zone of interest
Line2D oppositeBoundary1 = oppA.Bisector.SupportingLine.Opposite;
Line2D oppositeBoundary2 = oppB.Bisector.SupportingLine;
OrientedSide sideA = oppositeBoundary1.Side(incenter);
OrientedSide sideB = oppositeLine.Side(incenter);
OrientedSide sideC = oppositeBoundary2.Side(incenter);
if (sideA == OrientedSide.Negative && sideB == OrientedSide.Negative && sideC == OrientedSide.Negative)
{
double distance2 = (incenter - vertex.Position).Magnitude2;
if (distance2 > 0.0 && distance2 < minDistance2)
{
minDistance2 = distance2;
minIncenter = incenter;
}
}
}
}
});
}
return(minIncenter);
}
public override void ModifyLav(AngularBisectorNetwork network)
{
Debug.Assert(nodeV.List != null);
CircularLinkedList <Vertex> lav1 = nodeV.List;
// * Create two new nodes V1 and V2 with the same co-ordinates as the intersection point I
CircularLinkedListNode <Vertex> nodeV1 = new CircularLinkedListNode <Vertex>(new Vertex(this.Position));
CircularLinkedListNode <Vertex> nodeV2 = new CircularLinkedListNode <Vertex>(new Vertex(this.Position));
// * Search the opposite edge in SLAV sequentially
CircularLinkedListNode <Vertex> oppositeNode = lav1.FindPair(delegate(Vertex va, Vertex vb)
{
// Ignore testing againt the in and out edges of V
if (va == V || vb == V)
{
return(false);
}
// and the candiate "opposite" line
Line2D oppositeLine = new Line2D(va.outEdge.source.Position, va.outEdge.target.Position);
// TODO: Check which way round these lines are - so the the positive side defines our zone of interest
Line2D oppositeBoundary1 = va.Bisector.SupportingLine.Opposite;
Line2D oppositeBoundary2 = vb.Bisector.SupportingLine;
OrientedSide sideA = oppositeBoundary1.Side(this.Position);
OrientedSide sideB = oppositeLine.Side(this.Position);
OrientedSide sideC = oppositeBoundary2.Side(this.Position);
//return sideA == OrientedSide.Negative && sideB == OrientedSide.Negative && sideC == OrientedSide.Negative;
return(sideA == OrientedSide.Negative && sideB == OrientedSide.Negative && sideC == OrientedSide.Negative);
});
// TODO: Is this legitimate?
if (oppositeNode == null)
{
Debug.Assert(false);
return;
}
// oppositeNode is Y in the paper
Debug.Assert(oppositeNode != null);
// * insert both new nodes into the SLAV (break one LAV into two parts). Vertex V1 will be
// interconnected between the predecessor of V and the vertex/node which is an end point of
// the opposite line segment. V2 will be connected between the successor of V and the vertex/
// node which is a starting point of the opposite line segment. This step actually splits the
// polygon shape into two parts.
// Set up nodes according to the naming conventions in the Felkel et al paper.
CircularLinkedListNode <Vertex> nodeY = oppositeNode;
CircularLinkedListNode <Vertex> nodeX = oppositeNode.Next;
CircularLinkedListNode <Vertex> nodeM = nodeV.Previous;
CircularLinkedListNode <Vertex> nodeN = nodeV.Next;
// The LinkedList is split into two parts. The first part remains in the original list,
// the second part is placed into a new list.
CircularLinkedList <Vertex> lav2 = network.CreateLav();
// We search the list for either M or Y, whichever comes first. This tells us which
// algorithm to use to split the lav in two.
CircularLinkedListNode <Vertex> found = lav1.FindNode(node => node == nodeM || node == nodeY);
lav1.Remove(nodeV);
// Splice nodes from lav1 into lav2
Debug.Assert(found != null);
if (found == nodeY)
{
// Splice two sections of lav1 into lav2 with V1 and V2
// TODO: We have four nodes in a linked list defining two ranges First--->Y and N--->Last
// These ranges may be non-overlapping, or may be overlapping in some way. e.g. Y may come after N.
// 1) Find none overlapping range or ranges
// 2) Copy the range(s) to lav2
// 3) Insert nodeV2 into the correct place in lav2 after Y
// Another alternative 2
// 1. Is the break in the list between N and Y?
bool continuousNY = null != lav1.FindNodeFrom(nodeN, node => node == nodeY);
if (continuousNY)
{
lav2.AddLast(nodeV2);
lav2.SpliceLast(nodeN, nodeY);
lav2.IsCircular = true;
}
else // !continuousNY
{
lav2.SpliceLast(lav1.First, nodeY);
lav2.AddLast(nodeV2);
lav2.SpliceLast(nodeN, lav1.Last);
lav2.IsCircular = lav1.IsCircular;
}
// Alternative approach
//// 1. Remember whether lav1 is circular
//bool lav1Circularity = lav1.IsCircular;
//// 1a. Determine whether lav2 should be circular- by whether it is continuous between nodeN and nodeY
//bool continuousNY = null != lav1.FindNodeFrom(nodeN, node => node == nodeY);
//bool lav2Circularity = lav1Circularity || continuousNY;
//// 2. Make lav1 circular, so we can safely iterate from N to Y irrespective of the location of the list head
//lav1.IsCircular = true;
//// 3. Add nodeV2 into lav2
//lav2.AddLast(nodeV2);
//// 4. Splice from N to Y into Lav2
//lav2.SpliceLast(nodeN, nodeY);
//// 5. Restore the circularity of lav1 and lav2
//lav1.IsCircular = lav1Circularity;
//lav2.IsCircular = lav2Circularity;
// X--->M->V1
if (lav1.Count > 0) // <--- Is this needed?
{
Debug.Assert(lav1.First == nodeX);
Debug.Assert(lav1.Last == nodeM);
lav1.AddLast(nodeV1);
lav1.IsCircular = true;
}
}
else
{
Debug.Assert(found == nodeM);
// Splice one section of lav1 into lav2
// N--->Y->V2
lav2.SpliceFirst(nodeN, nodeY);
lav2.AddLast(nodeV2);
// First--->M->V2->X--->Last
if (lav1.Count > 0)
{
Debug.Assert(nodeM.Next == nodeX);
lav1.AddAfter(nodeM, nodeV1);
}
}
// * link the new nodes V1 and V2 with the appropriate edges
nodeV1.Value.inEdge = V.inEdge;
nodeV1.Value.outEdge = nodeY.Value.outEdge;
nodeV2.Value.inEdge = nodeY.Value.outEdge;
nodeV2.Value.outEdge = V.outEdge;
// f. for both nodes V1 and V2:
// * compute the new angle bisectors betwenne the line segment linked to them is step 2e
nodeV1.Value.Bisector = new Ray2D(nodeV1.Value.Bisector.Source, AngularBisector(nodeV1.Value.inEdge, nodeV1.Value.outEdge));
nodeV2.Value.Bisector = new Ray2D(nodeV2.Value.Bisector.Source, AngularBisector(nodeV2.Value.inEdge, nodeV2.Value.outEdge));
// * compute the intersections of these bisectors with the bisectors starting at their neighbour
// vertices according to the LAVs (e.g. at points N and Y and M and X in fig 6a.), the same
// way as in step 1c. New intersection points of both types may occur
// * store the nearest intersection into the priority queue
// TODO: [ Does this mean the nearest for V1 and the nearest for V2, or only the nearest of them both? ]
network.EnqueueNearestBisectorIntersection(lav1, nodeV1);
network.EnqueueNearestBisectorIntersection(lav2, nodeV2);
}
