THREE.LatheGeometry allows you to create shapes from a smooth curve. This curve is defined by a number of points (also called knots) and is most often called a spline. This spline is rotated around the central z axis of the object and results in vase-like and bell-like shapes. Once again, the easiest way to understand what THREE.LatheGeometry looks like is by looking at an example. This geometry is shown in 02-advanced-3d-geometries-lathe.html. The following screenshot taken from the example shows this geometry:

In the preceding screenshot, you can see the spline as the set of small red spheres. The positions of these spheres are passed in to THREE.LatheGeometry, together with a couple of other arguments. In this example, we rotate this spline for half a circle, and based on this spline, we extract the shape you can see. Before we look at all the arguments, let's look at the code used to create the spline and how THREE.LatheGeometry uses this spline:

function generatePoints...