ABSTRACT
This chapter sketches how the mechanics of masonry structures, and smooth and discrete geometry, are inseparably entwined, beginning with a historical overview of how stable structures were designed, covering some fundamental theory, and then surveying recent works in computer graphics on computational design and analysis of masonry structures. It considers freeform masonry structures, which though assembled of volumetric blocks, have a thin dimension. Reciprocal diagrams and their relationship to static equilibrium have been studied extensively, starting with James Maxwell, who observed the following fact. The importance of this relation is that it measures equilibrium purely in terms of the geometry of height; we will see that this relationship can be directly ported to the discrete setting, where these surfaces become piecewise-affine meshes. And the discretization reconnects with the reciprocal diagrams of Maxwell and Gaudí. The safe theorem certifies that if a block network contains a thrust network in equilibrium within its volume, then the block network is itself stable.
