Visualizing points in more than three dimensions seems to be impossible, because each axis needs to be orthogonal to every other axis in Cartesian coordinates. A straight-forward solution to this problem is to describe one N-dimensional point using N one-dimensional points - one for each dimension:

The point-line duality is the most fundamental concept for parallel coordinates, as it provides the basis for mapping patterns from Cartesian to parallel coordinates and vice versa. The duality consists of two parts:

1. points in Cartesian coordinates are mapped to lines in parallel coordinates and
2. points in parallel coordinates are represented by lines in Cartesian coordinates.