Parallel coordinates are a common way of visualizing and analyzing high-dimensional datasets. To show a set of points in an n-dimensional space, a backdrop is drawn consisting of n parallel lines, typically vertical and equally spaced. A point in n-dimensional space is represented as a polyline with vertices on the parallel axes; the position of the vertex on the i-th axis corresponds to the i-th coordinate of the point. This visualization is closely related to time series visualization, except that it is applied to data where the axes do not correspond to points in time, and therefore do not have a natural order. Therefore, different axis arrangements may be of interest. History Parallel coordinates were often said to be invented by Philbert Maurice d'Ocagne in 1885, but even though the words "Coordonnées parallèles" appear in the book title this work has nothing to do with the visualization techniques of the same name; the book only describes a method of coordinate transformation. But even before 1885, parallel coordinates were used, for example in Henry Gannetts "General Summary, Showing the Rank of States, by Ratios, 1880", or afterwards in Henry Gannetts "Rank of States and Territories in Population at Each Census, 1790-1890" in 1898. They were popularised again 87 years later by Alfred Inselberg in 1985 and systematically developed as a coordinate system starting from 1977. Some important applications are in collision avoidance algorithms for air traffic control (1987—3 USA patents), data mining (USA patent), computer vision (USA patent), Optimization, process control, more recently in intrusion detection and elsewhere. Higher dimensions On the plane with an xy cartesian coordinate system, adding more dimensions in parallel coordinates (often abbreviated ||-coords or PCP) involves adding more axes. The value of parallel coordinates is that certain geometrical properties in high dimensions transform into easily seen 2D patterns. For example, a set of points on a line in n-space transforms to a set of polylines in parallel coordinates all intersecting at n − 1 points. For n = 2 this yields a point-line duality pointing out why the mathematical foundations of parallel coordinates are developed in the projective rather than euclidean space. A pair of lines intersects at a unique point which has two coordinates and, therefore, can correspond to a unique line which is also specified by two parameters (or two points). By contrast, more than two points are required to specify a curve and