public void SerializationXml2()
{
Matrix33D m1 = new Matrix33D(12, 23, 45,
67, 89, 90,
43, 65, 87.3);
Matrix33D m2;
string fileName = "SerializationMatrix33D_DataContractSerializer.xml";
if (File.Exists(fileName))
{
File.Delete(fileName);
}
var serializer = new DataContractSerializer(typeof(Matrix33D));
using (var stream = new FileStream(fileName, FileMode.CreateNew, FileAccess.Write))
using (var writer = XmlDictionaryWriter.CreateTextWriter(stream, Encoding.UTF8))
serializer.WriteObject(writer, m1);
using (var stream = new FileStream(fileName, FileMode.Open, FileAccess.Read))
using (var reader = XmlDictionaryReader.CreateTextReader(stream, new XmlDictionaryReaderQuotas()))
m2 = (Matrix33D)serializer.ReadObject(reader);
Assert.AreEqual(m1, m2);
}
public void SerializationXml()
{
Matrix33D m1 = new Matrix33D(12, 23, 45,
67, 89, 90,
43, 65, 87.3);
Matrix33D m2;
string fileName = "SerializationMatrix33D.xml";
if (File.Exists(fileName))
{
File.Delete(fileName);
}
XmlSerializer serializer = new XmlSerializer(typeof(Matrix33D));
StreamWriter writer = new StreamWriter(fileName);
serializer.Serialize(writer, m1);
writer.Close();
serializer = new XmlSerializer(typeof(Matrix33D));
FileStream fileStream = new FileStream(fileName, FileMode.Open);
m2 = (Matrix33D)serializer.Deserialize(fileStream);
Assert.AreEqual(m1, m2);
}
public void Properties()
{
Matrix33D m = new Matrix33D(rowMajor, MatrixOrder.RowMajor);
Assert.AreEqual(1.0, m.M00);
Assert.AreEqual(2.0, m.M01);
Assert.AreEqual(3.0, m.M02);
Assert.AreEqual(4.0, m.M10);
Assert.AreEqual(5.0, m.M11);
Assert.AreEqual(6.0, m.M12);
Assert.AreEqual(7.0, m.M20);
Assert.AreEqual(8.0, m.M21);
Assert.AreEqual(9.0, m.M22);
m = Matrix33D.Zero;
m.M00 = 1.0;
m.M01 = 2.0;
m.M02 = 3.0;
m.M10 = 4.0;
m.M11 = 5.0;
m.M12 = 6.0;
m.M20 = 7.0;
m.M21 = 8.0;
m.M22 = 9.0;
Assert.AreEqual(new Matrix33D(rowMajor, MatrixOrder.RowMajor), m);
}
public void MultiplyTransposed()
{
var m = RandomHelper.Random.NextMatrix33D(1, 10);
var v = RandomHelper.Random.NextVector3D(1, 10);
Assert.AreEqual(m.Transposed * v, Matrix33D.MultiplyTransposed(m, v));
}
public void SerializationBinary()
{
Matrix33D m1 = new Matrix33D(12, 23, 45,
56, 67, 89,
90, 12, 43.3);
Matrix33D m2;
string fileName = "SerializationMatrix33D.bin";
if (File.Exists(fileName))
File.Delete(fileName);
FileStream fs = new FileStream(fileName, FileMode.Create);
BinaryFormatter formatter = new BinaryFormatter();
formatter.Serialize(fs, m1);
fs.Close();
fs = new FileStream(fileName, FileMode.Open);
formatter = new BinaryFormatter();
m2 = (Matrix33D)formatter.Deserialize(fs);
fs.Close();
Assert.AreEqual(m1, m2);
}
public void AbsoluteStatic()
{
Matrix33D m = new Matrix33D(-1, -2, -3, -4, -5, -6, -7, -8, -9);
Matrix33D absoluteM = Matrix33D.Absolute(m);
Assert.AreEqual(1, absoluteM.M00);
Assert.AreEqual(2, absoluteM.M01);
Assert.AreEqual(3, absoluteM.M02);
Assert.AreEqual(4, absoluteM.M10);
Assert.AreEqual(5, absoluteM.M11);
Assert.AreEqual(6, absoluteM.M12);
Assert.AreEqual(7, absoluteM.M20);
Assert.AreEqual(8, absoluteM.M21);
Assert.AreEqual(9, absoluteM.M22);
m = new Matrix33D(1, 2, 3, 4, 5, 6, 7, 8, 9);
absoluteM = Matrix33D.Absolute(m);
Assert.AreEqual(1, absoluteM.M00);
Assert.AreEqual(2, absoluteM.M01);
Assert.AreEqual(3, absoluteM.M02);
Assert.AreEqual(4, absoluteM.M10);
Assert.AreEqual(5, absoluteM.M11);
Assert.AreEqual(6, absoluteM.M12);
Assert.AreEqual(7, absoluteM.M20);
Assert.AreEqual(8, absoluteM.M21);
Assert.AreEqual(9, absoluteM.M22);
}
public void IsRotation()
{
Assert.IsTrue(!Matrix33D.Zero.IsRotation);
Assert.IsTrue(Matrix33D.Identity.IsRotation);
Assert.IsTrue(Matrix33D.CreateRotation(new Vector3D(1, 2, 3).Normalized, 0.5).IsRotation);
Assert.IsTrue(!new Matrix33D(1, 0, 0, 0, 1, 0, 0, 0, -1).IsRotation);
}
public void AbsoluteStatic()
{
Matrix33D m = new Matrix33D(-1, -2, -3, -4, -5, -6, -7, -8, -9);
Matrix33D absoluteM = Matrix33D.Absolute(m);
Assert.AreEqual(1, absoluteM.M00);
Assert.AreEqual(2, absoluteM.M01);
Assert.AreEqual(3, absoluteM.M02);
Assert.AreEqual(4, absoluteM.M10);
Assert.AreEqual(5, absoluteM.M11);
Assert.AreEqual(6, absoluteM.M12);
Assert.AreEqual(7, absoluteM.M20);
Assert.AreEqual(8, absoluteM.M21);
Assert.AreEqual(9, absoluteM.M22);
m = new Matrix33D(1, 2, 3, 4, 5, 6, 7, 8, 9);
absoluteM = Matrix33D.Absolute(m);
Assert.AreEqual(1, absoluteM.M00);
Assert.AreEqual(2, absoluteM.M01);
Assert.AreEqual(3, absoluteM.M02);
Assert.AreEqual(4, absoluteM.M10);
Assert.AreEqual(5, absoluteM.M11);
Assert.AreEqual(6, absoluteM.M12);
Assert.AreEqual(7, absoluteM.M20);
Assert.AreEqual(8, absoluteM.M21);
Assert.AreEqual(9, absoluteM.M22);
}
public void Transposed()
{
Matrix33D m = new Matrix33D(rowMajor, MatrixOrder.RowMajor);
Matrix33D mt = new Matrix33D(rowMajor, MatrixOrder.ColumnMajor);
Assert.AreEqual(mt, m.Transposed);
Assert.AreEqual(Matrix33D.Identity, Matrix33D.Identity.Transposed);
}
public void Trace()
{
Matrix33D m = new Matrix33D(new double[3, 3] { { 1, 2, 3 },
{ 2, 4, 5 },
{ 3, 5, 7 } });
Assert.AreEqual(12, m.Trace);
}
public void GetColumn()
{
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Assert.AreEqual(new Vector3D(1.0, 4.0, 7.0), m.GetColumn(0));
Assert.AreEqual(new Vector3D(2.0, 5.0, 8.0), m.GetColumn(1));
Assert.AreEqual(new Vector3D(3.0, 6.0, 9.0), m.GetColumn(2));
}
public void GetRow()
{
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Assert.AreEqual(new Vector3D(1.0, 2.0, 3.0), m.GetRow(0));
Assert.AreEqual(new Vector3D(4.0, 5.0, 6.0), m.GetRow(1));
Assert.AreEqual(new Vector3D(7.0, 8.0, 9.0), m.GetRow(2));
}
protected override PoseD Read(ContentReader input, PoseD existingInstance)
{
Vector3D position = input.ReadRawObject <Vector3D>();
Matrix33D orientation = input.ReadRawObject <Matrix33D>();
return(new PoseD(position, orientation));
}
public void MultiplyMatrix()
{
Matrix33D m = new Matrix33D(12, 23, 45,
67, 89, 90,
43, 65, 87);
Assert.AreEqual(Matrix33D.Zero, Matrix33D.Multiply(m, Matrix33D.Zero));
Assert.AreEqual(Matrix33D.Zero, Matrix33D.Multiply(Matrix33D.Zero, m));
Assert.AreEqual(m, Matrix33D.Multiply(m, Matrix33D.Identity));
Assert.AreEqual(m, Matrix33D.Multiply(Matrix33D.Identity, m));
Assert.IsTrue(Matrix33D.AreNumericallyEqual(Matrix33D.Identity, Matrix33D.Multiply(m, m.Inverse)));
Assert.IsTrue(Matrix33D.AreNumericallyEqual(Matrix33D.Identity, Matrix33D.Multiply(m.Inverse, m)));
Matrix33D m1 = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Matrix33D m2 = new Matrix33D(12, 23, 45,
67, 89, 90,
43, 65, 87);
Matrix33D result = Matrix33D.Multiply(m1, m2);
for (int column = 0; column < 3; column++)
{
for (int row = 0; row < 3; row++)
{
Assert.AreEqual(Vector3D.Dot(m1.GetRow(row), m2.GetColumn(column)), result[row, column]);
}
}
}
public void Constructors()
{
Matrix33D m = new Matrix33D(1.0, 2.0, 3.0f,
4.0, 5.0, 6.0f,
7.0, 8.0, 9.0);
for (int i = 0; i < 9; i++)
{
Assert.AreEqual(rowMajor[i], m[i]);
}
m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
for (int i = 0; i < 9; i++)
{
Assert.AreEqual(rowMajor[i], m[i]);
}
m = new Matrix33D(rowMajor, MatrixOrder.RowMajor);
for (int i = 0; i < 9; i++)
{
Assert.AreEqual(rowMajor[i], m[i]);
}
m = new Matrix33D(new List <double>(columnMajor), MatrixOrder.ColumnMajor);
for (int i = 0; i < 9; i++)
{
Assert.AreEqual(rowMajor[i], m[i]);
}
m = new Matrix33D(new List <double>(rowMajor), MatrixOrder.RowMajor);
for (int i = 0; i < 9; i++)
{
Assert.AreEqual(rowMajor[i], m[i]);
}
m = new Matrix33D(new double[3, 3] {
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 }
});
for (int i = 0; i < 9; i++)
{
Assert.AreEqual(rowMajor[i], m[i]);
}
m = new Matrix33D(new double[3][] { new double[3] {
1, 2, 3
},
new double[3] {
4, 5, 6
},
new double[3] {
7, 8, 9
} });
for (int i = 0; i < 9; i++)
{
Assert.AreEqual(rowMajor[i], m[i]);
}
}
public void CrossProductMatrix()
{
Vector3D v = new Vector3D(-1.0, -2.0, -3.0);
Vector3D w = new Vector3D(4.0, 5.0, 6.0);
Matrix33D m = v.ToCrossProductMatrix();
Assert.AreEqual(Vector3D.Cross(v, w), v.ToCrossProductMatrix() * w);
}
public void Subtraction()
{
Matrix33D m1 = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Matrix33D m2 = Matrix33D.One;
Matrix33D result = Matrix33D.Subtract(m1, m2);
for (int i = 0; i < 9; i++)
Assert.AreEqual(rowMajor[i] - 1.0, result[i]);
}
public void Determinant()
{
Matrix33D m = new Matrix33D(rowMajor, MatrixOrder.RowMajor);
Assert.AreEqual(0.0, m.Determinant);
Assert.AreEqual(0.0, Matrix33D.Zero.Determinant);
Assert.AreEqual(0.0, Matrix33D.One.Determinant);
Assert.AreEqual(1.0, Matrix33D.Identity.Determinant);
}
public void SubtractionOperator()
{
Matrix33D m1 = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Matrix33D m2 = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor) * 3;
Matrix33D result = m1 - m2;
for (int i = 0; i < 9; i++)
Assert.AreEqual(-rowMajor[i] * 2, result[i]);
}
public void Multiplication()
{
double s = 0.1234;
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
m = Matrix33D.Multiply(s, m);
for (int i = 0; i < 9; i++)
Assert.AreEqual(rowMajor[i] * s, m[i]);
}
public void Division()
{
double s = 0.1234;
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
m = Matrix33D.Divide(m, s);
for (int i = 0; i < 9; i++)
Assert.IsTrue(Numeric.AreEqual(rowMajor[i] / s, m[i]));
}
public void Negation()
{
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
for (int i = 0; i < 9; i++)
{
Assert.AreEqual(-rowMajor[i], Matrix33D.Negate(m)[i]);
}
}
public void ToArray1D()
{
Matrix33D m = new Matrix33D(1, 2, 3, 4, 5, 6, 7, 8, 9);
double[] array = m.ToArray1D(MatrixOrder.RowMajor);
for (int i = 0; i < 9; i++)
Assert.AreEqual(rowMajor[i], array[i]);
array = m.ToArray1D(MatrixOrder.ColumnMajor);
for (int i = 0; i < 9; i++)
Assert.AreEqual(columnMajor[i], array[i]);
}
public void FromMatrixWithZeroTrace()
{
QuaternionD q;
Matrix33D m = new Matrix33D(0, 1, 0,
0, 0, 1,
1, 0, 0);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(new QuaternionD(-0.5, 0.5, 0.5, 0.5), q));
}
public void Constants()
{
Matrix33D zero = Matrix33D.Zero;
for (int i = 0; i < 9; i++)
Assert.AreEqual(0.0, zero[i]);
Matrix33D one = Matrix33D.One;
for (int i = 0; i < 9; i++)
Assert.AreEqual(1.0, one[i]);
}
public void Transpose()
{
Matrix33D m = new Matrix33D(rowMajor, MatrixOrder.RowMajor);
m.Transpose();
Matrix33D mt = new Matrix33D(rowMajor, MatrixOrder.ColumnMajor);
Assert.AreEqual(mt, m);
Matrix33D i = Matrix33D.Identity;
i.Transpose();
Assert.AreEqual(Matrix33D.Identity, i);
}
public void InverseWithNearSingularMatrix()
{
Matrix33D m = new Matrix33D(0.0001, 0, 0,
0, 0.0001, 0,
0, 0, 0.0001);
Vector3D v = Vector3D.One;
Vector3D w = m * v;
Assert.IsTrue(Vector3D.AreNumericallyEqual(v, m.Inverse * w));
Assert.IsTrue(Matrix33D.AreNumericallyEqual(Matrix33D.Identity, m * m.Inverse));
}
public void ToList()
{
Matrix33D m = new Matrix33D(1, 2, 3, 4, 5, 6, 7, 8, 9);
IList<double> list = m.ToList(MatrixOrder.RowMajor);
for (int i = 0; i < 9; i++)
Assert.AreEqual(rowMajor[i], list[i]);
list = m.ToList(MatrixOrder.ColumnMajor);
for (int i = 0; i < 9; i++)
Assert.AreEqual(columnMajor[i], list[i]);
}
/// <summary>
/// Computes the covariance matrix for a list of 3-dimensional points (double-precision).
/// </summary>
/// <param name="points">The points.</param>
/// <returns>The covariance matrix.</returns>
/// <exception cref="ArgumentNullException">
/// <paramref name="points"/> is <see langword="null"/>.
/// </exception>
public static Matrix33D ComputeCovarianceMatrix(IList <Vector3D> points)
{
// Notes: See "Real-Time Collision Detection" p. 93
if (points == null)
{
throw new ArgumentNullException("points");
}
int numberOfPoints = points.Count;
float oneOverNumberOfPoints = 1f / numberOfPoints;
// Compute the center of mass.
Vector3D centerOfMass = Vector3D.Zero;
for (int i = 0; i < numberOfPoints; i++)
{
centerOfMass += points[i];
}
centerOfMass *= oneOverNumberOfPoints;
// Compute covariance matrix.
double c00 = 0;
double c11 = 0;
double c22 = 0;
double c01 = 0;
double c02 = 0;
double c12 = 0;
for (int i = 0; i < numberOfPoints; i++)
{
// Translate points so that center of mass is at origin.
Vector3D p = points[i] - centerOfMass;
// Compute covariance of translated point.
c00 += p.X * p.X;
c11 += p.Y * p.Y;
c22 += p.Z * p.Z;
c01 += p.X * p.Y;
c02 += p.X * p.Z;
c12 += p.Y * p.Z;
}
c00 *= oneOverNumberOfPoints;
c11 *= oneOverNumberOfPoints;
c22 *= oneOverNumberOfPoints;
c01 *= oneOverNumberOfPoints;
c02 *= oneOverNumberOfPoints;
c12 *= oneOverNumberOfPoints;
Matrix33D covarianceMatrix = new Matrix33D(c00, c01, c02,
c01, c11, c12,
c02, c12, c22);
return(covarianceMatrix);
}
public void Indexer1d()
{
Matrix33D m = new Matrix33D(rowMajor, MatrixOrder.RowMajor);
for (int i = 0; i < 9; i++)
Assert.AreEqual(rowMajor[i], m[i]);
m = Matrix33D.Zero;
for (int i = 0; i < 9; i++)
m[i] = rowMajor[i];
Assert.AreEqual(new Matrix33D(rowMajor, MatrixOrder.RowMajor), m);
}
public void CreateRotationZ()
{
double angle = (double)MathHelper.ToRadians(30);
Matrix33D m = Matrix33D.CreateRotationZ(angle);
Assert.IsTrue(Vector3D.AreNumericallyEqual(new Vector3D((double)Math.Cos(angle), (double)Math.Sin(angle), 0), m * Vector3D.UnitX));
QuaternionD q = QuaternionD.CreateRotation(Vector3D.UnitZ, angle);
Assert.IsTrue(Vector3D.AreNumericallyEqual(q.Rotate(Vector3D.One), m * Vector3D.One));
Assert.IsTrue(Matrix33D.AreNumericallyEqual(Matrix33D.CreateRotation(Vector3D.UnitZ, angle), m));
}
public void Addition()
{
Matrix33D m1 = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Matrix33D m2 = Matrix33D.One;
Matrix33D result = Matrix33D.Add(m1, m2);
for (int i = 0; i < 9; i++)
Assert.AreEqual(rowMajor[i] + 1.0, result[i]);
}
public void InvertException()
{
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
m.Invert();
}
public void GetColumnException1()
{
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
m.GetColumn(-1);
}
public void SetMinor()
{
Matrix44D m = Matrix44D.Zero;
Matrix33D minor = new Matrix33D(1.0, 2.0, 3.0f,
5.0, 6.0, 7.0f,
9.0, 10.0, 11.0);
m.Minor = minor;
Assert.AreEqual(minor, m.Minor);
}
public void MultiplyVectorOperator()
{
Vector3D v = new Vector3D(2.34, 3.45, 4.56);
Assert.AreEqual(v, Matrix33D.Identity * v);
Assert.AreEqual(Vector3D.Zero, Matrix33D.Zero * v);
Matrix33D m = new Matrix33D(12, 23, 45,
67, 89, 90,
43, 65, 87);
Assert.IsTrue(Vector3D.AreNumericallyEqual(v, m * m.Inverse * v));
for (int i = 0; i < 3; i++)
Assert.AreEqual(Vector3D.Dot(m.GetRow(i), v), (m * v)[i]);
}
public void Properties()
{
Matrix33D m = new Matrix33D(rowMajor, MatrixOrder.RowMajor);
Assert.AreEqual(1.0, m.M00);
Assert.AreEqual(2.0, m.M01);
Assert.AreEqual(3.0, m.M02);
Assert.AreEqual(4.0, m.M10);
Assert.AreEqual(5.0, m.M11);
Assert.AreEqual(6.0, m.M12);
Assert.AreEqual(7.0, m.M20);
Assert.AreEqual(8.0, m.M21);
Assert.AreEqual(9.0, m.M22);
m = Matrix33D.Zero;
m.M00 = 1.0;
m.M01 = 2.0;
m.M02 = 3.0;
m.M10 = 4.0;
m.M11 = 5.0;
m.M12 = 6.0;
m.M20 = 7.0;
m.M21 = 8.0;
m.M22 = 9.0;
Assert.AreEqual(new Matrix33D(rowMajor, MatrixOrder.RowMajor), m);
}
public void IsSymmetric()
{
Matrix33D m = new Matrix33D(new double[3, 3] { { 1, 2, 3 },
{ 2, 4, 5 },
{ 3, 5, 7 } });
Assert.AreEqual(true, m.IsSymmetric);
m = new Matrix33D(new double[3, 3] { { 1, 2, 3 },
{ 4, 5, 2 },
{ 7, 4, 1 } });
Assert.AreEqual(false, m.IsSymmetric);
}
public void MultiplicationOperator()
{
double s = 0.1234;
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
m = s * m;
for (int i = 0; i < 9; i++)
Assert.AreEqual(rowMajor[i] * s, m[i]);
m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
m = m * s;
for (int i = 0; i < 9; i++)
Assert.AreEqual(rowMajor[i] * s, m[i]);
}
public void Indexer1dException4()
{
Matrix33D m = new Matrix33D();
double x = m[9];
}
public void IsNaN()
{
const int numberOfRows = 3;
const int numberOfColumns = 3;
Assert.IsFalse(new Matrix33D().IsNaN);
for (int r = 0; r < numberOfRows; r++)
{
for (int c = 0; c < numberOfColumns; c++)
{
Matrix33D m = new Matrix33D();
m[r, c] = double.NaN;
Assert.IsTrue(m.IsNaN);
}
}
}
public void Indexer2d()
{
Matrix33D m = new Matrix33D(rowMajor, MatrixOrder.RowMajor);
for (int column = 0; column < 3; column++)
for (int row = 0; row < 3; row++)
Assert.AreEqual(columnMajor[column * 3 + row], m[row, column]);
m = Matrix33D.Zero;
for (int column = 0; column < 3; column++)
for (int row = 0; row < 3; row++)
m[row, column] = (double)(row * 3 + column + 1);
Assert.AreEqual(new Matrix33D(rowMajor, MatrixOrder.RowMajor), m);
}
public void InverseWithNearSingularMatrix()
{
Matrix33D m = new Matrix33D(0.0001, 0, 0,
0, 0.0001, 0,
0, 0, 0.0001);
Vector3D v = Vector3D.One;
Vector3D w = m * v;
Assert.IsTrue(Vector3D.AreNumericallyEqual(v, m.Inverse * w));
Assert.IsTrue(Matrix33D.AreNumericallyEqual(Matrix33D.Identity, m * m.Inverse));
}
public void Invert()
{
Assert.AreEqual(Matrix33D.Identity, Matrix33D.Identity.Inverse);
Matrix33D m = new Matrix33D(1, 2, 3,
2, 5, 8,
7, 6, -1);
Vector3D v = Vector3D.One;
Vector3D w = m * v;
Matrix33D im = m;
im.Invert();
Assert.IsTrue(Vector3D.AreNumericallyEqual(v, im * w));
Assert.IsTrue(Matrix33D.AreNumericallyEqual(Matrix33D.Identity, m * im));
}
public void GetRowException2()
{
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
m.GetRow(3);
}
public void QuaternionDFromMatrix33()
{
Vector3D v = Vector3D.One;
Matrix33D m = Matrix33D.Identity;
QuaternionD q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(Vector3D.UnitX, 0.3);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(Vector3D.UnitY, 1.0);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(Vector3D.UnitZ, 4.0);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.Identity;
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(-Vector3D.UnitX, 1.3);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(-Vector3D.UnitY, -1.4);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(-Vector3D.UnitZ, -0.1);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = new Matrix33D(0, 0, 1,
0, -1, 0,
1, 0, 0);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = new Matrix33D(-1, 0, 0,
0, 1, 0,
0, 0, -1);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
}
public void GetRow()
{
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Assert.AreEqual(new Vector3D(1.0, 2.0, 3.0), m.GetRow(0));
Assert.AreEqual(new Vector3D(4.0, 5.0, 6.0), m.GetRow(1));
Assert.AreEqual(new Vector3D(7.0, 8.0, 9.0), m.GetRow(2));
}
public void Indexer1dException2()
{
Matrix33D m = new Matrix33D();
m[9] = 0.0;
}
public void SerializationBinary()
{
Matrix33D m1 = new Matrix33D(12, 23, 45,
56, 67, 89,
90, 12, 43.3);
Matrix33D m2;
string fileName = "SerializationMatrix33D.bin";
if (File.Exists(fileName))
File.Delete(fileName);
FileStream fs = new FileStream(fileName, FileMode.Create);
BinaryFormatter formatter = new BinaryFormatter();
formatter.Serialize(fs, m1);
fs.Close();
fs = new FileStream(fileName, FileMode.Open);
formatter = new BinaryFormatter();
m2 = (Matrix33D)formatter.Deserialize(fs);
fs.Close();
Assert.AreEqual(m1, m2);
}
public void FromMatrixWithZeroTrace()
{
QuaternionD q;
Matrix33D m = new Matrix33D(0, 1, 0,
0, 0, 1,
1, 0, 0);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(new QuaternionD(-0.5, 0.5, 0.5, 0.5), q));
}
public void NegationOperator()
{
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
for (int i = 0; i < 9; i++)
Assert.AreEqual(-rowMajor[i], (-m)[i]);
}
public void Indexer1d()
{
Matrix33D m = new Matrix33D(rowMajor, MatrixOrder.RowMajor);
for (int i = 0; i < 9; i++)
Assert.AreEqual(rowMajor[i], m[i]);
m = Matrix33D.Zero;
for (int i = 0; i < 9; i++)
m[i] = rowMajor[i];
Assert.AreEqual(new Matrix33D(rowMajor, MatrixOrder.RowMajor), m);
}
public void GetMinor()
{
Matrix44D m = new Matrix44D(rowMajor, MatrixOrder.RowMajor);
Matrix33D minor = m.Minor;
Matrix33D expected = new Matrix33D(1.0, 2.0, 3.0f,
5.0, 6.0, 7.0f,
9.0, 10.0, 11.0);
Assert.AreEqual(expected, minor);
}
public void HashCode()
{
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Assert.AreNotEqual(Matrix33D.Identity.GetHashCode(), m.GetHashCode());
}
public void MultiplyMatrixOperator()
{
Matrix33D m = new Matrix33D(12, 23, 45,
67, 89, 90,
43, 65, 87);
Assert.AreEqual(Matrix33D.Zero, m * Matrix33D.Zero);
Assert.AreEqual(Matrix33D.Zero, Matrix33D.Zero * m);
Assert.AreEqual(m, m * Matrix33D.Identity);
Assert.AreEqual(m, Matrix33D.Identity * m);
Assert.IsTrue(Matrix33D.AreNumericallyEqual(Matrix33D.Identity, m * m.Inverse));
Assert.IsTrue(Matrix33D.AreNumericallyEqual(Matrix33D.Identity, m.Inverse * m));
Matrix33D m1 = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Matrix33D m2 = new Matrix33D(12, 23, 45,
67, 89, 90,
43, 65, 87);
Matrix33D result = m1 * m2;
for (int column = 0; column < 3; column++)
for (int row = 0; row < 3; row++)
Assert.AreEqual(Vector3D.Dot(m1.GetRow(row), m2.GetColumn(column)), result[row, column]);
}
public void SerializationJson()
{
Matrix33D m1 = new Matrix33D(12, 23, 45,
67, 89, 90,
43, 65, 87.3);
Matrix33D m2;
string fileName = "SerializationMatrix33D.json";
if (File.Exists(fileName))
File.Delete(fileName);
var serializer = new DataContractJsonSerializer(typeof(Matrix33D));
using (var stream = new FileStream(fileName, FileMode.CreateNew, FileAccess.Write))
serializer.WriteObject(stream, m1);
using (var stream = new FileStream(fileName, FileMode.Open, FileAccess.Read))
m2 = (Matrix33D)serializer.ReadObject(stream);
Assert.AreEqual(m1, m2);
}
//--------------------------------------------------------------
/// <summary>
/// Computes the derived values, like sun/moon positions, transformation matrices and light
/// intensities. This method must be called when the location or time has changed.
/// </summary>
/// <remarks>
/// This method must be called when the input properties <see cref="Latitude"/>,
/// <see cref="Longitude"/>, <see cref="Altitude"/>, or <see cref="Time"/>) have changed.
/// </remarks>
public void Update()
{
_epoch2000Centuries = ToEpoch2000Centuries(Time, true);
_epoch1990Days = ToEpoch1990Days(Time, false);
// To transform from ecliptic to equatorial, we rotate by the obliquity of the ecliptic.
_e = 0.409093 - 0.000227 * _epoch2000Centuries;
EclipticToEquatorial = Matrix33D.CreateRotationX(_e);
// GMST = Greenwich mean sidereal time (mittlere Greenwich-Sternzeit) in radians.
double gmst = 4.894961 + 230121.675315 * ToEpoch2000Centuries(Time, false);
EquatorialToGeographic = Matrix33D.CreateRotationZ(-gmst);
// The earth axis slowly changes over time (precession). The precession movement repeats
// itself approx. all 26000 years. When we move from to horizontal or geographics,
// we need to apply the precession.
// In Game Engine Gems:
//var Rx = Matrix33D.CreateRotationX(0.1118 * _epoch2000Centuries);
//var Ry = Matrix33D.CreateRotationY(-0.00972 * _epoch2000Centuries);
//var Rz = Matrix33D.CreateRotationZ(0.01118 * _epoch2000Centuries);
//var precession = Rz * (Ry * Rx);
// In original article:
var Ry = Matrix33D.CreateRotationY(-0.00972 * _epoch2000Centuries);
var Rz = Matrix33D.CreateRotationZ(0.01118 * _epoch2000Centuries);
var precession = Rz * Ry * Rz;
// In game engine gems precession is applied in EclipticToWorld and in
// EquatorialToWorld. This makes no sense since precession cannot be valid for both
// coordinate systems. --> We assume the precession is given in equatorial space.
//EclipticToWorld = rLat * rLong * EclipticToEquatorial * precession;
// Latitude rotation
var rLat = Matrix33D.CreateRotationY(MathHelper.ToRadians(Latitude) - ConstantsD.PiOver2);
// Longitude rotation
// LMST = Local mean sidereal time (mittlere Ortssternzeit) in radians.
double lmst = gmst + MathHelper.ToRadians(Longitude);
var rLong = Matrix33D.CreateRotationZ(-lmst);
// Earth radius at the equator. (We assume a perfect sphere. We do not support geodetic
// systems with imperfect earth spheres.)
const double earthRadius = 6378.137 * 1000;
var equatorialToHorizontalTranslation = new Vector3D(0, -earthRadius - Altitude, 0);
// Switching of the coordinate axes between Equatorial (z up) and Horizontal (y up).
var axisSwitch = new Matrix33D(0, 1, 0,
0, 0, 1,
1, 0, 0);
EquatorialToWorld = new Matrix44D(axisSwitch * rLat * rLong * precession,
equatorialToHorizontalTranslation);
_equatorialToWorldNoPrecession = new Matrix44D(axisSwitch * rLat * rLong,
equatorialToHorizontalTranslation);
//WorldToGeographic = EquatorialToGeographic * EquatorialToWorld.Minor.Transposed;
ComputeSunPosition();
ComputeMoonPosition();
ComputeEarthPosition();
//for (int i = 0; i < NumberOfPlanets; i++)
//{
// var planet = (VisiblePlanets)i;
// if (planet != VisiblePlanets.Earth)
// ComputePlanetData(planet);
//}
}
public void GetColumn()
{
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Assert.AreEqual(new Vector3D(1.0, 4.0, 7.0), m.GetColumn(0));
Assert.AreEqual(new Vector3D(2.0, 5.0, 8.0), m.GetColumn(1));
Assert.AreEqual(new Vector3D(3.0, 6.0, 9.0), m.GetColumn(2));
}
public void EqualityOperators()
{
Matrix33D m1 = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Matrix33D m2 = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
Assert.IsTrue(m1 == m2);
Assert.IsFalse(m1 != m2);
for (int i = 0; i < 9; i++)
{
m2 = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
m2[i] += 0.1;
Assert.IsFalse(m1 == m2);
Assert.IsTrue(m1 != m2);
}
}
public void Multiplication()
{
double s = 0.1234;
Matrix33D m = new Matrix33D(columnMajor, MatrixOrder.ColumnMajor);
m = Matrix33D.Multiply(s, m);
for (int i = 0; i < 9; i++)
Assert.AreEqual(rowMajor[i] * s, m[i]);
}
