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# 2.2.7.4 Join with Cornu Easement

Creating a Cornu Modifying a Cornu Cornu Easements

A Cornu is a form of curve that uses a mathematical approach to creating a curve between two sets of end conditions.

The curve is designed to change curvature linearly along its length - which is the characteristic of a railway easement because it minimizes sudden changes in acceleration towards the center of curvature.

The conditions used at each end are the radius, angle and position.

Cornus can have added constraints in the form of track "pins" that force the curve to smoothly pass through that point while still respecting the end conditions.

Cornus can be used in XtrackCAD to both Join tracks smoothly and form smooth curves that are not joined to other tracks.

Because Cornu are mathematically generated, they can also be regenerated at will and so Cornu Joins have the unique characteristic in XTrackCAD that they remain connected even if the tracks at the ends are moved or even change shape.

Cornu Joins will use whatever space is available - that is their "tightness" (rate of change of curvature) is variable and dynamic. The minimum radius is calculated and will show as an exception, but the acceptable rate of change of curvature is the choice of the designer.

It is not always the case that the Cornu will be the most efficient way to get from A to B - because of its shape it will be the smoothest. If you want to bias the result, you can add TrackPins (Section 2.2.7.5).