The tour algorithm is a way of systematically generating and displaying projections of high-dimensional spaces in order for the viewer to examine the multivariate distribution of data. We explore to what extend it can be used in modern particle physics, where both the model parameter space and the space of experimental observables are generally multivariate. The aim of this work is to visualise how experimental observations constrain the high-dimensional parameter space of particle physics models. Moreover we want to compare how predictions from different models are distributed in the observable space to understand which model best describes the experimental results and how future experiments may distinguish between the models under consideration. We investigate what type of projections are useful in these tasks and how new projection pursuit indices may be defined to guide the user to interesting projections of the data.