**THE VISH VISUALISATION SHELL** is a highly versatile infrastructure developed as a plugin module custom developed for a variety of scientific disciplines that require mathematical models based in terms of space and time. Handling large amounts of data, VISH can simulate geometry used to describe every object in the Universe.

#### Highly systematic approach to Visualization,

The Vish visualization environment is heavily based on mathematical models describing the structure of space and time, in particular

- Topology
- Differential Geometry
- Geometric Algebra

This approach allows a very systematic treatment of data sets and visualization tasks, as general as mathematics itself. Datasets and visualization methods are classified via their mathematical properties (such as dimensionality or multiplicity, see the **Fiber Bundle Data Model** for details ), independent from a particular application domain. All data are formulated via Grid and Field objects, the various existing or possible relationships between these objects define available numerical or visualization methods on them.

## Grid Objects

They define a certain geometric entity, on which data “may life”. Their primary property of concern is its dimensionality:

- Points (“particle sets”, “point clouds”) [visualization modules for points]
- Lines [visualization modules for lines]
- Surfaces [visualization modules for surfaces]
- Volumes [visualization modules for volumes]

All these data can be time-dependent, a “time series” is a sequence of Grid objects associated with some physical time each. It is a natural consequence of the chosen mathematical data model that higher dimensional data inherit the properties of lower dimensional data. For instance, surfaces always can be treatened as a point cloud as well, consequently all visualization modules for point clouds can also be applied to surfaces. The time evolution of a data set yields data set of one dimension higher – consequently visualization modules for lines can be applied to the time evolution of a particle set.

## Field Objects

Field objects are data living on a Grid object. For instance, such could be a temperature given at each point of a particle set or a surface, or a velocity defining the motion of each point.