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 to be the axis of a right conoid, then the right conoid can be represented by the parametric equations:
where is some function for representing the height of the moving line.
Examples
A typical example of right conoids is given by the parametric equations
The image on the right shows how the coplanar lines generate the right conoid.
Other right conoids include: Helicoid: Whitney umbrella: Wallis's conical edge: Plücker's conoid: hyperbolic paraboloid: (with x-axis and y-axis as its axes).
See also
Conoid
Helicoid
Whitney umbrella
Ruled surface
External links
Right Conoid from MathWorld. Plücker's conoid from MathWorld