What is Double Orthogonal Projection

Among the famous dynamic string models conceived by Théodore Olivier (1793-1853) as a primary didactic tool to teach Descriptive Geometry, there are some that were strictly related to classic problems of stereotomy. This is the case of the biais passé, which was both a clear illustration of a special warped ruled surface and an example of how constructors dealt with the problem of building a skew arch, solving structural and practical stone cutting demands. The representation of the biais passé in Olivier's model achieved a perfect correspondence to its épure with Monge's Descriptive Geometry. This follow from the long development of representational tools, since the 13th century sketch of an oblique passage, as well as the improvement of constructive procedures for skew arches. Paradoxically, when Olivier presented his string model, the importance of the biais passé was already declining. Meanwhile other ruled surfaces were appropriated by architecture, some of which acquiring, beyond their inherent structural efficiency, a relevant aesthetic value.