Homemade name.

 

Cartesian parametrization  n > 0, traced on the cone . Cylindrical equation: .

The conical roses are the curves traced on a cone of revolution for which the projection on the mediatrix plane of the cone are planar roses.
They can be considered as conical "lifts" of roses.
 
 

Lift of the circle (n = 1): Viviani curve

Lift of the quatrefoil curve (n = 2)

Lift of the trifolium (n = 3)

 

In the same way, any curve given by the polar coordinates  can be "lifted on a cone" as . Here is, for example, a "lift" of a cardioid.

Compare to the clelias (spherical lifts of roses), and the 3D basins (lifts on paraboloids).
 

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© Robert FERRÉOL 2018