Is there a mathematical function for a sinusoidal function that each wave is omega shaped? I am interested to know if there is any possibility to define the function or equation for a sinusoidal function , similar to |sine(x)| but with each wave as an Omega shape , as you can see in the image, there is a continuous variation from S shaped Omega to C shaped, so it seems to me that there can be a function that could also consider this.
clearly it would be something like a system of equations :
x=x(t)
y=y(t)
later I would need to draw these functions  in 2D space, so knowing that the shape of S shaped omega is in contrast with the definition of a function ( no more than one point should be cut along each vertical line cutting the function)
but I hope I would be able to do this through the definition of some cloud of points in a programming software

 A: A series of circular arcs will give you a family that includes the "S"- and "C"-shaped curves. ("U" doesn't fit the pattern, so I'll ignore it here.)
Specifically, consider these arcs of measure $2\alpha$ (in radians), with a fixed opening of $2a$ at the "bottom" or "top". The radius of the arcs is $a\csc\alpha$, and the displacement of their centers from the horizontal is $-a\cot\alpha$.

Parameterizing with $t$, define
$$k := \left\lfloor \frac{t+1}{2} \right\rfloor$$
(that is, the "floor" of $\frac12(t+1)$).
This tells us which arc we're trying to draw. The arc will have center $(x_k,y_k) := (2 ak, (-1)^{k + 1} a \cot\alpha)$ and radius $r := a\csc\alpha$; our parameterization will look like
$$\begin{cases}
x(t) = x_k + \phantom{(-1)^k} r \sin(t - 2 k)\alpha\; \\
y(t) = y_k + (-1)^k\,r\cos(t-2 k)\alpha
\end{cases}$$
Here are a few variations, for $\alpha$ at (the radian equivalent of) $30^\circ$, $45^\circ$, $60^\circ$, $90^\circ$ (the "C" curve), $120^\circ$, $135^\circ$, $150^\circ$ (the threshold when neighboring arcs touch), and $160^\circ$.

