Studying cosmological evolutions of galaxy clusters, deviation of light rays around black holes, gravitational waves produced by black hole mergers requires dealing with diverse discretization types such as particles sets, curvilinear grids, adaptive mesh refinements as well as tensor data beyond scalar and vector fields. Scientific Visualization is an essential tool to analyse and present data from computation or observations. Nowadays a huge variety of visualization tools exist, but applying them to a particular problem still faces unexpected hurdles and complications, starting frequently with the allegedly simple problem of using the right file format. Once data are provide for visualization, one often faces limitations due to new requirements that had not been considered originally, and presumably straightforward operations are not possible. A systematic approach treating data sets primarily based on their mathematical properties - instead of application-specific - reveals unexpected potential, thereby providing an "exploration framework" instead of just a set of tools with pre-defined capabilities. In this talk the "visualization shell" Vish is presented, and its approach of modelling data sets using the mathematical background of fiber bundles, topology and geometric algebra. Generic Data sets for scientific visualization are formulated via a non-cyclic graph of six levels, each of them representing a semantic property of the data. Only two of them, the "Grid" and "Field" level are exposed to the end-user, thereby providing a intuitive way to construct complex visualizations from simple "building blocks". This approach will be examplified via visualization methods that have been originally developed for astrophysical data, but transport over easily to medical visualization and computational fluid dynamics as well.