Research

Geometry + Design + Materials + Interdisciplinarity

I am presently working on problems in 3D machine learning, especially learning the structure-property relationship for 3-dimensional geometries. I'm particularly interested in the properties of lattices, microstructures and metamaterials.

Previous work focused on design-sensitive offsetting of 3D mesh geometry for CAD applications in architecture. My doctoral research focused on describing a theory of rigidity for periodic frameworks. This is loosely related to the study of zeolites. My masters thesis was about Penrose tilings, but mostly it was about pictures.

I'm also interested in other problems in design computation, architectural geometry, shape modelling, discrete geometry, scientific simulation, tilings, computational geometry, and problems with a discrete flavour that have applications to biology, materials science and crystallography. I'm very interested in the idea and practice of interdisciplinarity, and I've collaborated with mathematicians, computer scientists, architects, artists, engineers, physicists and geologists.

Featured Projects

2020

Other Works

Inductive constructions for combinatorial local and global rigidity. With Anthony Nixon. In the Handbook of Geometric Constraint Systems Principles, Meera Sitharam, Audrey St. John, Jessica Sidman eds., CRC Press 2018.
Scaffolding a Skeleton. With Athina Panotopoulou, Kathrin Welker, Evelyne Hubert and Géraldine Morin. In the proceedings of Women In Shape: Modelling Boundaries of Objects in 2- and 3-Dimensions, 2018.
Anchored boundary conditions for locally isostatic networks. with Louis Theran, Anthony Nixon, Mahdi Sadjadi, Brigitte Servatius and M.F. Thorpe. Physical Review E, 2015.
Inductive constructions for frameworks on a two-dimensional fixed torus, Discrete and Computational Geometry, 54(1), 2015.
Periodic rigidity on a variable torus using inductive constructions. With Anthony Nixon. Electronic Journal of Combinatorics, 22(1), 2015.
The rigidity of periodic frameworks as graphs on a fixed torus. Contributions to Discrete Mathematics, 9(1), 2014.
One brick at a time: a survey of inductive constructions in rigidity theory. With Anthony Nixon. Fields Communications Series, volume 70, "Rigidity and Symmetry," a volume edited by Robert Connelly, Asia Weiss and Walter Whiteley, 2014.
The rigidity of periodic body-bar frameworks on the three-dimensional fixed torus. Phil. Trans. R. Soc. A 2014 372, 2013.
Swapping blocks and holes in spherical frameworks With Wendy Finbow-Singh and Walter Whiteley. SIAM Journal on Discrete Mathematics, 26(1), 280 -- 304, 2012.
Geometric and combinatorial rigidity of periodic frameworks as graphs on the torus. PhD thesis, York University, Toronto. 2011.
Finite motions from periodic frameworks with added symmetry. with Bernd Schulze and Walter Whiteley. International Journal of Solids and Structures, 48, 1711 -- 1728, 2011.
Non-local growth of Penrose tilings. Masters thesis, University of British Columbia, Vancouver. 2005.

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Research

Featured Projects

Using graph neural networks to approximate mechanical response on 3D lattice structures

Constructing Belief: Using Bayesian Belief Networks to Measure and Manage Uncertainty in Digital Design

Beyond the model: toward a unified framework for geometry creation, visualization, interaction and iteration

Face-offsetting polygon meshes with variable offset rates

Exact Face-Offsetting for Polygonal Meshes

Non-local growth of Penrose tilings

Other Works