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MakeHomogenousMatrix[m, v] creates a homogeneous transformation matrix from a 3 x 3 rotation matrix m and a 3 x 1 translation vector v. |

MakeHomogenousMatrix[m] creates a homogeneous transformation matrix from a 3 x 3 rotation matrix m with a {0,0,0} translation vector. |

MakeHomogenousMatrix[v] creates a homogeneous transformation matrix from a 3 x 1 translation vector v and with a 3 x 3 identity matrix. |

MakeHomogenousMatrix[o, z] creates a homogeneous transformation matrix of a coordinate frame defined by its vector of origin o and the direction vector of the z-axis z. |

MakeHomogenousMatrix[] creates a 4x4 identity matrix |

- The homogeneous matrix is a 4 x 4 matrix with the last row {0, 0, 0, 1} .The homogeneous matrix can represent a transformation matrix or describe the spatial placement of a coordinate frame.

- If the homogeneous matrix represent the transformation of A frame to B frame then the 3 x 3 upper left minor matrix represents the rotation, which takes A frame into B and the last column represents the translational vector, which takes the origin of A frame into B.

- If the spatial placement of a coordinate frame is A, than the column vector of 3 x 3 upper left minor matrix represent the unit direction vector of x, y, z axis of A frame and the last column of A matrix is the origin of the frame