Constructive texturing based on hypervolume modeling

coordinate variables x1, . . ., xn from subsequent interpretation of the model in ‘real’ terms (which can be, in particular, a visualization). The concept of multimedia types is exploited here. A special mapping giving each coordinate an interpretation has been proposed (for instance, ‘x’, ‘y’, ‘z’ types can correspond to Cartesian coordinates; ‘t’, to ‘dynamic’ coordinate representing continuous values that can be linearly or non-linearly mapped onto physical time; ‘u’ and ‘v’, to 2D ‘spreadsheet’ coordinates etc.—an example has already been given in subsection 4.4). It is important that HyperFun tools have special features allowing users to fulfill this mapping procedure. With introducing a set of scalar functions for representing object attributes, one can propose a similar methodology. This means that within a HyperFun program, the object’s attributes are considered as abstract real-valued functions; as to their actual meaning, it can be determined later using an appropriate application program. There can obviously be models that could greatly benefit from such a technology that actually allows us to introduce ‘generic’ objects with subsequent generation of their different instances. For example, the same attribute can be treated (without change of the program in HyperFun!) as color, or as transparency, or as density, or as temperature, depending on circumstances and available application software features. Moreover, it is possible to assign simultaneously a few multimedia types to the same attribute. However, if the user considers it appropriate, it is possible to fix the attribute’s meaning as early as the modeling stage. If this is the case (as with the examples in this paper), the library of specialized functions introduced in the previous subsection can be especially useful.