Helmerttransformation

Top  Previous  Next

The Helmerttransformation is used to move the co-ordinates of the Digitizers in the Sollkoordinaten of the data bank. The transformation can carry out a translation, a rotation around small corners and a Skalierung. The Skalierung is carried out in X axis and Y axis with the same graduation. The transformation is based on an amount from points (at least two) from which the co-ordinates are in both systems bekann. They are called identical points. Practically The points whose Sollkoordinaten are in the data bank bekann e.g. the corner points of a plan, are digitized, after the plan on the Digitizer was fixed.

 

Attention: x is the high-level value, y is the legal value.

 

Given:

 

yAP, i

xAP, i                Co-ordinates of the identical points in the old system

yNP, i

xNP, i                Koorditanten of the identical points in the new system

yA

xA                Co-ordinates of a point in the old system (before the transformation)

n                Number of the identical points

 

In request:

 

yN

xN                Co-ordinates of the point (yA, xA) after the transformation in the new system)

 

Calculation:

 

The main focus in the old system

 

image5_449 image5_450

 

The main focus in the new system

 

image5_451 image5_452

 

The transformation constants o and a.

 

an is the change of the graduation, o is the rotation.

 

image5_453

image5_454