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Multivariate relations can be visualized unambiguously with parallel coordinates. After a brief overview of the fundamentals, the most recent results are illustrated with pointers to some applications. This includes the visualization of "close" families of planes and hyperplanes, a central problem in many fields (geometric modeling, computer vision, statistics), visualizing the properties of complex surfaces (and their corresponding multidimensional relations) like the winding helicoid, and algorithms based on hypersurfaces for classification (as in data mining) and decision support for multi-parameter problems. No background in visualization is assumed in the narrative.