/// <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();
}
