Right conoid

{{Short description|Ruled surface made of lines orthogonal to an axis}}

In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the axis of the right conoid.

Using a Cartesian coordinate system in three-dimensional space, if we take the {{nowrap|{{mvar|z}}-axis}} to be the axis of a right conoid, then the right conoid can be represented by the parametric equations:

: $x=v\cos u$

: $y=v\sin u$

: $z=h(u)$

where {{math|h(u)}} is some function for representing the height of the moving line.

Examples

A typical example of right conoids is given by the parametric equations

: $x=v\cos u, y=v\sin u, z=2\sin u$

The image on the right shows how the coplanar lines generate the right conoid.

Other right conoids include:

{{springer|title=Conoid|id=p/c025210}}
[http://mathworld.wolfram.com/RightConoid.html Right Conoid] from MathWorld.
[http://mathworld.wolfram.com/PlueckersConoid.html Plücker's conoid] from MathWorld