Let's say you have set of points $\mathbf{P}_{i}$, which is the vertices of last O-mesh. You can simulate the deformation or movement of last O-mesh by using second law's of Newton or Langevin equation:
$$\frac{\partial^{2} \mathbf{P}_{i}}{\partial t^{2}} + \gamma \frac{\partial \mathbf{P}_{i}}{\partial t} = \alpha \mathbf{f}_{int} + \beta \mathbf{f}_{ext} + \delta \mathbf{f}_{rigidity}$$
Where $\gamma$ is viscous term, $\mathbf{f}_{int}$ and $\mathbf{f}_{ext}$ are internal force that wants to shrink the O-mesh and external force that want to expand the O-mesh respectively, as well as $\alpha$ and $\beta$ are the strength of internal and external forces respectively. Finally $\delta$ amd $\mathbf{f}_{rigidity}$ are rigidity coefficient and rigidity force that do not let to have a high deformation.
The external force could be modeled by assuming a spring attached to your red circle and initial configuration of your O-mesh as:
$$\mathbf{f}_{ext} = - k ||\mathbf{P}_{i} - \mathbf{P}^{*}|| \mathbf{n}$$
Where $k$ is spring constant and $\mathbf{P}^{*}$ is the vertex of red circle at the intersection of normal direction from $\mathbf{P}_{i}$ to the red circle and $\mathbf{n}$ is that normal direction.
Internal force $\mathbf{f}_{int}$ should be approximated by calculating the gradient of distance function of red circle. For example, define a function as:
$$
\phi(\mathbf{P}_{i})=
\begin{cases}
1,& \text{if } \mathbf{P}_{i} \text{is outside red circle}\\
0, & \text{otherwise}
\end{cases}
$$
Then spatial gradient of $\phi$ could be used as an approximation for internal force: $$\mathbf{f}_{int} = -\nabla \phi$$
Finally the rigidity force $\mathbf{f}_{rigidity}$ can be approximated by:
$$\mathbf{f}_{rigidity}(\mathbf{P}_{i}) = \hat{\mathbf{P}} - \mathbf{P}_{i}$$
Where $$\hat{\mathbf{P}} = \mathbf{P}_{i} + \frac{\sum_{j \in \mathcal{N}_{A}} \Delta l_{ij} (\frac{\mathbf{P}_{i} - \mathbf{P}_{j}}{||\mathbf{P}_{i} - \mathbf{P}_{j}||})}{|\mathcal{N}_{A}|}$$ and $\mathcal{N}_{A}$ are the group of neighboring vertices of $\mathbf{P}_{i}$ and $\Delta l_{ij} = \hat{l}_{ij} - l_{ij}$, where $\hat{l}_{ij}$ is initial distance of neighboring vertices at $t = 0$ and $l_{ij}$ is the current distance of neighboring vertices from $i$ to $j$.
By using this description and discretizing it by using finite difference you should be able to deform your O-mesh to fit it into that red circle. Keep in mind that there is no intrinsic values for $\gamma$, $\alpha$, $\beta$, and $\delta$. You should find them by experimenting different values. But, when you have large $\gamma$ your solution would have minimum oscillation due to high damping coefficient. On the other hand if you increase $\alpha$ it tends to shrink and if you increase the $\beta$ it tends to expand. Finally, increasing $\delta$ would prevent the mesh to be deformed too much.
I'm not sure this is the solution that you are looking for or not and as I said in my comments it would be pretty complicated.
