public static VNode ProcessCircleEvent(VCircleEvent e, VNode root, VoronoiGraph vg, out VDataNode[] circleCheckList) { VEdgeNode eo; VDataNode b = e.NodeN; VDataNode a = LeftDataNode(b); VDataNode c = RightDataNode(b); if (a == null || b.Parent == null || c == null || !a.DataPoint.Equals(e.NodeL.DataPoint) || !c.DataPoint.Equals(e.NodeR.DataPoint)) { circleCheckList = new VDataNode[] { }; return root; // Abbruch da sich der Graph verändert hat } VEdgeNode eu = (VEdgeNode)b.Parent; circleCheckList = new[] { a, c }; //1. Create the new Vertex Vector2 vNew = new Vector2(e.Center.X, e.Center.Y); // VNew[0] = Fortune.ParabolicCut(a.DataPoint[0],a.DataPoint[1],c.DataPoint[0],c.DataPoint[1],ys); // VNew[1] = (ys + a.DataPoint[1])/2 - 1/(2*(ys-a.DataPoint[1]))*(VNew[0]-a.DataPoint[0])*(VNew[0]-a.DataPoint[0]); vg.Vertices.Add(vNew); //2. Find out if a or c are in a distand part of the tree (the other is then b's sibling) and assign the new vertex if (eu.Left == b) // c is sibling { eo = EdgeToRightDataNode(a); // replace eu by eu's Right eu.Parent.Replace(eu, eu.Right); } else // a is sibling { eo = EdgeToRightDataNode(b); // replace eu by eu's Left eu.Parent.Replace(eu, eu.Left); } eu.Edge.AddVertex(vNew); // ///////////////////// uncertain // if(eo==eu) // return root; // ///////////////////// eo.Edge.AddVertex(vNew); //2. Replace eo by new Edge VoronoiEdge ve = new VoronoiEdge(); ve.LeftData = a.DataPoint; ve.RightData = c.DataPoint; ve.AddVertex(vNew); vg.Edges.Add(ve); VEdgeNode ven = new VEdgeNode(ve, false); ven.Left = eo.Left; ven.Right = eo.Right; if (eo.Parent == null) return ven; eo.Parent.Replace(eo, ven); return root; }
/// <summary> /// Will return the new root (unchanged except in start-up) /// </summary> public static VNode ProcessDataEvent(VDataEvent e, VNode root, VoronoiGraph vg, double ys, out VDataNode[] circleCheckList) { if (root == null) { root = new VDataNode(e.DataPoint); circleCheckList = new[] { (VDataNode)root }; return root; } //1. Find the node to be replaced VNode c = FindDataNode(root, ys, e.DataPoint.X); //2. Create the subtree (ONE Edge, but two VEdgeNodes) VoronoiEdge ve = new VoronoiEdge(); ve.LeftData = ((VDataNode)c).DataPoint; ve.RightData = e.DataPoint; ve.VVertexA = Fortune.VVUnkown; ve.VVertexB = Fortune.VVUnkown; vg.Edges.Add(ve); VNode subRoot; if (Math.Abs(ve.LeftData.Y - ve.RightData.Y) < 1e-10) { if (ve.LeftData.X < ve.RightData.X) { subRoot = new VEdgeNode(ve, false); subRoot.Left = new VDataNode(ve.LeftData); subRoot.Right = new VDataNode(ve.RightData); } else { subRoot = new VEdgeNode(ve, true); subRoot.Left = new VDataNode(ve.RightData); subRoot.Right = new VDataNode(ve.LeftData); } circleCheckList = new[] { (VDataNode)subRoot.Left, (VDataNode)subRoot.Right }; } else { subRoot = new VEdgeNode(ve, false); subRoot.Left = new VDataNode(ve.LeftData); subRoot.Right = new VEdgeNode(ve, true); subRoot.Right.Left = new VDataNode(ve.RightData); subRoot.Right.Right = new VDataNode(ve.LeftData); circleCheckList = new[] { (VDataNode)subRoot.Left, (VDataNode)subRoot.Right.Left, (VDataNode)subRoot.Right.Right }; } //3. Apply subtree if (c.Parent == null) return subRoot; c.Parent.Replace(c, subRoot); return root; }
/// <summary> /// Applies an optional cleanup method needed by Benjamine Ditter for /// laser data calculations. This is not used by the MapWindow calculations /// </summary> /// <param name="vg">The output voronoi graph created in the Compute Voronoi Graph section</param> /// <param name="minLeftRightDist">A minimum left to right distance</param> /// <returns>The Voronoi Graph after it has been filtered.</returns> public static VoronoiGraph FilterVg(VoronoiGraph vg, double minLeftRightDist) { VoronoiGraph vgErg = new VoronoiGraph(); foreach (VoronoiEdge ve in vg.Edges) { if (ve.LeftData.Distance(ve.RightData) >= minLeftRightDist) vgErg.Edges.Add(ve); } foreach (VoronoiEdge ve in vgErg.Edges) { vgErg.Vertices.Add(ve.VVertexA); vgErg.Vertices.Add(ve.VVertexB); } return vgErg; }
/// <summary> /// The original algorithm simply allows edges that have one defined point and /// another "NAN" point. Simply excluding the not a number coordinates fails /// to preserve the known direction of the ray. We only need to extend this /// long enough to encounter the bounding box, not infinity. /// </summary> /// <param name="graph">The VoronoiGraph with the edge list</param> /// <param name="bounds">The polygon bounding the datapoints</param> private static void HandleBoundaries(VoronoiGraph graph, IEnvelope bounds) { List<ILineString> boundSegments = new List<ILineString>(); List<VoronoiEdge> unboundEdges = new List<VoronoiEdge>(); // Identify bound edges for intersection testing foreach (VoronoiEdge edge in graph.Edges) { if(edge.VVertexA.ContainsNan() || edge.VVertexB.ContainsNan()) { unboundEdges.Add(edge); continue; } boundSegments.Add(new LineString(new List<Coordinate>{edge.VVertexA.ToCoordinate(), edge.VVertexB.ToCoordinate()})); } // calculate a length to extend a ray to look for intersections IEnvelope env = bounds; double h = env.Height; double w = env.Width; double len = Math.Sqrt(w * w + h * h); // len is now long enough to pass entirely through the dataset no matter where it starts foreach (VoronoiEdge edge in unboundEdges) { // the unbound line passes thorugh start Coordinate start = (edge.VVertexB.ContainsNan()) ? edge.VVertexA.ToCoordinate() : edge.VVertexB.ToCoordinate(); // the unbound line should have a direction normal to the line joining the left and right source points double dx = edge.LeftData.X - edge.RightData.X; double dy = edge.LeftData.Y - edge.RightData.Y; double l = Math.Sqrt(dx*dx + dy*dy); // the slope of the bisector between left and right double sx = -dy/l; double sy = dx/l; Coordinate center = bounds.Center(); if((start.X > center.X && start.Y > center.Y) || (start.X < center.X && start.Y < center.Y)) { sx = dy/l; sy = -dx/l; } Coordinate end1 = new Coordinate(start.X + len*sx, start.Y + len * sy); Coordinate end2 = new Coordinate(start.X - sx * len, start.Y - sy * len); Coordinate end = (end1.Distance(center) < end2.Distance(center)) ? end2 : end1; if(bounds.Contains(end)) { end = new Coordinate(start.X - sx * len, start.Y - sy * len); } if (edge.VVertexA.ContainsNan()) { edge.VVertexA = new Vector2(end.ToArray()); } else { edge.VVertexB = new Vector2(end.ToArray()); } } }
/// <summary> /// Calculates a list of edges and junction vertices by using the specified points. /// This defaults to not using any tolerance for determining if points are equal, /// and will not use the cleanup algorithm, which breaks the HandleBoundaries /// method in the Voronoi class. /// </summary> /// <param name="vertices">The original points to use during the calculation</param> /// <returns>A VoronoiGraph structure containing the output geometries</returns> public static VoronoiGraph ComputeVoronoiGraph(double[] vertices) { //BinaryPriorityQueue pq = new BinaryPriorityQueue(); SortedDictionary<VEvent, VEvent> pq = new SortedDictionary<VEvent, VEvent>(); Dictionary<VDataNode, VCircleEvent> currentCircles = new Dictionary<VDataNode, VCircleEvent>(); VoronoiGraph vg = new VoronoiGraph(); VNode rootNode = null; for(int i = 0; i < vertices.Length/2; i++) { //pq.Push(new VDataEvent(new Vector(vertex))); VDataEvent e = new VDataEvent(new Vector2(vertices, i*2)); if (pq.ContainsKey(e)) continue; pq.Add(e, e); } while (pq.Count > 0) { //VEvent ve = pq.Pop() as VEvent; VEvent ve = pq.First().Key; pq.Remove(ve); VDataNode[] circleCheckList = new VDataNode[] { }; if (ve is VDataEvent) { rootNode = VNode.ProcessDataEvent(ve as VDataEvent, rootNode, vg, ve.Y, out circleCheckList); } else if (ve is VCircleEvent) { currentCircles.Remove(((VCircleEvent)ve).NodeN); if (!((VCircleEvent)ve).Valid) continue; rootNode = VNode.ProcessCircleEvent(ve as VCircleEvent, rootNode, vg, out circleCheckList); } else if (ve != null) throw new Exception("Got event of type " + ve.GetType() + "!"); foreach (VDataNode vd in circleCheckList) { if (currentCircles.ContainsKey(vd)) { currentCircles[vd].Valid = false; currentCircles.Remove(vd); } if (ve == null) continue; VCircleEvent vce = VNode.CircleCheckDataNode(vd, ve.Y); if (vce == null) continue; //pq.Push(vce); pq.Add(vce, vce); currentCircles[vd] = vce; } if (!(ve is VDataEvent)) continue; Vector2 dp = ((VDataEvent)ve).DataPoint; foreach (VCircleEvent vce in currentCircles.Values) { if (MathTools.Dist(dp.X, dp.Y, vce.Center.X, vce.Center.Y) < vce.Y - vce.Center.Y && Math.Abs(MathTools.Dist(dp.X, dp.Y, vce.Center.X, vce.Center.Y) - (vce.Y - vce.Center.Y)) > 1e-10) vce.Valid = false; } } // This is where the MapWindow version should exit since it uses the HandleBoundaries // function instead. The following code is needed for Benjamin Ditter's original process to work. if (!DoCleanup) return vg; VNode.CleanUpTree(rootNode); foreach (VoronoiEdge ve in vg.Edges) { if (ve.Done) continue; if (ve.VVertexB != VVUnkown) continue; ve.AddVertex(VVInfinite); if (Math.Abs(ve.LeftData.Y - ve.RightData.Y) < 1e-10 && ve.LeftData.X < ve.RightData.X) { Vector2 t = ve.LeftData; ve.LeftData = ve.RightData; ve.RightData = t; } } ArrayList minuteEdges = new ArrayList(); foreach (VoronoiEdge ve in vg.Edges) { if (ve.IsPartlyInfinite || !ve.VVertexA.Equals(ve.VVertexB)) continue; minuteEdges.Add(ve); // prevent rounding errors from expanding to holes foreach (VoronoiEdge ve2 in vg.Edges) { if (ve2.VVertexA.Equals(ve.VVertexA)) ve2.VVertexA = ve.VVertexA; if (ve2.VVertexB.Equals(ve.VVertexA)) ve2.VVertexB = ve.VVertexA; } } foreach (VoronoiEdge ve in minuteEdges) { vg.Edges.Remove(ve); } return vg; }