public void ToDenseVector()
{
var l = Math.Sqrt(1 * 1 + 2 * 2 + 3 * 3);
var uv = new UnitVector3D(1 / l, 2 / l, 3 / l);
var denseVector = uv.ToVector();
Assert.AreEqual(3, denseVector.Count);
Assert.AreEqual(1 / l, denseVector[0], 1e-6);
Assert.AreEqual(2 / l, denseVector[1], 1e-6);
Assert.AreEqual(3 / l, denseVector[2], 1e-6);
}
/// <summary>
/// Gets a rotation matrix corresponding to a forward vector.
/// </summary>
/// <param name="forward">The specified forward vector.</param>
/// <returns>The corresponding rotation matrix.</returns>
/// <remarks>The X axis of the matrix will correspond to the specified forward vector.</remarks>
public static Matrix <double> ToRotationMatrix(this UnitVector3D forward)
{
// Compute left and up directions from the given forward direction.
var left = UnitVector3D.ZAxis.CrossProduct(forward);
var up = forward.CrossProduct(left);
// Create a corresponding 3x3 matrix from the 3 directions.
var rotationMatrix = Matrix <double> .Build.Dense(3, 3);
rotationMatrix.SetColumn(0, forward.ToVector());
rotationMatrix.SetColumn(1, left.ToVector());
rotationMatrix.SetColumn(2, up.ToVector());
return(rotationMatrix);
}
public static Vector <double> solve(
List <double[]> Vertices,
List <int[]> TrianglesVertices,
List <double[]> FacetNormals,
Vector <double> X, Point3D oRoot,
UnitVector3D vDir1,
UnitVector3D vDir2)
{
UnitVector3D dx, dy, dz;
dx = new UnitVector3D(new double[] { 1, 0, 0 });
dy = new UnitVector3D(new double[] { 0, 1, 0 });
dz = new UnitVector3D(new double[] { 0, 0, 1 });
UnitVector3D PlaneNormal = vDir1.CrossProduct(vDir2);
double E = 200 * 10 ^ 6;
double v = 0.3;
double h = 1;
double[,] MatrixK = new double[Vertices.Count * 3, Vertices.Count * 3];
double[] Vectorq = new double[Vertices.Count * 3];
double[,] MatrixD = new double[3, 3];
MatrixD[0, 0] = (E / ((1 + v) * (1 - 2 * v))) * (1 - v);
MatrixD[0, 1] = (E / ((1 + v) * (1 - 2 * v))) * (v);
MatrixD[1, 1] = (E / ((1 + v) * (1 - 2 * v))) * (1 - v);
MatrixD[1, 0] = (E / ((1 + v) * (1 - 2 * v))) * (v);
MatrixD[2, 2] = (E / ((1 + v) * (1 - 2 * v))) * (1 - v / 2);
Matrix <double> D = Matrix <double> .Build.DenseOfArray(MatrixD);
for (int j = 0; j < TrianglesVertices.Count; j++)
{
int[] tri = TrianglesVertices[j];
UnitVector3D dx0, dy0, dz0;
UnitVector3D dxn, dyn, dzn;
Point3D p1, p2, p3;
Point3D p10, p20, p30;
Point3D p1n, p2n, p3n;
Point3D p11, p21, p31;
p1 = new Point3D(Vertices[tri[0]]);
p2 = new Point3D(Vertices[tri[1]]);
p3 = new Point3D(Vertices[tri[2]]);
p1n = new Point3D(new double[] { X[tri[0] * 2], X[tri[0] * 2 + 1], 0 });
p2n = new Point3D(new double[] { X[tri[1] * 2], X[tri[1] * 2 + 1], 0 });
p3n = new Point3D(new double[] { X[tri[2] * 2], X[tri[2] * 2 + 1], 0 });
dx0 = new UnitVector3D(p2.X - p1.X, p2.Y - p1.Y, p2.Z - p1.Z);
dz0 = new UnitVector3D(FacetNormals[j]);
dy0 = dz0.CrossProduct(dx0);
dxn = new UnitVector3D(p2n.X - p1n.X, p2n.Y - p1n.Y, p2n.Z - p1n.Z);
dzn = PlaneNormal;
dyn = dxn.CrossProduct(dzn);
p10 = new Point3D(new double[] { 0, 0, 0 });
p20 = new Point3D(new double[] { p2.ToVector().DotProduct(dx0.ToVector()) - p1.ToVector().DotProduct(dx0.ToVector()), 0, 0 });
p30 = new Point3D(new double[] { p3.ToVector().DotProduct(dx0.ToVector()) - p1.ToVector().DotProduct(dx0.ToVector()), p3.ToVector().DotProduct(dy0.ToVector()) - p1.ToVector().DotProduct(dy0.ToVector()), 0 });
p11 = new Point3D(new double[] { 0, 0, 0 });
p21 = new Point3D(new double[] { p2n.ToVector().DotProduct(dxn.ToVector()) - p1n.ToVector().DotProduct(dxn.ToVector()), 0, 0 });
p31 = new Point3D(new double[] { p3n.ToVector().DotProduct(dxn.ToVector()) - p1n.ToVector().DotProduct(dxn.ToVector()), p3n.ToVector().DotProduct(dyn.ToVector()) - p1n.ToVector().DotProduct(dyn.ToVector()), 0 });
double[,] Transform = new double[3 * 3, 3 * 3];
for (int i = 0; i < 3; i++)
{
Transform[i * 3 + 0, i * 3 + 0] = Math.Cos(dx0.AngleTo(dx).Radians);
Transform[i * 3 + 0, i * 3 + 1] = Math.Cos(dx0.AngleTo(dy).Radians);
Transform[i * 3 + 0, i * 3 + 2] = Math.Cos(dx0.AngleTo(dz).Radians);
Transform[i * 3 + 1, i * 3 + 0] = Math.Cos(dy0.AngleTo(dx).Radians);
Transform[i * 3 + 1, i * 3 + 1] = Math.Cos(dy0.AngleTo(dy).Radians);
Transform[i * 3 + 1, i * 3 + 2] = Math.Cos(dy0.AngleTo(dz).Radians);
Transform[i * 3 + 2, i * 3 + 0] = Math.Cos(dyn.AngleTo(dx).Radians);
Transform[i * 3 + 2, i * 3 + 1] = Math.Cos(dyn.AngleTo(dy).Radians);
Transform[i * 3 + 2, i * 3 + 2] = Math.Cos(dyn.AngleTo(dz).Radians);
}
double A = (p10.X * (p20.Y - p30.Y) + p20.X * (p30.Y - p10.Y) + p30.X * (p10.Y - p20.Y)) / 2;
double[,] MatrixB = new double[3, 3 * 3];
MatrixB[0, 0] = (1 / (2 * A)) * (p20.Y - p30.Y);
MatrixB[1, 1] = (1 / (2 * A)) * (p30.X - p20.X);
MatrixB[2, 0] = (1 / (2 * A)) * (p30.X - p20.X);
MatrixB[2, 1] = (1 / (2 * A)) * (p20.Y - p30.Y);
MatrixB[0, 3] = (1 / (2 * A)) * (p30.Y - p10.Y);
MatrixB[1, 4] = (1 / (2 * A)) * (p10.X - p30.X);
MatrixB[2, 3] = (1 / (2 * A)) * (p10.X - p30.X);
MatrixB[2, 4] = (1 / (2 * A)) * (p30.Y - p10.Y);
MatrixB[0, 6] = (1 / (2 * A)) * (p10.Y - p20.Y);
MatrixB[1, 7] = (1 / (2 * A)) * (p20.X - p10.X);
MatrixB[2, 6] = (1 / (2 * A)) * (p20.X - p10.X);
MatrixB[2, 7] = (1 / (2 * A)) * (p10.Y - p20.Y);
Matrix <double> T = Matrix <double> .Build.DenseOfArray(Transform);
Console.WriteLine(T);
Matrix <double> B = Matrix <double> .Build.DenseOfArray(MatrixB);
Console.WriteLine(B);
Matrix <double> Ke = B.Transpose() * D * B * h * A;
Console.WriteLine(Ke);
Ke = T.Transpose() * Ke * T;
Console.WriteLine(Ke);
for (int i1 = 0; i1 < 3; i1++)
{
for (int i2 = 0; i2 < 3; i2++)
{
for (int l = 0; l < 3; l++)
{
for (int c = 0; c < 3; c++)
{
MatrixK[tri[i1] * 3 + l, tri[i2] * 3 + c] += Ke[i1 * 3 + l, i2 * 3 + c];
}
}
}
}
Matrix <double> Temp = Matrix <double> .Build.DenseOfArray(MatrixK);
Console.WriteLine(Temp);
double[] vectorqt = new double[3 * 3];
vectorqt[0 * 3] += p11.X - p10.X;
vectorqt[0 * 3 + 1] += p11.Y - p10.Y;
vectorqt[1 * 3] += p21.X - p20.X;
vectorqt[1 * 3 + 1] += p21.Y - p20.Y;
vectorqt[2 * 3] += p31.X - p30.X;
vectorqt[2 * 3 + 1] += p31.Y - p30.Y;
Vector <double> qt = Vector <double> .Build.DenseOfArray(vectorqt);
Console.WriteLine(qt);
qt = T.Transpose() * qt * T;
Console.WriteLine(qt);
for (int i1 = 0; i1 < 3; i1++)
{
for (int l = 0; l < 3; l++)
{
Vectorq[tri[i1] * 3 + l] -= qt[i1 * 3 + l];
}
}
Vector <double> VTemp = Vector <double> .Build.DenseOfArray(Vectorq);
Console.WriteLine(VTemp);
}
Matrix <double> K = Matrix <double> .Build.DenseOfArray(MatrixK);
Console.WriteLine(K);
Vector <double> q = Vector <double> .Build.DenseOfArray(Vectorq);
Console.WriteLine(q);
Vector <double> Fi = K * q;
Console.WriteLine(Fi);
double w = 0.5;
Vector <double> qi = Vector <double> .Build.DenseOfArray(q.ToArray());
Vector <double> dqi = Vector <double> .Build.Dense(Vertices.Count);
for (int i = 0; i < 100; i++)
{
// Console.WriteLine(dqi);
dqi = K.Solve(Fi);
Console.WriteLine(dqi);
// Console.WriteLine(qi);
qi = qi + w * dqi;
// Console.WriteLine(qi);
// Console.WriteLine(Fi);
Fi = K * qi;
// Console.WriteLine(Fi);
}
return(qi);
}
public void ToDenseVector()
{
var l = Math.Sqrt(1 * 1 + 2 * 2 + 3 * 3);
var uv = new UnitVector3D(1 / l, 2 / l, 3 / l);
var denseVector = uv.ToVector();
Assert.AreEqual(3, denseVector.Count);
Assert.AreEqual(1 / l, denseVector[0], 1e-6);
Assert.AreEqual(2 / l, denseVector[1], 1e-6);
Assert.AreEqual(3 / l, denseVector[2], 1e-6);
}
public Vector <double> ToVector()
{
return(UnitVector3D1.ToVector());
}
public static Vector<double> solve(
List<double[]> Vertices,
List<int[]> TrianglesVertices,
List<double[]> FacetNormals,
Vector<double> X, Point3D oRoot,
UnitVector3D vDir1,
UnitVector3D vDir2)
{
UnitVector3D dx, dy, dz;
dx = new UnitVector3D(new double[] { 1, 0, 0 });
dy = new UnitVector3D(new double[] { 0, 1, 0 });
dz = new UnitVector3D(new double[] { 0, 0, 1 });
UnitVector3D PlaneNormal = vDir1.CrossProduct(vDir2);
double E = 200 * 10 ^ 6;
double v = 0.3;
double h = 1;
double[,] MatrixK = new double[Vertices.Count * 3, Vertices.Count * 3];
double[] Vectorq = new double[Vertices.Count * 3];
double[,] MatrixD = new double[3, 3];
MatrixD[0, 0] = (E / ((1 + v) * (1 - 2 * v))) * (1 - v);
MatrixD[0, 1] = (E / ((1 + v) * (1 - 2 * v))) * (v);
MatrixD[1, 1] = (E / ((1 + v) * (1 - 2 * v))) * (1 - v);
MatrixD[1, 0] = (E / ((1 + v) * (1 - 2 * v))) * (v);
MatrixD[2, 2] = (E / ((1 + v) * (1 - 2 * v))) * (1 - v / 2);
Matrix<double> D = Matrix<double>.Build.DenseOfArray(MatrixD);
for (int j = 0; j < TrianglesVertices.Count; j++) {
int[] tri = TrianglesVertices[j];
UnitVector3D dx0, dy0, dz0;
UnitVector3D dxn, dyn, dzn;
Point3D p1, p2, p3;
Point3D p10, p20, p30;
Point3D p1n, p2n, p3n;
Point3D p11, p21, p31;
p1 = new Point3D(Vertices[tri[0]]);
p2 = new Point3D(Vertices[tri[1]]);
p3 = new Point3D(Vertices[tri[2]]);
p1n = new Point3D(new double[] { X[tri[0] * 2], X[tri[0] * 2 + 1], 0 });
p2n = new Point3D(new double[] { X[tri[1] * 2], X[tri[1] * 2 + 1], 0 });
p3n = new Point3D(new double[] { X[tri[2] * 2], X[tri[2] * 2 + 1], 0 });
dx0 = new UnitVector3D(p2.X - p1.X, p2.Y - p1.Y, p2.Z - p1.Z);
dz0 = new UnitVector3D(FacetNormals[j]);
dy0 = dz0.CrossProduct(dx0);
dxn = new UnitVector3D(p2n.X - p1n.X, p2n.Y - p1n.Y, p2n.Z - p1n.Z);
dzn = PlaneNormal;
dyn = dxn.CrossProduct(dzn);
p10 = new Point3D(new double[] { 0, 0, 0 });
p20 = new Point3D(new double[] { p2.ToVector().DotProduct(dx0.ToVector()) - p1.ToVector().DotProduct(dx0.ToVector()), 0, 0 });
p30 = new Point3D(new double[] { p3.ToVector().DotProduct(dx0.ToVector()) - p1.ToVector().DotProduct(dx0.ToVector()), p3.ToVector().DotProduct(dy0.ToVector()) - p1.ToVector().DotProduct(dy0.ToVector()), 0 });
p11 = new Point3D(new double[] { 0, 0, 0 });
p21 = new Point3D(new double[] { p2n.ToVector().DotProduct(dxn.ToVector()) - p1n.ToVector().DotProduct(dxn.ToVector()), 0, 0 });
p31 = new Point3D(new double[] { p3n.ToVector().DotProduct(dxn.ToVector()) - p1n.ToVector().DotProduct(dxn.ToVector()), p3n.ToVector().DotProduct(dyn.ToVector()) - p1n.ToVector().DotProduct(dyn.ToVector()), 0 });
double[,] Transform = new double[3 * 3, 3 * 3];
for (int i = 0; i < 3; i++) {
Transform[i * 3 + 0, i * 3 + 0] = Math.Cos(dx0.AngleTo(dx).Radians);
Transform[i * 3 + 0, i * 3 + 1] = Math.Cos(dx0.AngleTo(dy).Radians);
Transform[i * 3 + 0, i * 3 + 2] = Math.Cos(dx0.AngleTo(dz).Radians);
Transform[i * 3 + 1, i * 3 + 0] = Math.Cos(dy0.AngleTo(dx).Radians);
Transform[i * 3 + 1, i * 3 + 1] = Math.Cos(dy0.AngleTo(dy).Radians);
Transform[i * 3 + 1, i * 3 + 2] = Math.Cos(dy0.AngleTo(dz).Radians);
Transform[i * 3 + 2, i * 3 + 0] = Math.Cos(dyn.AngleTo(dx).Radians);
Transform[i * 3 + 2, i * 3 + 1] = Math.Cos(dyn.AngleTo(dy).Radians);
Transform[i * 3 + 2, i * 3 + 2] = Math.Cos(dyn.AngleTo(dz).Radians);
}
double A = (p10.X * (p20.Y - p30.Y) + p20.X * (p30.Y - p10.Y) + p30.X * (p10.Y - p20.Y)) / 2;
double[,] MatrixB = new double[3, 3 * 3];
MatrixB[0, 0] = (1 / (2 * A)) * (p20.Y - p30.Y);
MatrixB[1, 1] = (1 / (2 * A)) * (p30.X - p20.X);
MatrixB[2, 0] = (1 / (2 * A)) * (p30.X - p20.X);
MatrixB[2, 1] = (1 / (2 * A)) * (p20.Y - p30.Y);
MatrixB[0, 3] = (1 / (2 * A)) * (p30.Y - p10.Y);
MatrixB[1, 4] = (1 / (2 * A)) * (p10.X - p30.X);
MatrixB[2, 3] = (1 / (2 * A)) * (p10.X - p30.X);
MatrixB[2, 4] = (1 / (2 * A)) * (p30.Y - p10.Y);
MatrixB[0, 6] = (1 / (2 * A)) * (p10.Y - p20.Y);
MatrixB[1, 7] = (1 / (2 * A)) * (p20.X - p10.X);
MatrixB[2, 6] = (1 / (2 * A)) * (p20.X - p10.X);
MatrixB[2, 7] = (1 / (2 * A)) * (p10.Y - p20.Y);
Matrix<double> T = Matrix<double>.Build.DenseOfArray(Transform);
Console.WriteLine(T);
Matrix<double> B = Matrix<double>.Build.DenseOfArray(MatrixB);
Console.WriteLine(B);
Matrix<double> Ke = B.Transpose() * D * B * h * A;
Console.WriteLine(Ke);
Ke = T.Transpose() * Ke * T;
Console.WriteLine(Ke);
for (int i1 = 0; i1 < 3; i1++) {
for (int i2 = 0; i2 < 3; i2++) {
for (int l = 0; l < 3; l++) {
for (int c = 0; c < 3; c++) {
MatrixK[tri[i1] * 3 + l, tri[i2] * 3 + c] += Ke[i1 * 3 + l, i2 * 3 + c];
}
}
}
}
Matrix<double> Temp = Matrix<double>.Build.DenseOfArray(MatrixK);
Console.WriteLine(Temp);
double[] vectorqt = new double[3 * 3];
vectorqt[0 * 3] += p11.X - p10.X;
vectorqt[0 * 3 + 1] += p11.Y - p10.Y;
vectorqt[1 * 3] += p21.X - p20.X;
vectorqt[1 * 3 + 1] += p21.Y - p20.Y;
vectorqt[2 * 3] += p31.X - p30.X;
vectorqt[2 * 3 + 1] += p31.Y - p30.Y;
Vector<double> qt = Vector<double>.Build.DenseOfArray(vectorqt);
Console.WriteLine(qt);
qt = T.Transpose() * qt * T;
Console.WriteLine(qt);
for (int i1 = 0; i1 < 3; i1++) {
for (int l = 0; l < 3; l++) {
Vectorq[tri[i1] * 3 + l] -= qt[i1 * 3 + l];
}
}
Vector<double> VTemp = Vector<double>.Build.DenseOfArray(Vectorq);
Console.WriteLine(VTemp);
}
Matrix<double> K = Matrix<double>.Build.DenseOfArray(MatrixK);
Console.WriteLine(K);
Vector<double> q = Vector<double>.Build.DenseOfArray(Vectorq);
Console.WriteLine(q);
Vector<double> Fi = K * q;
Console.WriteLine(Fi);
double w = 0.5;
Vector<double> qi = Vector<double>.Build.DenseOfArray(q.ToArray());
Vector<double> dqi = Vector<double>.Build.Dense(Vertices.Count);
for (int i = 0; i < 100; i++) {
// Console.WriteLine(dqi);
dqi = K.Solve(Fi);
Console.WriteLine(dqi);
// Console.WriteLine(qi);
qi = qi + w * dqi;
// Console.WriteLine(qi);
// Console.WriteLine(Fi);
Fi = K * qi;
// Console.WriteLine(Fi);
}
return qi;
}