/// <summary>
/// Transposes a matrix.
/// </summary>
/// <param name="m">A <see cref="Matrix3D"/> instance.</param>
/// <returns>A new <see cref="Matrix3D"/> instance containing the transposed matrix.</returns>
public static Matrix3D Transpose(Matrix3D m)
{
Matrix3D t = new Matrix3D(m);
t.Transpose();
return t;
}
/// <summary>
/// Build a 3x3 matrix from from the current matrix without the given row and column.
/// </summary>
/// <param name="row">The row to remove.</param>
/// <param name="column">The column to remove.</param>
/// <returns>A <see cref="Matrix3D"/> instance containing the result Minor.</returns>
public Matrix3D Minor(int row, int column)
{
int r = 0;
Matrix3D result = new Matrix3D();
for (int iRow = 0; iRow < 4; iRow++)
{
int c = 0;
if (iRow != row)
{
for (int iCol = 0; iCol < 4; iCol++)
{
if (iCol != column)
{
result[r,c] = this[iRow, iCol];
c++;
}
}
r++;
}
}
return result;
}
/// <summary>
/// Transforms a given vector by a matrix.
/// </summary>
/// <param name="matrix">A <see cref="Matrix3D"/> instance.</param>
/// <param name="vector">A <see cref="Vector3D"/> instance.</param>
/// <returns>A new <see cref="Vector3D"/> instance containing the result.</returns>
public static Vector3D Transform(Matrix3D matrix, Vector3D vector)
{
return new Vector3D(
(matrix.M11 * vector.X) + (matrix.M12 * vector.Y) + (matrix.M13 * vector.Z),
(matrix.M21 * vector.X) + (matrix.M22 * vector.Y) + (matrix.M23 * vector.Z),
(matrix.M31 * vector.X) + (matrix.M32 * vector.Y) + (matrix.M33 * vector.Z));
}
/// <summary>
/// Transforms a given vector by a matrix and put the result in a vector.
/// </summary>
/// <param name="matrix">A <see cref="Matrix3D"/> instance.</param>
/// <param name="vector">A <see cref="Vector3D"/> instance.</param>
/// <param name="result">A <see cref="Vector3D"/> instance to hold the result.</param>
public static void Transform(Matrix3D matrix, Vector3D vector, ref Vector3D result)
{
result.X = (matrix.M11 * vector.X) + (matrix.M12 * vector.Y) + (matrix.M13 * vector.Z);
result.Y = (matrix.M21 * vector.X) + (matrix.M22 * vector.Y) + (matrix.M23 * vector.Z);
result.Z = (matrix.M31 * vector.X) + (matrix.M32 * vector.Y) + (matrix.M33 * vector.Z);
}
/// <summary>
/// Subtracts a matrix from a matrix and put the result in a third matrix.
/// </summary>
/// <param name="a">A <see cref="Matrix3D"/> instance to subtract from.</param>
/// <param name="b">A <see cref="Matrix3D"/> instance to subtract.</param>
/// <param name="result">A <see cref="Matrix3D"/> instance to hold the result.</param>
/// <remarks>result[x][y] = a[x][y] - b[x][y]</remarks>
public static void Subtract(Matrix3D a, Matrix3D b, ref Matrix3D result)
{
result.M11 = a.M11 - b.M11;
result.M12 = a.M12 - b.M12;
result.M13 = a.M13 - b.M13;
result.M21 = a.M21 - b.M21;
result.M22 = a.M22 - b.M22;
result.M23 = a.M23 - b.M23;
result.M31 = a.M31 - b.M31;
result.M32 = a.M32 - b.M32;
result.M33 = a.M33 - b.M33;
}
/// <summary>
/// Subtracts a scalar from a matrix and put the result in a third matrix.
/// </summary>
/// <param name="a">A <see cref="Matrix3D"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <param name="result">A <see cref="Matrix3D"/> instance to hold the result.</param>
public static void Subtract(Matrix3D a, double s, ref Matrix3D result)
{
result.M11 = a.M11 - s;
result.M12 = a.M12 - s;
result.M13 = a.M13 - s;
result.M21 = a.M21 - s;
result.M22 = a.M22 - s;
result.M23 = a.M23 - s;
result.M31 = a.M31 - s;
result.M32 = a.M32 - s;
result.M33 = a.M33 - s;
}
/// <summary>
/// Subtracts a matrix from a matrix.
/// </summary>
/// <param name="a">A <see cref="Matrix3D"/> instance to subtract from.</param>
/// <param name="b">A <see cref="Matrix3D"/> instance to subtract.</param>
/// <returns>A new <see cref="Matrix3D"/> instance containing the difference.</returns>
/// <remarks>result[x][y] = a[x][y] - b[x][y]</remarks>
public static Matrix3D Subtract(Matrix3D a, Matrix3D b)
{
return new Matrix3D(
a.M11 - b.M11, a.M12 - b.M12, a.M13 - b.M13,
a.M21 - b.M21, a.M22 - b.M22, a.M23 - b.M23,
a.M31 - b.M31, a.M32 - b.M32, a.M33 - b.M33
);
}
/// <summary>
/// Subtracts a scalar from a matrix.
/// </summary>
/// <param name="a">A <see cref="Matrix3D"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A new <see cref="Matrix3D"/> instance containing the difference.</returns>
public static Matrix3D Subtract(Matrix3D a, double s)
{
return new Matrix3D(
a.M11 - s, a.M12 - s, a.M13 - s,
a.M21 - s, a.M22 - s, a.M23 - s,
a.M31 - s, a.M32 - s, a.M33 - s
);
}
/// <summary>
/// Multiplies two matrices.
/// </summary>
/// <param name="a">A <see cref="Matrix3D"/> instance.</param>
/// <param name="b">A <see cref="Matrix3D"/> instance.</param>
/// <returns>A new <see cref="Matrix3D"/> instance containing the result.</returns>
public static Matrix3D Multiply(Matrix3D a, Matrix3D b)
{
return new Matrix3D(
a.M11 * b.M11 + a.M12 * b.M21 + a.M13 * b.M31,
a.M11 * b.M12 + a.M12 * b.M22 + a.M13 * b.M32,
a.M11 * b.M13 + a.M12 * b.M23 + a.M13 * b.M33,
a.M21 * b.M11 + a.M22 * b.M21 + a.M23 * b.M31,
a.M21 * b.M12 + a.M22 * b.M22 + a.M23 * b.M32,
a.M21 * b.M13 + a.M22 * b.M23 + a.M23 * b.M33,
a.M31 * b.M11 + a.M32 * b.M21 + a.M33 * b.M31,
a.M31 * b.M12 + a.M32 * b.M22 + a.M33 * b.M32,
a.M31 * b.M13 + a.M32 * b.M23 + a.M33 * b.M33
);
}
/// <summary>
/// Multiplies two matrices and put the result in a third matrix.
/// </summary>
/// <param name="a">A <see cref="Matrix3D"/> instance.</param>
/// <param name="b">A <see cref="Matrix3D"/> instance.</param>
/// <param name="result">A <see cref="Matrix3D"/> instance to hold the result.</param>
public static void Multiply(Matrix3D a, Matrix3D b, ref Matrix3D result)
{
result.M11 = a.M11 * b.M11 + a.M12 * b.M21 + a.M13 * b.M31;
result.M12 = a.M11 * b.M12 + a.M12 * b.M22 + a.M13 * b.M32;
result.M13 = a.M11 * b.M13 + a.M12 * b.M23 + a.M13 * b.M33;
result.M21 = a.M21 * b.M11 + a.M22 * b.M21 + a.M23 * b.M31;
result.M22 = a.M21 * b.M12 + a.M22 * b.M22 + a.M23 * b.M32;
result.M23 = a.M21 * b.M13 + a.M22 * b.M23 + a.M23 * b.M33;
result.M31 = a.M31 * b.M11 + a.M32 * b.M21 + a.M33 * b.M31;
result.M32 = a.M31 * b.M12 + a.M32 * b.M22 + a.M33 * b.M32;
result.M33 = a.M31 * b.M13 + a.M32 * b.M23 + a.M33 * b.M33;
}
/// <summary>
/// Adds a matrix and a scalar and put the result in a third matrix.
/// </summary>
/// <param name="a">A <see cref="Matrix3D"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <param name="result">A <see cref="Matrix3D"/> instance to hold the result.</param>
public static void Add(Matrix3D a, double s, ref Matrix3D result)
{
result.M11 = a.M11 + s;
result.M12 = a.M12 + s;
result.M13 = a.M13 + s;
result.M21 = a.M21 + s;
result.M22 = a.M22 + s;
result.M23 = a.M23 + s;
result.M31 = a.M31 + s;
result.M32 = a.M32 + s;
result.M33 = a.M33 + s;
}
/// <summary>
/// Adds two matrices and put the result in a third matrix.
/// </summary>
/// <param name="a">A <see cref="Matrix3D"/> instance.</param>
/// <param name="b">A <see cref="Matrix3D"/> instance.</param>
/// <param name="result">A <see cref="Matrix3D"/> instance to hold the result.</param>
public static void Add(Matrix3D a, Matrix3D b, ref Matrix3D result)
{
result.M11 = a.M11 + b.M11;
result.M12 = a.M12 + b.M12;
result.M13 = a.M13 + b.M13;
result.M21 = a.M21 + b.M21;
result.M22 = a.M22 + b.M22;
result.M23 = a.M23 + b.M23;
result.M31 = a.M31 + b.M31;
result.M32 = a.M32 + b.M32;
result.M33 = a.M33 + b.M33;
}
/// <summary>
/// Adds a matrix and a scalar.
/// </summary>
/// <param name="a">A <see cref="Matrix3D"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A new <see cref="Matrix3D"/> instance containing the sum.</returns>
public static Matrix3D Add(Matrix3D a, double s)
{
return new Matrix3D(
a.M11 + s, a.M12 + s, a.M13 + s,
a.M21 + s, a.M22 + s, a.M23 + s,
a.M31 + s, a.M32 + s, a.M33 + s
);
}
/// <summary>
/// Adds two matrices.
/// </summary>
/// <param name="a">A <see cref="Matrix3D"/> instance.</param>
/// <param name="b">A <see cref="Matrix3D"/> instance.</param>
/// <returns>A new <see cref="Matrix3D"/> instance containing the sum.</returns>
public static Matrix3D Add(Matrix3D a, Matrix3D b)
{
return new Matrix3D(
a.M11 + b.M11, a.M12 + b.M12, a.M13 + b.M13,
a.M21 + b.M21, a.M22 + b.M22, a.M23 + b.M23,
a.M31 + b.M31, a.M32 + b.M32, a.M33 + b.M33
);
}
/// <summary>
/// Initializes a new instance of the <see cref="Matrix3D"/> class using a given matrix.
/// </summary>
public Matrix3D(Matrix3D m)
{
_m11 = m.M11; _m12 = m.M12; _m13 = m.M13;
_m21 = m.M21; _m22 = m.M22; _m23 = m.M23;
_m31 = m.M31; _m32 = m.M32; _m33 = m.M33;
}