// Creating Unity Transformation matrix using 3x3 Rotation matrix and translation vector acquired from RigidTransform
UnityEngine.Matrix4x4 AccordToUnityMatrix(UnityEngine.Matrix4x4 UnityM, Accord.Math.Matrix3x3 RotationM, Accord.Math.Vector3 Trans)
{
UnityM.m00 = RotationM.V00;
UnityM.m10 = RotationM.V10;
UnityM.m20 = RotationM.V20;
UnityM.m01 = RotationM.V01;
UnityM.m11 = RotationM.V11;
UnityM.m21 = RotationM.V21;
UnityM.m02 = RotationM.V02;
UnityM.m12 = RotationM.V12;
UnityM.m22 = RotationM.V22;
UnityM.m03 = Trans.X;
UnityM.m13 = Trans.Y;
UnityM.m23 = Trans.Z;
UnityM.m30 = 0;
UnityM.m31 = 0;
UnityM.m32 = 0;
UnityM.m33 = 1;
return(UnityM);
}
/// <summary>
/// Adds specified value to all components of the specified matrix.
/// </summary>
///
/// <param name="matrix">Matrix to add value to.</param>
/// <param name="value">Value to add to all components of the specified matrix.</param>
///
/// <returns>Returns new matrix with all components equal to corresponding components of the
/// specified matrix increased by the specified value.</returns>
///
public static Matrix3x3 operator +( Matrix3x3 matrix, float value )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = matrix.V00 + value;
m.V01 = matrix.V01 + value;
m.V02 = matrix.V02 + value;
m.V10 = matrix.V10 + value;
m.V11 = matrix.V11 + value;
m.V12 = matrix.V12 + value;
m.V20 = matrix.V20 + value;
m.V21 = matrix.V21 + value;
m.V22 = matrix.V22 + value;
return m;
}
/// <summary>
/// Multiplies matrix by the specified factor.
/// </summary>
///
/// <param name="matrix">Matrix to multiply.</param>
/// <param name="factor">Factor to multiple the specified matrix by.</param>
///
/// <returns>Returns new matrix with all components equal to corresponding components of the
/// specified matrix multiples by the specified factor.</returns>
///
public static Matrix3x3 Multiply( Matrix3x3 matrix, float factor )
{
return matrix * factor;
}
/// <summary>
/// Multiplies matrix by the specified factor.
/// </summary>
///
/// <param name="matrix">Matrix to multiply.</param>
/// <param name="factor">Factor to multiple the specified matrix by.</param>
///
/// <returns>Returns new matrix with all components equal to corresponding components of the
/// specified matrix multiples by the specified factor.</returns>
///
public static Matrix3x3 operator *( Matrix3x3 matrix, float factor )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = matrix.V00 * factor;
m.V01 = matrix.V01 * factor;
m.V02 = matrix.V02 * factor;
m.V10 = matrix.V10 * factor;
m.V11 = matrix.V11 * factor;
m.V12 = matrix.V12 * factor;
m.V20 = matrix.V20 * factor;
m.V21 = matrix.V21 * factor;
m.V22 = matrix.V22 * factor;
return m;
}
/// <summary>
/// Creates rotation matrix around Z axis.
/// </summary>
///
/// <param name="radians">Rotation angle around Z axis in radians.</param>
///
/// <returns>Returns rotation matrix to rotate an object around Z axis.</returns>
///
public static Matrix3x3 CreateRotationZ( float radians )
{
Matrix3x3 m = new Matrix3x3( );
float cos = (float) System.Math.Cos( radians );
float sin = (float) System.Math.Sin( radians );
m.V00 = m.V11 = cos;
m.V01 = -sin;
m.V10 = sin;
m.V22 = 1;
return m;
}
/// <summary>
/// Calculate adjugate of the matrix, adj(A).
/// </summary>
///
/// <returns>Returns adjugate of the matrix.</returns>
///
public Matrix3x3 Adjugate( )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = V11 * V22 - V12 * V21;
m.V01 = -( V01 * V22 - V02 * V21 );
m.V02 = V01 * V12 - V02 * V11;
m.V10 = -( V10 * V22 - V12 * V20 );
m.V11 = V00 * V22 - V02 * V20;
m.V12 = -( V00 * V12 - V02 * V10 );
m.V20 = V10 * V21 - V11 * V20;
m.V21 = -( V00 * V21 - V01 * V20 );
m.V22 = V00 * V11 - V01 * V10;
return m;
}
/// <summary>
/// Adds corresponding components of two matrices.
/// </summary>
///
/// <param name="matrix1">The matrix to add to.</param>
/// <param name="matrix2">The matrix to add to the first matrix.</param>
///
/// <returns>Returns a matrix which components are equal to sum of corresponding
/// components of the two specified matrices.</returns>
///
public static Matrix3x3 operator +( Matrix3x3 matrix1, Matrix3x3 matrix2 )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = matrix1.V00 + matrix2.V00;
m.V01 = matrix1.V01 + matrix2.V01;
m.V02 = matrix1.V02 + matrix2.V02;
m.V10 = matrix1.V10 + matrix2.V10;
m.V11 = matrix1.V11 + matrix2.V11;
m.V12 = matrix1.V12 + matrix2.V12;
m.V20 = matrix1.V20 + matrix2.V20;
m.V21 = matrix1.V21 + matrix2.V21;
m.V22 = matrix1.V22 + matrix2.V22;
return m;
}
/// <summary>
/// Transpose the matrix, A<sup>T</sup>.
/// </summary>
///
/// <returns>Return a matrix which equals to transposition of this matrix.</returns>
///
public Matrix3x3 Transpose( )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = V00;
m.V01 = V10;
m.V02 = V20;
m.V10 = V01;
m.V11 = V11;
m.V12 = V21;
m.V20 = V02;
m.V21 = V12;
m.V22 = V22;
return m;
}
/// <summary>
/// Multiplies two specified matrices.
/// </summary>
///
/// <param name="matrix1">Matrix to multiply.</param>
/// <param name="matrix2">Matrix to multiply by.</param>
///
/// <returns>Return new matrix, which the result of multiplication of the two specified matrices.</returns>
///
public static Matrix3x3 operator *( Matrix3x3 matrix1, Matrix3x3 matrix2 )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = matrix1.V00 * matrix2.V00 + matrix1.V01 * matrix2.V10 + matrix1.V02 * matrix2.V20;
m.V01 = matrix1.V00 * matrix2.V01 + matrix1.V01 * matrix2.V11 + matrix1.V02 * matrix2.V21;
m.V02 = matrix1.V00 * matrix2.V02 + matrix1.V01 * matrix2.V12 + matrix1.V02 * matrix2.V22;
m.V10 = matrix1.V10 * matrix2.V00 + matrix1.V11 * matrix2.V10 + matrix1.V12 * matrix2.V20;
m.V11 = matrix1.V10 * matrix2.V01 + matrix1.V11 * matrix2.V11 + matrix1.V12 * matrix2.V21;
m.V12 = matrix1.V10 * matrix2.V02 + matrix1.V11 * matrix2.V12 + matrix1.V12 * matrix2.V22;
m.V20 = matrix1.V20 * matrix2.V00 + matrix1.V21 * matrix2.V10 + matrix1.V22 * matrix2.V20;
m.V21 = matrix1.V20 * matrix2.V01 + matrix1.V21 * matrix2.V11 + matrix1.V22 * matrix2.V21;
m.V22 = matrix1.V20 * matrix2.V02 + matrix1.V21 * matrix2.V12 + matrix1.V22 * matrix2.V22;
return m;
}
/// <summary>
/// Multiplies two specified matrices.
/// </summary>
///
/// <param name="matrix1">Matrix to multiply.</param>
/// <param name="matrix2">Matrix to multiply by.</param>
///
/// <returns>Return new matrix, which the result of multiplication of the two specified matrices.</returns>
///
public static Matrix3x3 Multiply( Matrix3x3 matrix1, Matrix3x3 matrix2 )
{
return matrix1 * matrix2;
}
/// <summary>
/// Creates a diagonal matrix using the specified vector as diagonal elements.
/// </summary>
///
/// <param name="vector">Vector to use for diagonal elements of the matrix.</param>
///
/// <returns>Returns a diagonal matrix.</returns>
///
public static Matrix3x3 CreateDiagonal( Vector3 vector )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = vector.X;
m.V11 = vector.Y;
m.V22 = vector.Z;
return m;
}
/// <summary>
/// Creates a matrix from 3 columns specified as vectors.
/// </summary>
///
/// <param name="column0">First column of the matrix to create.</param>
/// <param name="column1">Second column of the matrix to create.</param>
/// <param name="column2">Third column of the matrix to create.</param>
///
/// <returns>Returns a matrix from specified columns.</returns>
///
public static Matrix3x3 CreateFromColumns( Vector3 column0, Vector3 column1, Vector3 column2 )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = column0.X;
m.V10 = column0.Y;
m.V20 = column0.Z;
m.V01 = column1.X;
m.V11 = column1.Y;
m.V21 = column1.Z;
m.V02 = column2.X;
m.V12 = column2.Y;
m.V22 = column2.Z;
return m;
}
/// <summary>
/// Creates a matrix from 3 rows specified as vectors.
/// </summary>
///
/// <param name="row0">First row of the matrix to create.</param>
/// <param name="row1">Second row of the matrix to create.</param>
/// <param name="row2">Third row of the matrix to create.</param>
///
/// <returns>Returns a matrix from specified rows.</returns>
///
public static Matrix3x3 CreateFromRows( Vector3 row0, Vector3 row1, Vector3 row2 )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = row0.X;
m.V01 = row0.Y;
m.V02 = row0.Z;
m.V10 = row1.X;
m.V11 = row1.Y;
m.V12 = row1.Z;
m.V20 = row2.X;
m.V21 = row2.Y;
m.V22 = row2.Z;
return m;
}
/// <summary>
/// Adds specified value to all components of the specified matrix.
/// </summary>
///
/// <param name="matrix">Matrix to add value to.</param>
/// <param name="value">Value to add to all components of the specified matrix.</param>
///
/// <returns>Returns new matrix with all components equal to corresponding components of the
/// specified matrix increased by the specified value.</returns>
///
public static Matrix3x3 Add( Matrix3x3 matrix, float value )
{
return matrix + value;
}
/// <summary>
/// Adds corresponding components of two matrices.
/// </summary>
///
/// <param name="matrix1">The matrix to add to.</param>
/// <param name="matrix2">The matrix to add to the first matrix.</param>
///
/// <returns>Returns a matrix which components are equal to sum of corresponding
/// components of the two specified matrices.</returns>
///
public static Matrix3x3 Add( Matrix3x3 matrix1, Matrix3x3 matrix2 )
{
return matrix1 + matrix2;
}
/// <summary>
/// Tests whether the matrix equals to the specified one.
/// </summary>
///
/// <param name="matrix">The matrix to test equality with.</param>
///
/// <returns>Returns <see langword="true"/> if the two matrices are equal or <see langword="false"/> otherwise.</returns>
///
public bool Equals( Matrix3x3 matrix )
{
return ( this == matrix );
}
/// <summary>
/// Subtracts corresponding components of two matrices.
/// </summary>
///
/// <param name="matrix1">The matrix to subtract from.</param>
/// <param name="matrix2">The matrix to subtract from the first matrix.</param>
///
/// <returns>Returns a matrix which components are equal to difference of corresponding
/// components of the two specified matrices.</returns>
///
public static Matrix3x3 operator -( Matrix3x3 matrix1, Matrix3x3 matrix2 )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = matrix1.V00 - matrix2.V00;
m.V01 = matrix1.V01 - matrix2.V01;
m.V02 = matrix1.V02 - matrix2.V02;
m.V10 = matrix1.V10 - matrix2.V10;
m.V11 = matrix1.V11 - matrix2.V11;
m.V12 = matrix1.V12 - matrix2.V12;
m.V20 = matrix1.V20 - matrix2.V20;
m.V21 = matrix1.V21 - matrix2.V21;
m.V22 = matrix1.V22 - matrix2.V22;
return m;
}
/// <summary>
/// Multiply transposition of this matrix by itself, A<sup>T</sup>*A.
/// </summary>
///
/// <returns>Returns a matrix which is the result of multiplying this matrix's transposition by itself.</returns>
///
public Matrix3x3 MultiplyTransposeBySelf( )
{
Matrix3x3 m = new Matrix3x3( );
m.V00 = V00 * V00 + V10 * V10 + V20 * V20;
m.V10 = m.V01 = V00 * V01 + V10 * V11 + V20 * V21;
m.V20 = m.V02 = V00 * V02 + V10 * V12 + V20 * V22;
m.V11 = V01 * V01 + V11 * V11 + V21 * V21;
m.V21 = m.V12 = V01 * V02 + V11 * V12 + V21 * V22;
m.V22 = V02 * V02 + V12 * V12 + V22 * V22;
return m;
}
/// <summary>
/// Subtracts corresponding components of two matrices.
/// </summary>
///
/// <param name="matrix1">The matrix to subtract from.</param>
/// <param name="matrix2">The matrix to subtract from the first matrix.</param>
///
/// <returns>Returns a matrix which components are equal to difference of corresponding
/// components of the two specified matrices.</returns>
///
public static Matrix3x3 Subtract( Matrix3x3 matrix1, Matrix3x3 matrix2 )
{
return matrix1 - matrix2;
}
/// <summary>
/// Calculate Singular Value Decomposition (SVD) of the matrix, such as A=U*E*V<sup>T</sup>.
/// </summary>
///
/// <param name="u">Output parameter which gets 3x3 U matrix.</param>
/// <param name="e">Output parameter which gets diagonal elements of the E matrix.</param>
/// <param name="v">Output parameter which gets 3x3 V matrix.</param>
///
/// <remarks><para>Having components U, E and V the source matrix can be reproduced using below code:
/// <code>
/// Matrix3x3 source = u * Matrix3x3.Diagonal( e ) * v.Transpose( );
/// </code>
/// </para></remarks>
///
public void SVD( out Matrix3x3 u, out Vector3 e, out Matrix3x3 v )
{
double[,] uArray = new double[3, 3]
{
{ V00, V01, V02 },
{ V10, V11, V12 },
{ V20, V21, V22 }
};
double[,] vArray;
double[] eArray;
svd.svdcmp( uArray, out eArray, out vArray );
// build U matrix
u = new Matrix3x3( );
u.V00 = (float) uArray[0, 0];
u.V01 = (float) uArray[0, 1];
u.V02 = (float) uArray[0, 2];
u.V10 = (float) uArray[1, 0];
u.V11 = (float) uArray[1, 1];
u.V12 = (float) uArray[1, 2];
u.V20 = (float) uArray[2, 0];
u.V21 = (float) uArray[2, 1];
u.V22 = (float) uArray[2, 2];
// build V matrix
v = new Matrix3x3( );
v.V00 = (float) vArray[0, 0];
v.V01 = (float) vArray[0, 1];
v.V02 = (float) vArray[0, 2];
v.V10 = (float) vArray[1, 0];
v.V11 = (float) vArray[1, 1];
v.V12 = (float) vArray[1, 2];
v.V20 = (float) vArray[2, 0];
v.V21 = (float) vArray[2, 1];
v.V22 = (float) vArray[2, 2];
// build E Vector3
e = new Vector3( );
e.X = (float) eArray[0];
e.Y = (float) eArray[1];
e.Z = (float) eArray[2];
}
/// <summary>
/// Multiplies specified matrix by the specified vector.
/// </summary>
///
/// <param name="matrix">Matrix to multiply by vector.</param>
/// <param name="vector">Vector to multiply matrix by.</param>
///
/// <returns>Returns new vector which is the result of multiplication of the specified matrix
/// by the specified vector.</returns>
///
public static Vector3 Multiply( Matrix3x3 matrix, Vector3 vector )
{
return matrix * vector;
}
/// <summary>
/// Creates 4x4 tranformation matrix from 3x3 rotation matrix.
/// </summary>
///
/// <param name="rotationMatrix">Source 3x3 rotation matrix.</param>
///
/// <returns>Returns 4x4 rotation matrix.</returns>
///
/// <remarks><para>The source 3x3 rotation matrix is copied into the top left corner of the result 4x4 matrix,
/// i.e. it represents 0th, 1st and 2nd row/column. The <see cref="V33"/> element is set to 1 and the rest
/// elements of 3rd row and 3rd column are set to zeros.</para></remarks>
///
public static Matrix4x4 CreateFromRotation(Matrix3x3 rotationMatrix)
{
Matrix4x4 m = Matrix4x4.Identity;
m.V00 = rotationMatrix.V00;
m.V01 = rotationMatrix.V01;
m.V02 = rotationMatrix.V02;
m.V10 = rotationMatrix.V10;
m.V11 = rotationMatrix.V11;
m.V12 = rotationMatrix.V12;
m.V20 = rotationMatrix.V20;
m.V21 = rotationMatrix.V21;
m.V22 = rotationMatrix.V22;
return m;
}
// Select alternate pose estimation
private void alternatePoseButton_Click(object sender, EventArgs e)
{
rotationMatrix = alternateRotationMatrix;
translationVector = alternateTranslationVector;
UpdateEstimationInformation();
pictureBox.Invalidate();
}
