next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |

CYLINDRICAL TANGENT WAVE

Homemade name. |

Cartesian parametrization:
n > 0.
Cylindrical equation: . |

The cylindrical tangent waves are the coiling of a tangentoid around a cylinder (in other words, if we make a cylindrical tangent wave roll on a plane, we get a tangentoid).

For integral values of *n*, the number of branches is equal to *n*.

For *n* = 1, we get the horopter curve.

For *n *= 2, we get the section of a rectangular hyperbolic paraboloid by a cylinder of revolution with axis a generatrix.

For *n* = 4, we get the section of a Zindler conoid by a cylinder of revolution with the same axis.

When we apply the central projection onto the sphere with center O and radius a, the cylindrical tangent wave becomes the clelia . |
Figure made by Alain Esculier |

See also the cylindrical sine waves.

next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |

© Robert FERRÉOL
2018