Discrete Optimization in Architecture

the long version

This book explores the extremely modular systems that meet two criteria: they allow the creation of structurally sound free-form structures, and they are comprised of as few types of modules as possible. Divided into two parts, it presents Pipe-Z (PZ) and Truss-Z (TZ) systems. PZ is more fundamental and forms spatial mathematical knots by assembling one type of unit (PZM). The shape of PZ is controlled by relative twists of a sequence of congruent PZMs. TZ is a skeletal system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic unit subjected to affine transformations (mirror reflection, rotation and combination of both). .