Conoid

In geometry a conoid (from Greek κωνος  'cone' and -ειδης  'similar') is a ruled surface, whose rulings (lines) fulfill the additional conditions: The conoid is a right conoid if its axis is perpendicular to its directrix plane.

Because of (1) any conoid is a Catalan surface and can be represented parametrically by Any curve x(u0,v) with fixed parameter u = u0 is a ruling, c(u) describes the directrix and the vectors r(u) are all parallel to the directrix plane.

The parametric representation describes a parabolic conoid with the equation

There are a lot of conoids with singular points, which are investigated in algebraic geometry.

Like other ruled surfaces conoids are of high interest with architects, because they can be built using beams or bars.