My first idea is this will result in a elliptic torus. The horizontal semi-axis a=R and the vertical semi-axis b=R*cos(beta). assuming the titled or inclined angle is beta. The distance away from the z-axisis c and it is a constant. But it looks not when I plot the surface in 3D using the elliptic equation given on wolfram elliptic.(adsbygoogle = window.adsbygoogle || []).push({});

The green dot points are generated by rotating the red line around the z axis and then plot the corresponding circle in 3D space.

The surface I created using the torus equation is somehow like the bottom one:

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# Surface function for a circle tilted with an angle and then rotating around z axis

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