7 Parameter Position Vector Rotation (Bursa-Wolfe) – Global Mapper

The Seven Parameter PVR (also known as the Bursa-Wolfe) method incorporates three translations, three rotations, and a scale correction factor. The rotations are defined as positive clockwise, as may be imagined to be seen by an observer in the origin of the coordinate frame, looking in the positive direction of the axis about which the rotation is taking place. The GeoCalc implementation of the Seven Parameter PVR method uses the "Helmert" style of transformation. This family of transformations is usually performed in three steps. First, a geodetic input point is transformed to 3D geocentric coordinates according to the horizontal datum. Then a core transformation is performed, and finally the geocentric coordinates are transformed back to geodetic coordinates. The control parameters for a Helmert transformation specify the details of the core transformation. In general, the core transformation consists of a rotation around the x axis, a rotation around the y axis, a rotation around the z axis, a scaling that is the same for all dimensions, and a vector shift (any combination of x, y and z), performed in that order.

The parameters to define a Seven Parameter PVR transformation are:

Parameter	Often Noted as
X Translation	dX
Y Translation	dY
Z Translation	dZ
X Rotation	rX
Y Rotation	rY
Z Rotation	rZ
Scale	k

There are two types of rotation sense:

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.

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.

To properly define a Seven Parameter translation, you MUST know which rotation sense is used for your transformation parameters. See the Seven Parameter CFR Transformation Method if you wish to perform a CFR transformation.