// The return value is whether we should try a second pass if this is called on the first pass,
        // using spliceTarget to wrap up dead-ends on the target side.
        bool ExtendSpliceWorker(VisibilityVertex spliceSource, Directions extendDir, Directions spliceTargetDir
                                , LineSegment maxDesiredSegment, LineSegment maxVisibilitySegment
                                , bool isOverlapped, out VisibilityVertex spliceTarget)
        {
            // This is called after having created at least one extension vertex (initially, the
            // first one added outside the obstacle), so we know extendVertex will be there. spliceSource
            // is the vertex to the OppositeDir(spliceTargetDir) of that extendVertex.
            VisibilityVertex extendVertex = StaticGraphUtility.FindNextVertex(spliceSource, spliceTargetDir);

            spliceTarget = StaticGraphUtility.FindNextVertex(extendVertex, spliceTargetDir);
            for (; ;)
            {
                if (!GetNextSpliceSource(ref spliceSource, spliceTargetDir, extendDir))
                {
                    break;
                }

                // spliceSource is now on the correct edge relative to the desired nextExtendPoint.
                // spliceTarget is in the opposite direction of the extension-line-to-spliceSource.
                Point nextExtendPoint = StaticGraphUtility.FindBendPointBetween(extendVertex.Point
                                                                                , spliceSource.Point, CompassVector.OppositeDir(spliceTargetDir));

                // We test below for being on or past maxDesiredSegment; here we may be skipping
                // over maxDesiredSegmentEnd which is valid since we want to be sure to go to or
                // past limitRect, but be sure to stay within maxVisibilitySegment.
                if (IsPointPastSegmentEnd(maxVisibilitySegment, nextExtendPoint))
                {
                    break;
                }

                spliceTarget = GetSpliceTarget(ref spliceSource, spliceTargetDir, nextExtendPoint);

                //StaticGraphUtility.Test_DumpVisibilityGraph(ObstacleTree, VisGraph);

                if (null == spliceTarget)
                {
                    // This may be because spliceSource was created just for Group boundaries.  If so,
                    // skip to the next nextExtendVertex location.
                    if (this.IsSkippableSpliceSourceWithNullSpliceTarget(spliceSource, extendDir))
                    {
                        continue;
                    }

                    // We're at a dead-end extending from the source side, or there is an intervening obstacle, or both.
                    // Don't splice across lateral group boundaries.
                    if (ObstacleTree.SegmentCrossesAnObstacle(spliceSource.Point, nextExtendPoint))
                    {
                        return(false);
                    }
                }

                // We might be walking through a point where a previous chain dead-ended.
                VisibilityVertex nextExtendVertex = VisGraph.FindVertex(nextExtendPoint);
                if (null != nextExtendVertex)
                {
                    if ((null == spliceTarget) || (null != this.VisGraph.FindEdge(extendVertex.Point, nextExtendPoint)))
                    {
                        // We are probably along a ScanSegment so visibility in this direction has already been determined.
                        // Stop and don't try to continue extension from the opposite side.  If we continue splicing here
                        // it might go across an obstacle.
                        if (null == spliceTarget)
                        {
                            Debug_VerifyNonOverlappedExtension(isOverlapped, extendVertex, nextExtendVertex, spliceSource: null, spliceTarget: null);
                            FindOrAddEdge(extendVertex, nextExtendVertex, isOverlapped ? ScanSegment.OverlappedWeight : ScanSegment.NormalWeight);
                        }
                        return(false);
                    }

                    // This should always have been found in the find-the-next-target loop above if there is
                    // a vertex (which would be nextExtendVertex, which we just found) between spliceSource
                    // and spliceTarget.  Even for a sparse graph, an edge should not skip over a vertex.
                    StaticGraphUtility.Assert(spliceTarget == StaticGraphUtility.FindNextVertex(nextExtendVertex, spliceTargetDir)
                                              , "no edge exists between an existing nextExtendVertex and spliceTarget"
                                              , ObstacleTree, VisGraph);
                }
                else
                {
                    StaticGraphUtility.Assert((null == spliceTarget) ||
                                              spliceTargetDir == PointComparer.GetPureDirection(nextExtendPoint, spliceTarget.Point)
                                              , "spliceTarget is not to spliceTargetDir of nextExtendVertex"
                                              , ObstacleTree, VisGraph);
                    nextExtendVertex = this.AddVertex(nextExtendPoint);
                }
                FindOrAddEdge(extendVertex, nextExtendVertex, isOverlapped ? ScanSegment.OverlappedWeight : ScanSegment.NormalWeight);

                Debug_VerifyNonOverlappedExtension(isOverlapped, extendVertex, nextExtendVertex, spliceSource, spliceTarget);

                // This will split the edge if targetVertex is non-null; otherwise we are at a dead-end
                // on the target side so must not create a vertex as it would be inside an obstacle.
                FindOrAddEdge(spliceSource, nextExtendVertex, isOverlapped ? ScanSegment.OverlappedWeight : ScanSegment.NormalWeight);
                if (isOverlapped)
                {
                    isOverlapped = this.SeeIfSpliceIsStillOverlapped(extendDir, nextExtendVertex);
                }
                extendVertex = nextExtendVertex;

                // Test GetDirections because it may return Directions. None.
                if (0 == (extendDir & PointComparer.GetDirections(nextExtendPoint, maxDesiredSegment.End)))
                {
                    // At or past the desired max extension point, so we're done.
                    spliceTarget = null;
                    break;
                }
            }
            return(null != spliceTarget);
        }