Parallel coordinates is based on projective geometry, and has a point-line duality with orthogonal (cartesian) coordinates. Points in orthogonal coordinates become lines in parallel coordinates.
Few parallel coordinates applications take advantage of the fact that you can show lines in orthogonal coordinates as points in parallel coordinates though. It's one of the few effective ways of representing hyperplanes and hyperlines. Interpreting that is tricky though. Even people who "get" traditional parallel coordinates would have a tough time at first.
Think of it as a multidimensional scatterplot, where lines are a necessary concession to map N-space to 2-space.
Few parallel coordinates applications take advantage of the fact that you can show lines in orthogonal coordinates as points in parallel coordinates though. It's one of the few effective ways of representing hyperplanes and hyperlines. Interpreting that is tricky though. Even people who "get" traditional parallel coordinates would have a tough time at first.
Think of it as a multidimensional scatterplot, where lines are a necessary concession to map N-space to 2-space.
http://en.wikipedia.org/wiki/Duality_(projective_geometry)