/// <summary> /// Run example. /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Euclidean_vector#Scalar_multiplication">Multiply vector by scalar</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Euclidean_vector#Dot_product">Multiply vector by vector (compute the dot product between two vectors)</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction">Vector addition and subtraction</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Outer_product">Outer Product of two vectors</seealso> public void Run() { // Initialize IFormatProvider to print matrix/vector data var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create vector "X" var vectorX = new DenseVector(new[] { 1.0, 2.0, 3.0, 4.0, 5.0 }); Console.WriteLine(@"Vector X"); Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Create vector "Y" var vectorY = new DenseVector(new[] { 5.0, 4.0, 3.0, 2.0, 1.0 }); Console.WriteLine(@"Vector Y"); Console.WriteLine(vectorY.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Multiply vector by scalar // 1. Using Multiply method and getting result into different vector instance var resultV = vectorX.Multiply(3.0); Console.WriteLine(@"Multiply vector by scalar using method Multiply. (result = X.Multiply(3.0))"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using operator "*" resultV = 3.0 * vectorX; Console.WriteLine(@"Multiply vector by scalar using operator *. (result = 3.0 * X)"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Using Multiply method and updating vector itself vectorX.Multiply(3.0, vectorX); Console.WriteLine(@"Multiply vector by scalar using method Multiply. (X.Multiply(3.0, X))"); Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Multiply vector by vector (compute the dot product between two vectors) // 1. Using operator "*" var dotProduct = vectorX * vectorY; Console.WriteLine(@"Dot product between two vectors using operator *. (result = X * Y)"); Console.WriteLine(dotProduct); Console.WriteLine(); // 2. Using DotProduct method and getting result into different vector instance dotProduct = vectorX.DotProduct(vectorY); Console.WriteLine(@"Dot product between two vectors using method DotProduct. (result = X.DotProduct(Y))"); Console.WriteLine(dotProduct.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Pointwise multiplies vector with another vector // 1. Using PointwiseMultiply method and getting result into different vector instance resultV = vectorX.PointwiseMultiply(vectorY); Console.WriteLine(@"Pointwise multiplies vector with another vector using method PointwiseMultiply. (result = X.PointwiseMultiply(Y))"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using PointwiseMultiply method and updating vector itself vectorX.PointwiseMultiply(vectorY, vectorX); Console.WriteLine(@"Pointwise multiplies vector with another vector using method PointwiseMultiply. (X.PointwiseMultiply(Y, X))"); Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Pointwise divide vector with another vector // 1. Using PointwiseDivide method and getting result into different vector instance resultV = vectorX.PointwiseDivide(vectorY); Console.WriteLine(@"Pointwise divide vector with another vector using method PointwiseDivide. (result = X.PointwiseDivide(Y))"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using PointwiseDivide method and updating vector itself vectorX.PointwiseDivide(vectorY, vectorX); Console.WriteLine(@"Pointwise divide vector with another vector using method PointwiseDivide. (X.PointwiseDivide(Y, X))"); Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Addition // 1. Using operator "+" resultV = vectorX + vectorY; Console.WriteLine(@"Add vectors using operator +. (result = X + Y)"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using Add method and getting result into different vector instance resultV = vectorX.Add(vectorY); Console.WriteLine(@"Add vectors using method Add. (result = X.Add(Y))"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Using Add method and updating vector itself vectorX.Add(vectorY, vectorX); Console.WriteLine(@"Add vectors using method Add. (X.Add(Y, X))"); Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Subtraction // 1. Using operator "-" resultV = vectorX - vectorY; Console.WriteLine(@"Subtract vectors using operator -. (result = X - Y)"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using Subtract method and getting result into different vector instance resultV = vectorX.Subtract(vectorY); Console.WriteLine(@"Subtract vectors using method Subtract. (result = X.Subtract(Y))"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Using Subtract method and updating vector itself vectorX.Subtract(vectorY, vectorX); Console.WriteLine(@"Subtract vectors using method Subtract. (X.Subtract(Y, X))"); Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Divide by scalar // 1. Using Divide method and getting result into different vector instance resultV = vectorX.Divide(3.0); Console.WriteLine(@"Divide vector by scalar using method Divide. (result = A.Divide(3.0))"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using Divide method and updating vector itself vectorX.Divide(3.0, vectorX); Console.WriteLine(@"Divide vector by scalar using method Divide. (X.Divide(3.0, X))"); Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Outer Product of two vectors // 1. Using instanse method OuterProduct var resultM = vectorX.OuterProduct(vectorY); Console.WriteLine(@"Outer Product of two vectors using method OuterProduct. (X.OuterProduct(Y))"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using static method of the Vector class resultM = Vector.OuterProduct(vectorX, vectorY); Console.WriteLine(@"Outer Product of two vectors using method OuterProduct. (Vector.OuterProduct(X,Y))"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); }
private static void SetRealVertices(Workspace workspace) { Vector<double> fittedPlaneVector = GeometryHelper.FitPlaneToPoints(workspace.PointCloud.ToArray()); if (fittedPlaneVector == null) { return; } Point3D projectedPoint = GeometryHelper.ProjectPoint3DToPlane(workspace.PointCloud.First(), fittedPlaneVector); Vector<double> planeNormal = new DenseVector(new[] { fittedPlaneVector[0], fittedPlaneVector[1], fittedPlaneVector[2] }); Point3D[] vertices3D = workspace.Vertices3D; Point[] vertices = workspace.Vertices.ToArray(); for (int i = 0; i < vertices.Length; i++) { Vector<double> pointOnPlane = new DenseVector(new[] { projectedPoint.X, projectedPoint.Y, projectedPoint.Z }); Vector<double> pointOnLine = new DenseVector(new double[] { vertices3D[i].X, vertices3D[i].Y, vertices3D[i].Z }); double d = (pointOnPlane.Subtract(pointOnLine)).DotProduct(planeNormal) / (pointOnLine.DotProduct(planeNormal)); Vector<double> intersection = pointOnLine + pointOnLine.Multiply(d); workspace.FittedVertices[i] = new Point3D(intersection[0], intersection[1], intersection[2]); } workspace.PlaneVector = fittedPlaneVector; }
public void SetRealVertices(Workspace workspace) { Vector<double> fittedPlaneVector = GeometryHelper.FitPlaneToPoints(workspace.PointCloud.ToArray()); if (fittedPlaneVector == null) { return; } Point3D projectedPoint = GeometryHelper.ProjectPoint3DToPlane(workspace.PointCloud.First(), fittedPlaneVector); Vector<double> planeNormal = new DenseVector(new[] { fittedPlaneVector[0], fittedPlaneVector[1], fittedPlaneVector[2] }); CameraSpacePoint[] csps = { new CameraSpacePoint() }; Point[] vertices = workspace.Vertices.ToArray(); for (int i = 0; i < vertices.Length; i++) { Point vertex = vertices[i]; kinectStreamer.CoordinateMapper.MapDepthPointsToCameraSpace( new[] { new DepthSpacePoint { X = (float)vertex.X, Y = (float)vertex.Y } }, new ushort[] { 1 }, csps); Vector<double> pointOnPlane = new DenseVector(new[] { projectedPoint.X, projectedPoint.Y, projectedPoint.Z }); Vector<double> pointOnLine = new DenseVector(new double[] { csps[0].X, csps[0].Y, csps[0].Z }); double d = (pointOnPlane.Subtract(pointOnLine)).DotProduct(planeNormal) / (pointOnLine.DotProduct(planeNormal)); Vector<double> intersection = pointOnLine + pointOnLine.Multiply(d); workspace.FittedVertices[i] = new Point3D(intersection[0], intersection[1], intersection[2]); } workspace.PlaneVector = fittedPlaneVector; }
/// <summary> /// Construct an initial simplex, given starting guesses for the constants, and /// initial step sizes for each dimension /// </summary> private static Vector<double>[] InitializeVertices(SimplexConstant[] simplexConstants) { int numDimensions = simplexConstants.Length; Vector<double>[] vertices = new Vector<double>[numDimensions + 1]; // define one point of the simplex as the given initial guesses Vector<double> p0 = new DenseVector(numDimensions); for (int i = 0; i < numDimensions; i++) { p0[i] = simplexConstants[i].Value; } // now fill in the vertices, creating the additional points as: // P(i) = P(0) + Scale(i) * UnitVector(i) vertices[0] = p0; for (int i = 0; i < numDimensions; i++) { double scale = simplexConstants[i].InitialPerturbation; Vector unitVector = new DenseVector(numDimensions); unitVector[i] = 1; vertices[i + 1] = p0.Add(unitVector.Multiply(scale)); } return vertices; }
/// <summary> /// Compute the centroid of all points except the worst /// </summary> /// <param name="vertices"></param> /// <param name="errorProfile"></param> /// <returns></returns> private static Vector ComputeCentroid(Vector<double>[] vertices, ErrorProfile errorProfile) { int numVertices = vertices.Length; // find the centroid of all points except the worst one Vector centroid = new DenseVector(numVertices - 1); for (int i = 0; i < numVertices; i++) { if (i != errorProfile.HighestIndex) { centroid = (Vector) centroid.Add(vertices[i]); } } return (Vector) centroid.Multiply(1.0d / (numVertices - 1)); }
public static Point3D ProjectPoint3DToPlane(Point3D point, Vector<double> planeVectors) { double distance = CalculatePointPlaneDistance(point, planeVectors); double a = planeVectors[0]; double b = planeVectors[1]; double c = planeVectors[2]; Vector<double> planeNormal = new DenseVector(new[] { a, b, c }); double x = point.X; double y = point.Y; double z = point.Z; Vector<double> pointVector = new DenseVector(new[] { x, y, z }); pointVector.Subtract(planeNormal.Multiply(distance)); return new Point3D { X = pointVector[0], Y = pointVector[1], Z = pointVector[2] }; }
public static double[] bar3gfBarnes(double[][] ec,double[] ep, double[] ed, double ten) { // Compute the internal force vector for a cable element according to: // FORM-FINDING AND ANALYSIS OF PRESTRESSED NETS AND MEMBRANES // by M. R. BARNES (1988) //ed = [a_1 a_2 ... a_6]; Element nodal displacements //ep = [E A]; element properties //ten = [ten]; Specified initial element tension //OUTPUT: //ef = F_int = [f_1 f_2 ... f_6]'; //ec format: [x,y,z][node1,node2...] //ed format: [node1x, node1y, node1z, node2x...] double l0 = getElementLength(ec); double[][] ecUpdated = updateEcWithDisp(ec, ed); double l = getElementLength(ecUpdated); //Current length //Current element force double tm = ten + (ep[0] * ep[1] / l0) * (l - l0); //Direction vector Vector v = new DenseVector(3); for (int i = 0; i < 3; i++) { v[i] = ecUpdated[i][0] - ecUpdated[i][1]; } double vl = v.Norm(2); Vector x = new DenseVector(6); for (int i = 0; i < 3; i++) { x[i] = v[i] / vl; } //Reverse direction vector for (int i = 0; i < 3; i++) { x[i+3] = -v[i] / vl; } return x.Multiply(tm).ToArray(); }