Configuration space representation in parallel coordinates

By means of a system of parallel coordinates, a nonprojective mapping from R^N to R² is obtained for any positive integer N. In this way multivariate data and relations can be represented in the Euclidean plane (embedded in the projective plane). Basically, R² with Cartesian coordinates is augmented by N parallel axes, one for each variable. The N joint variables of a robotic device can be represented graphically by using parallel coordinates. Two key reasons motivate this kind of approach: first, some properties of the relation are better perceived visually from the parallel coordinate representation; and secondly, new algorithms and data structures can be obtained from this representation. The main features of parallel coordinates are described, and an example is presented of their use for configuration space representation of a mechanical are. The purpose of the example is to show the potential of the representation for the cases where Cartesian coordinates cannot be used