My research is in Discrete Geometry.

Architectural Geometry + Shape Modelling + Design Computation

Research Summary

I am presently working on problems in architectural geometry, shape modelling and computational geometry. I'm particularly interested in design-sensitive offsetting of 3D mesh geometry for CAD applications. Previously my research focused on describing a theory of rigidity for periodic frameworks. This is loosely related to the study of zeolites.

I'm also interested in other problems in design computation, discrete geometry, scientific simulation, tilings, computational geometry, and problems with a discrete flavour that have applications to biology 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.

I am a partner at MESH Consultants Inc, and a visiting researcher at the Fields Institute for Research in the Mathematical Sciences. At MESH we are working to develop a new tool for computational design, prototyping and geometry-rich app generation.

Previously, I was a postdoctoral scholar in the Department of Mathematical Sciences at Worcester Polytechnic Institute. I was also a postdoctoral fellow at the Fields Institute in Toronto, in connection with the Thematic Program on Discrete Geometry and Applications.

I completed my PhD in mathematics at York University. I was working with Walter Whiteley in the area of discrete geometry, specifically rigidity theory. I did my Masters degree at the University of British Columbia, where I worked with Bill Casselman. My thesis was about Penrose Tiles, but it was mostly about pictures.

Here are some other things

Current projects and other stuff.

Penrose Zeolites

A non-periodic network of corner sharing triangles, based on the Penrose tiling.

The hendecahedron

You can pack space with hendecahedra, eleven-sided polyhedra.