14 Parameter Time-Dependant

The 14 Parameter Time-Dependant transformation, also known as a fourteen parameter transformation, is an algorithm for shifting between two independent reference frames. This methodology contains seven parameters that define a relationship between the two frames at a given instant in time (t₀). Additionally, seven velocity parameters are defined as for the X,Y,Z position and rotations, and the scale factor value that represent changes over time. The user provides an input reference coordinate point, and a date (tn) (specified in the Target coordinate system definition) for the realization of the output point. The velocity parameters are then used to generate a coordinate translation between the reference frames at the given time (t_n).

Both Coordinate Frame Rotation and Position Vector Rotation definitions of the 14 Parameter Time-Dependent transform are available. To properly define the parameters, you MUST know which rotation sense is used for your transformation parameters.

Coordinate Frame Rotation

Rotation is positive counter-clockwise, as may be imagined to be seen by an observer at the origin of the coordinate frame, looking in the positive direction of the axis about which the rotation is taking place.

Position Vector Rotation

The rotations are defined as positive clockwise, as may be imagined to be seen by an observer at the origin of the coordinate frame, looking in the positive direction of the axis about which the rotation is taking place.