Mathematical Sciences Seminar - Symmetry and computer-aided design
When:
—
Venue:
Birkbeck Main Building, Malet Street
No booking required
Engineers use computer-aided design (CAD) software to model structures before they are built. These CAD drawings show where the different parts of the structure are connected together (the joints), and also contain geometric information such as lengths or angles between different parts. Given such a drawing, we want to be able to quickly calculate whether the corresponding structure will be rigid or flexible.
One way to speed up these calculations is to ignore the specific values given by the geometric information, and just use the combinatorial information. A common way to do this is to consider the bar-and-joint graph of a structure, where each vertex corresponds to a joint, and each edge to a length constraint. However this model has two major short-comings: it does not record where the angle constraints occur, and it can only be applied when our structure is generic (i.e. the coordinates of the joints are algebraically independent over the rationals).
Typically real-world structures are non-generic, and often exhibit symmetry. So in this talk I will discuss recent advances in modelling symmetric structures using group-labelled graphs, and will explain how I am extending these results to a model which also records angle-like constraints.
Contact name:
Department of Economics, Mathematics and Statistics