Using Cartesian Product for Animation

In the field of geometric modelling for animation, 4D modelling (time being the fourth dimension) seems to be a natural extension of 3D modelling. But time dimension is not easy to apprehend and 4D objects are difficult to interpret and to control in general. We study the application of space-time Cartesian product to construct 4D space-time objects; Cartesian product is applied to space-time objects for which topological dimension is lesser than 4, and which are easy to interpret as animations. We propose here an interpretation of such objects, and we show how 4D space-time objects, resulting from Cartesian product, can be interpreted (and therefore controlled) according to the operands of Cartesian product.