Hyperbolic Helicoid

A hyperbolic helicoid with torsion τ. The colormap is simply the parameter v.

Click button to open the graphic in a separate full window. The figure can be rotated by clicking and dragging with a mouse or swiping on a touch device, as well as zoomed in or out with a mouse wheel or pinching on a touch device.

The surface is defined by the parametric equations

$\begin{align} x &= \frac{ \sinh v \cos \tau u }{ 1 + \cosh u \cosh v } \\ y &= \frac{ \sinh v \sin \tau u }{ 1 + \cosh u \cosh v }\\ z &= \frac{ \cosh v \sinh u }{ 1 + \cosh u \cosh v } \end{align}$

Complete code for this example:

Examples Page