Planar (Intrados and Extrados Surface)

Planar or flat intrados are often the product of straightforward materialisation processes that obviate efforts from aesthetic finishing of the intrados surface and concentrates efforts in the definition of the contact surfaces (see Contact surface ).

Various materialisation processes do not favour the modelling of the underside, the voussoir surface in which the raw material is fixed to the working table – examples of this limitation include, among other, milling, circular sawing or material extrusion. In the case of milling or circular sawing, it is necessary to flip the block for a different milling session; material extrusion is dependent on a previous mould replicating the intrados surface in which the additive material shall be deposited.

Adding to the fact that the large majority of solid raw materials are obtainable from the producer as cuboid stock materials; that stereotomic bond is essentially dependent on the geometric accuracy of the contact surfaces; and that accessible computation allow for a feasible planar form finding (see Figure 108), this kind of intrados (or extrados) has been widely used to materialize stereotomy (Azambuja Varela and Merritt, 2016), (Kaczynski et al., 2011), (Matthias Rippmann et al., 2016), (Azambuja Varela and Sousa, 2018)). Planarized configurations can be optimized by computer iterative processes that search for a solution of coincident intrados adjacent edges by slightly moving intrados vertices around the initial point; depending on the gaussian curvature and the magnitude of the principal curvature, a solution might not be feasible and a scaling effect appears, stressing the individuality of each voussoir.