Tag | (3006,00C6) |
---|---|

Type | Required (1) |

Keyword | FrameOfReferenceTransformationMatrix |

Value Multiplicity | 16 |

Value Representation | Decimal String (DS) |

A 4x4 homogeneous transformation matrix. Matrix elements shall be listed in row-major order. See Section C.20.2.1.1.

The Frame of Reference Transformation Matrix (3006,00C6) ^{A}M_{B} describes how to transform a point (^{B}x,^{B}y,^{B}z) with respect to RCS_{B} into (^{A}x,^{A}y,^{A}z) with respect to RCS_{A} according to Equation C.20.2-1.

**Equation C.20.2-1. **

The Matrix Registration is expressible as multiple matrices, each in a separate Item of Matrix Sequence (0070,030A). Equation C.20.2-2 specifies the order of the matrix multiplication where
**M _{1}
**
,

**Equation C.20.2-2. **

where

Registration often involves two or more RCS, each with a corresponding Frame of Reference Transformation Matrix. For example, another Frame of Reference Transformation Matrix ^{A}M_{C} can describe how to transform a point (
^{C}x,^{C}y,^{C}z) with respect to RCS
_{C}
into (
^{A}x,^{A}y,^{A}z) with respect to RCS_{A}. It is straightforward to find the Frame of Reference Transformation Matrix
^{B}
M
_{C}
that describes how to transform the point (
^{C}x,^{C}y,^{C}z) with respect to RCS_{C} into the point (
^{B}x,^{B}y,^{B}z) with respect to RCS_{B}. The solution is to invert ^{A}M_{B} and multiply by ^{A}M_{C}, as shown in Equation C.20.2-3.

**Equation C.20.2-3. **

If two or more transformation matrices describe the relation between Patient coordinates and a device-centric Well-known Frame of Reference, any calculations assuming transitivity via the Well-known Frame of Reference must be performed with great care to assure that both registrations reflect the same positioning of the patient with respect to the common Well-known Frame of Reference.