public static LengthSquared ( double x ) : double | ||
x | double | |
Résultat | double |
/// <summary> /// Creates the Delaunay triangulation of the input data. /// Be careful with concurrency, because during the computation, the vertex position arrays get resized. /// </summary> /// <param name="data"></param> /// <returns></returns> public static DelaunayTriangulation <TVertex, TCell> Create(IEnumerable <TVertex> data) { if (data == null) { throw new ArgumentException("data can't be null."); } if (!(data is IList <TVertex>)) { data = data.ToArray(); } if (data.Count() == 0) { return new DelaunayTriangulation <TVertex, TCell> { Cells = Enumerable.Empty <TCell>() } } ; int dimension = data.First().PositionArray.Length; // Resize the arrays and lift the data. foreach (var p in data) { double lenSq = MathHelper.LengthSquared(p.PositionArray); var v = p.PositionArray; Array.Resize(ref v, dimension + 1); p.PositionArray = v; p[dimension] = lenSq; } // Find the convex hull var delaunayFaces = ConvexHullInternal.GetConvexFacesInternal <TVertex, TCell>(data); // Resize the data back foreach (var p in data) { var v = p.PositionArray; Array.Resize(ref v, dimension); p.PositionArray = v; } // Remove the "upper" faces for (var i = delaunayFaces.Count - 1; i >= 0; i--) { var candidate = delaunayFaces[i]; if (candidate.Normal[dimension] >= 0) { for (int fi = 0; fi < candidate.AdjacentFaces.Length; fi++) { var f = candidate.AdjacentFaces[fi]; if (f != null) { for (int j = 0; j < f.AdjacentFaces.Length; j++) { if (object.ReferenceEquals(f.AdjacentFaces[j], candidate)) { f.AdjacentFaces[j] = null; } } } } var li = delaunayFaces.Count - 1; delaunayFaces[i] = delaunayFaces[li]; delaunayFaces.RemoveAt(li); } } // Create the "TCell" representation. int cellCount = delaunayFaces.Count; var cells = new TCell[cellCount]; for (int i = 0; i < cellCount; i++) { var face = delaunayFaces[i]; var pointCloud = new TVertex[dimension + 1]; for (int j = 0; j <= dimension; j++) { pointCloud[j] = (TVertex)face.Vertices[j].Vertex; } cells[i] = new TCell { Vertices = pointCloud, Adjacency = new TCell[dimension + 1] }; face.Tag = i; } for (int i = 0; i < cellCount; i++) { var face = delaunayFaces[i]; var cell = cells[i]; for (int j = 0; j <= dimension; j++) { if (face.AdjacentFaces[j] == null) { continue; } cell.Adjacency[j] = cells[face.AdjacentFaces[j].Tag]; } } return(new DelaunayTriangulation <TVertex, TCell> { Cells = cells }); }
/// <summary> /// Finds (dimension + 1) initial points. /// </summary> /// <param name="extremes"></param> /// <returns></returns> private List <VertexWrap> FindInitialPoints(List <VertexWrap> extremes) { List <VertexWrap> initialPoints = new List <VertexWrap>();// { extremes[0], extremes[1] }; VertexWrap first = null, second = null; double maxDist = 0; double[] temp = new double[Dimension]; for (int i = 0; i < extremes.Count - 1; i++) { var a = extremes[i]; for (int j = i + 1; j < extremes.Count; j++) { var b = extremes[j]; MathHelper.SubtractFast(a.PositionData, b.PositionData, temp); var dist = MathHelper.LengthSquared(temp); if (dist > maxDist) { first = a; second = b; maxDist = dist; } } } initialPoints.Add(first); initialPoints.Add(second); for (int i = 2; i <= Dimension; i++) { double maximum = 0.000001; VertexWrap maxPoint = null; for (int j = 0; j < extremes.Count; j++) { var extreme = extremes[j]; if (initialPoints.Contains(extreme)) { continue; } var val = GetSquaredDistanceSum(extreme, initialPoints); if (val > maximum) { maximum = val; maxPoint = extreme; } } if (maxPoint != null) { initialPoints.Add(maxPoint); } else { int vCount = InputVertices.Count; for (int j = 0; j < vCount; j++) { var point = InputVertices[j]; if (initialPoints.Contains(point)) { continue; } var val = GetSquaredDistanceSum(point, initialPoints); if (val > maximum) { maximum = val; maxPoint = point; } } if (maxPoint != null) { initialPoints.Add(maxPoint); } else { ThrowSingular(); } } } return(initialPoints); }
/// <summary> /// Finds (dimension + 1) initial points. /// </summary> /// <param name="extremes"></param> /// <returns></returns> private List <int> FindInitialPoints(List <int> extremes) { List <int> initialPoints = new List <int>(); int first = -1, second = -1; double maxDist = 0; double[] temp = new double[Dimension]; for (int i = 0; i < extremes.Count - 1; i++) { var a = extremes[i]; for (int j = i + 1; j < extremes.Count; j++) { var b = extremes[j]; MathHelper.SubtractFast(a, b, temp); var dist = MathHelper.LengthSquared(temp); if (dist > maxDist) { first = a; second = b; maxDist = dist; } } } initialPoints.Add(first); initialPoints.Add(second); for (int i = 2; i <= Dimension; i++) { double maximum = double.NegativeInfinity; int maxPoint = -1; for (int j = 0; j < extremes.Count; j++) { var extreme = extremes[j]; if (initialPoints.Contains(extreme)) { continue; } var val = GetSquaredDistanceSum(extreme, initialPoints); if (val > maximum) { maximum = val; maxPoint = extreme; } } if (maxPoint >= 0) { initialPoints.Add(maxPoint); } else { int vCount = Vertices.Length; for (int j = 0; j < vCount; j++) { if (initialPoints.Contains(j)) { continue; } var val = GetSquaredDistanceSum(j, initialPoints); if (val > maximum) { maximum = val; maxPoint = j; } } if (maxPoint >= 0) { initialPoints.Add(maxPoint); } else { ThrowSingular(); } } } return(initialPoints); }