Intermediate Level

Architecture

A conoid is a surface generated by a straight line, the generatrix, that moves parallel to a plane, the directrix plane, while simultaneously intersecting a straight line segment, the axis of the conoid, and a line, the diretrix, which can be open or closed.

Gaudí and Calatrava used conoids with sinusoidal directrixes for the roofs of the ‘Sagrada Família’ schools in Barcelona and ‘Bodegas Ysios’ in Laguardia.

These surfaces, of equation $$z = a\ x\ sin\frac{y}{b}$$, are called surfaces of Gaudí, since he was the first architect to use them in his works.

The application Forms and Formulas allows manipulating the parameters a, b and c of this equation, in order to model sinusoidal conoids with different formats.