Format RigidMatrix into an F# code string that can be used to recreate the matrix.

Nicely formats the Matrix to a Grid of 4x3.

Returns the first column vector. M11, M12 and M13.

Returns the second column vector. M21, M22 and M23.

Returns the third column vector. M31, M32 and M33.

Checks if the Matrix is an Identity Matrix in the form of:

 1  0  0  0
 0  1  0  0
 0  0  1  0

Converts the 3x4 RigidMatrix to a general 4x4 Matrix.

Returns the 12 elements column-major order:

[| M11 M12 M13 M21 M22 M23 M31 M32 M33 X41 Y42 Z43 |]

Returns the 12 elements in row-major order:

[| M11 M21 M31 X41 M12 M22 M32 Y42 M13 M23 M33 Z43 |]

Returns the translation or fourth column vector. X41, Y42 and Z43.

Multiplies (or applies) a RigidMatrix to a 3D point.

Multiplies (or applies) a RigidMatrix to a 3D unit-vector. Since a 3D vector represents a direction or translation in space, but not a location, all translations are ignored. (Homogeneous Vector)

Multiplies (or applies) a RigidMatrix to a 3D vector. Since a 3D vector represents a direction or translation in space, but not a location, all translations are ignored. (Homogeneous Vector)

Multiplies matrixA with matrixB. The resulting transformation will first do matrixA and then matrixB.

Add a vector translation to an existing RigidMatrix.

Add a X, Y and Z translation to an existing RigidMatrix.

Create immutable a 4x3 Transformation Matrix. Checks the input values to ensure they form a valid RigidMatrix. This Constructor takes arguments in row-major order:

M11 M21 M31 X41 M12 M22 M32 Y42 M13 M23 M33 Z43

Tries to create a 3x4 RigidMatrix from a general 4x4 matrix. Fails if the input matrix does scale, shear, flip, mirror, reflect or project. However, translation is allowed.

Create a RigidMatrix from a Quaternion.

Creates a RigidMatrix to transform from one Plane or Coordinate System to another Plane.

Creates a rotation around an Axis RigidMatrix. A positive angle rotates counter-clockwise when the axis vector is pointing towards the observer (right-hand rule).

Creates a rotation around an Axis RigidMatrix. A positive angle rotates counter-clockwise when the axis vector is pointing towards the observer (right-hand rule).

Creates a rotation matrix around an Axis at a given center point. A positive angle rotates counter-clockwise when the axis vector is pointing towards the observer (right-hand rule).

Creates a rotation matrix around an Axis at a given center point. A positive angle rotates counter-clockwise when the axis vector is pointing towards the observer (right-hand rule).

Creates a rotation around the X-axis RigidMatrix by angle in Degrees (not Radians). A positive rotation will be from Y towards Z-axis, so counter-clockwise when the X-axis vector is pointing towards the observer. (right-hand rule) The resulting RigidMatrix will be:

 1 0      0        0
 0 cos(θ) -sin(θ)  0
 0 sin(θ) cos(θ)   0

Creates a rotation around the Y-axis RigidMatrix by angle in Degrees (not Radians). A positive rotation will be from Z towards X-axis, so counter-clockwise when the Y-axis vector is pointing towards the observer.( right-hand rule) The resulting RigidMatrix will be:

 cos(θ)  0 sin(θ) 0
 0       1 0      0
 -sin(θ) 0 cos(θ) 0

Creates a rotation around the Z-axis RigidMatrix by angle in Degrees (not Radians). A positive rotation will be from X toward Y-axis, so counter-clockwise when the Z-axis vector is pointing towards the observer. (right-hand rule) The resulting RigidMatrix will be:

 cos(θ) -sin(θ) 0 0
 sin(θ) cos(θ)  0 0
 0      0       1 0

Creates a RigidMatrix to transform from World plane or Coordinate System to given Plane. Also called Change of Basis.

Creates a translation RigidMatrix. The resulting RigidMatrix will be:

 1  0  0  v.X
 0  1  0  v.Y
 0  0  1  v.Z

Creates a translation RigidMatrix. The resulting matrix will be:

 1  0  0  x
 0  1  0  y
 0  0  1  z

Creates a translation RigidMatrix. The resulting RigidMatrix will be:

 1  0  0  x
 0  1  0  0
 0  0  1  0

Creates a translation RigidMatrix. The resulting RigidMatrix will be:

 1  0  0  0
 0  1  0  y
 0  0  1  0

Creates a translation RigidMatrix. The resulting RigidMatrix will be:

 1  0  0  0
 0  1  0  0
 0  0  1  z

Creates a rotation from one vectors direction to another vectors direction. If the tips of the two unitized vectors have a distance less than 1e-12 the identity matrix is returned. If the tips of the two vectors are almost exactly opposite, that is if tips of the two vectors are less than 1e-12 apart when summed, there is no valid unique 180 degree rotation that can be found, so an exception is raised. Fails if either vector is too short (length less than 1e-6).

Creates a rotation from one unit-vectors direction to another unit-vectors direction. If the tips of the two unitized vectors have a distance less than 1e-12 the identity matrix is returned. If the tips of the two vectors are almost exactly opposite, that is if tips of the two vectors are less than 1e-12 apart when summed, there is no valid unique 180 degree rotation that can be found, so an exception is raised.

Checks if two Matrices are equal within tolerance. By comparing the fields M11 to Z43 each with the given tolerance. Use a tolerance of 0.0 to check for an exact match.

Returns the Identity RigidMatrix:

 1  0  0  0
 0  1  0  0
 0  0  1  0

Inverts the RigidMatrix. A RigidMatrix can always be inverted. (as opposed to a general Matrix)

Multiplies matrixA with matrixB. The resulting transformation will first do matrixA and then matrixB.

Removes the translation part by setting X41, Y42 and Z43 to 0.0.

Converts the 3x4 RigidMatrix to a general 4x4 Matrix.

Tries to create a 3x4 RigidMatrix from a general 4x4 matrix. Returns None if the input matrix does scale, shear, flip, mirror, reflect or project. However, translation is allowed.