In geometry a conoid (from Greek κωνος 'cone', and -ειδης 'similar') is a ruled surface, whose rulings (lines) fulfill the additional conditions: (1) All rulings are parallel to a plane, the directrix plane.(2) All rulings intersect a fixed line, the axis. The conoid is a right conoid if its axis is perpendicular to its directrix plane. Hence all rulings are perpendicular to the axis. Because of (1) any conoid is a Catalan surface and can be represented parametrically by . If the directrix is a circle, the conoid is called a circular conoid.