The lidar produces a point cloud—a set of data points in a three-dimensional space. Remember that the lidar emits laser beams. A beam reflecting off of a surface and returning to the receiver generates a single data point of the point cloud. If we assume that the lidar device is the center of the coordinate system and each laser beam is a vector, then a point is defined by the vector's direction and magnitude. Therefore, the point cloud is an unordered set of vectors. Alternatively, we can define the points by their Cartesian coordinates in 
space, as illustrated in the left side of the following diagram. In this case, the point cloud is a set of vectors 
, where each vector 
contains the three coordinates of the point. For the sake of clarity, each point is represented as a cube:
