Hopf Torus (2/3): the bent equatorial case

Posted on May 1, 2018 by Stéphane Laurent
Tags: R, graphics, rgl

In this second part, we will see what happens when we map the points lying on a bent equator.

The sphere with the bent equator will be plotted thanks to the following functions.

To rotate the equator to the bent equator, we used the rotation matrix \[ R_x = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos \alpha & -\sin \alpha \\ 0 & \sin \alpha & \cos \alpha \end{pmatrix} \]

Now, let’s see the Hopf torus.

We get a deformed torus, still made of circles: