Abstract: The present invention provides a graphical user interface and software architecture that empowers the user to create new vectors, axes, points, coordinate systems, and other elements, and combinations thereof. The explicit means of creating coordinate systems and primitives are carried out via user input, imported data from files, or any other means of supplying numerical data to computer programs. In addition to geometrical relationships, coordinate system definitions can describe rates of change in the primitives, thus providing additional ways to create vectors.