The possibility to study such fundamental notions of modern mathematics as “space” and “spatial transformation” is almost absent in educational software. Instead, this software handles affine transformations of objects lying in 2D or 3D space: specifically, compositions of rotations, translations and homothety, all applied to geometric figures. It is relatively easy to implement affine transformations of the whole space programmatically due to internal nature of computer graphics mechanism. The problem is to support nonlinear spatial transformations in a manner that is user-friendly and seamless.
This is the first part of three papers which describes the author’s noncommercial software “VisuMatica”, its 2D- and 3D-nonlinear transformational abilities and their didactic potential. As result, the software becomes a powerful tool, which helps to discover the unity of mathematics, to visualize and dynamically explore new mathematical environments and phenomena. In particular, the paper includes discussion of nonlinear space transformations” application to studies of algebra, complex analysis, vector fields, differential equations and modeling.