This paper presents new techniques for seamlessly transitioning between parallel coordinate plots, star plots, and scatter plots. The star plot serves as a mediator visualization between parallel coordinate plots and scatter plots since it uses lines to represent data items as parallel coordinates do and can arrange axes orthogonally as used for scatter plots. The design of the transitions also motivated a new variant of the star plot, the polycurve star plot, that uses curved lines instead of straight ones and has advantages both in terms of space utilization and the detection of clusters. Furthermore, we developed a geometrically motivated method to embed scatter points from a scatter plot into star plots and parallel coordinate plots to track the transition of structural information such as clusters and correlations between the different plot types. The integration of our techniques into an interactive analysis tool for exploring multivariate data demonstrates the advantages and utility of our approach over a multi-view approach for scatter plots and parallel coordinate plots, which we confirmed in a user study and concrete usage scenarios.