Marie Smith – Uformia

Supervisors:
Prof Alexander Pasko
Dr Oleg Fryazinov

Industry Mentor:
Cherie Stamm

Numerical Analysis of Functionally Defined Volumes for Design and Simulation

In the processes of engineering design, game development, and physical simulations, numerical analysis methods (such as finite element methods) are used to deal with systems that at first seem quite unyielding to symbolic analytical examination.

In physics, it is often the case that a system of well defined differential equations can be written for a relatively simple physical problem, but the symbolic analytical solution is considered too difficult to find, even though such a solution is known to exist. For these cases, numerical analysis is used – but even so – it is still very difficult to execute with timeliness for systems with any level of complexity.

This is the case for the geometric representation of everyday objects as well. A piecewise continuous function exists that describes any real everyday object, but one does not bother to write this function down, because it was considered too hard to find and, until recently, would have been of little practical use.

With the recent development of parallel computing, revised affine arithmetic, and rapid volumetric modeling that results in complete piecewise continuous symbolic geometric models, a window has been opened in the world of analysis. It should now be possible to use these highly mathematically precise volumetric models to analyze and numerically simulate the behavior of these real objects with much greater accuracy and speed.