This is a grasshopper recreation of a design pattern 'Controller' found in Robert Woodbury's Elements of Parametric Design. A hyperbola of one sheet is generated.
The hyperboloid of one sheet is generated from straight lines connecting a bottom circle to a top circle rotated around a vertical axis running that runs through both center points. The amount of rotation is determined by a controller created out of a circle and 2 lines staring from the circle's center and ending on its circumference.
The grasshopper definitions can be downloaded here.