Prof. Alexander Pasko calls his direction as "Digital Materialization" (https://en.wikipedia.org/wiki/Digital_materialization
), where he is a world leader. This direction is a two-way conversion between matter and digital information. For the representation of geometric, material, optical and other properties of heterogeneous volumetric objects this group uses the Function Representation (FRep) (http://www.hyperfun.org/FRep
), where the vector-function represents all necessary properties. The function is evaluated at the given point and has a binary (or an n-ary) construction tree behind. The function can be flexibly parameterized by the user. The basic building blocks, such as spheres, cubes, cylinders, and others, are represented with equations. The morphological and topological operations (rotation, translation, merging, cutting, intersecting, etc.), applied to the basic elements, are expressed via mathematical operations over the equations that represent these elements. Combining all the equations and operations in a special order, a sequence of mathematical formulas could be derived that represents geometrical objects of very complex shape (Figure 1).