In the previous article, we briefly mentioned coordinate systems while looking at how they

played a role when defining the MicroStation design cube and setting up the Terrasolid software. A brief mention was fine for that setup, but if we wish to delve into more details on transformations and changing projections in the various software packages to help you do more with LIDAR data, then it is helpful to start with some of the basics. As such, this article will provide an introduction to coordinate systems, geoids, datums and projections.

**Understanding the Earth**

The shape of the Earth can be thought of either as a sphere or a spheroid, depending upon the scale in which the user is interested. A sphere is based upon a circle and is often used to define the shape of the Earth on a small scale. A spheroid is based upon an ellipsoid and is used to define the shape of the Earth on a large scale.

The decision on whether or not to define the Earth using a sphere or spheroid shape will determine how coordinates are defined and what type of coordinate system is used. Figure 1 shows the difference between a sphere and a spheroid (ellipsoid), where ‘a’ and ‘b’ within the image represent the semi major axis and the semi minor axis. In a sphere, the semi major axis is going to equal the semi minor axis, while in an ellipsoid, the semi major axis is going to be larger than the semi minor axis. An ellipsoid is centered at the predicted Earth center and different ellipsoid models have different semi major and semi minor axes.