In some workflows, users apply a known mathematical transform to available data and get the coordinates in a standard geographic coordinate system. For example, a mining company may have survey data for a particular site to which Helmert transform can be applied to get the data to the local government agency’s preferred geographic coordinate system. Bentley’s geocoordination capability supports this concept.

Currently, only specialized Helmert linear transforms are supported. These supported Helmert transforms are a combination of rotation about the z-axis, uniform scaling of x and y, and offset in the x, y, and z direction. The mathematical formulation is:

x’ = s cos (r) * x – s sin (r) * y + c
y’ = s sin (r) * x + s cos (r) * y + d
z’ = z + e

Where s is the scale factor, r is the rotation, and c, d, and e are the offsets in the x, y, and z direction respectively. The x, y, and z variables are data in the input coordinate system, and x’, y’, and z’ are the easting, northing, and elevation in the geographic coordinate system. This is often written as:

x’ = a * x – b * y + c
y’ = b * x + a * y + d
z’ = z + e

where

a = s cos (r)
b = s sin (r)

You can enter the a, b, c, d, and e values to define a Helmert local transform.