Basis for an axis reference system is an axis, the geometrical definition of a poly-line in a projected system. An axis can for example represent a road, a railway track, the center line of a tunnel, a pipeline, or any other linear structure.

Axis definitions are stored in the context of a domains; axis definitions are available in the domain they are created in and in any of its subordinate domains.

The geometrical definition of an axis is always based on a projected system. This is the basis for converting spatial data from axis reference systems to other spatial systems and for performing various spatial calculations.

The geometrical definition is an ordered list of 3D points with coordinates X (Easting), Y (Northing) and Z (Elevation) expressed in the underlying projected system. Unlike spatial calculations in projected systems spatial calculations in axis reference systems always respect the elevation i.e. calculation are always done based on the 3D axis.

For real world axes (used for planning of streets, railway lines etc) a series of X,Y and Elevation points is only an approximation; clearly the number of points influences the accuracy of this approximation. The axis approximated by a series of points will (usually) be shorter than the length of the real world axis, however by specifying enough points the error can be kept in a range that is suitable to your needs.

If you are only interested in a part of a real world axis it is not necessary to specify the geometry of the whole real world axis. You can define a  (horizontal and sloped) offset for the first point of the axis. However bear in mind that all calculations that need the actual axis geometry can only be performed in the area where the axis geometry is defined.

The surrounding axis points for a given offset are the axis points where the offset of the first point is smaller or equal the given offset and the offset of the second point is greater than the given offset.

The bearing of an axis at a specific offset is the bearing of the axis projected to the X,Y plane in that point. The bearing is defined by the two surrounding axis points.

Bearing is measured clockwise from the direction of the Y axis in the underlying projected coordinate system (North direction) i.e. the bearing is always a value in the interval [0, 360)°. If the axis is parallel to the Z axis of the underlying projected coordinate system at a given axis offset the bearing at that offset is zero i.e. North. The bearing of the last axis point is the same as the bearing of the fore-last axis point.

The direction of an axis at a specific offset is the direction of the axis projected to the X,Y plane in that point. The direction is the direction of the vector defined by the two surrounding axis points. If the two surrounding points are superimposable in X,Y (i.e. describe a strictly vertical part of the axis) the bearing is 0.

Direction is measured counter clockwise from the direction of the X axis (Easting) in the underlying projected coordinate system i.e. the direction is always a value in the interval [0, 2π)rad. If the axis is parallel to the Z axis of the underlying projected coordinate system at a given axis offset the direction at that offset is π/2.

The inclination of an axis at a specific offset is the inclination of the vector formed by the surrounding axis points i.e. the angle of that vector with the horizontal plane. The inclination of the last axis point equals the inclination of the fore-last axis point. The the inclination a value out of the range [-90,90]°.