The speaker will report on recent progress in unifying the two traditionally separate phases in freeform architecture, namely (i) shape design and (ii) ratio- nalization in view of the actual fabrication. In particular, we will discuss direct design methods for constrained meshes and related architectural structures, design space exploration based on local approximations of constraint manifolds and the design of structures in static equilibrium.

This talk will introduce a variety of twist-hinged and fold-hinged dissections of regular polygons and stars, and other figures such as polyominoes. The emphasis will be on both appreciating and understanding these fascinating mathematical recreations. I will employ algorithmic and tessellation-based techniques, as well as symmetry and other geometric properties, to design the dissections. The goal will be to minimize the number of pieces, subject to the dissection being suitably hinged. Animations and video will be used to demonstrate the hinged dissections, in addition to actual physical models.

This talk will review the design and realization processes for a few large-scale sculptures based on Collins' geometrical inspirations, involving materials that include: compressed snow, translucent epoxy, cast bronze, and carved granite.