However, the lemniscate of Bernoulli may be visually more pleasing; it has a parametrization very similar to the lemniscate of Gerono, except that both axes are scaled by a factor of 1/(sin(t)^2 + 1) = 2/(3 - cos(2t)):
scale = 2 / (3 - cos(2t));
x = scale cos(t);
y = scale * sin(2*t) / 2;
It looks like this:
x = cos(t); y = sin(2t) / 2; and looks like this:
Lemniscate of Gerono animation https://i.sstatic.net/VKBgs.gif
However, the lemniscate of Bernoulli may be visually more pleasing; it has a parametrization very similar to the lemniscate of Gerono, except that both axes are scaled by a factor of 1/(sin(t)^2 + 1) = 2/(3 - cos(2t)):
scale = 2 / (3 - cos(2t)); x = scale cos(t); y = scale * sin(2*t) / 2; It looks like this:
Lemniscate of Bernoulli animation https://i.sstatic.net/nOPMx.gif
per: https://gamedev.stackexchange.com/questions/43691/how-can-i-...