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I am quite new to meshing and mesh manipulation. I am working on a problem consiting of meshes $A$, $B$, and $C$. The mesh $C$ completely encloses the meshes $A$ and $B$ as shown in the attached figure. I applied a rigid rotation to the mesh $B$, and want to morph the mesh $B$ accordingly. I have provided a simplified version of the meshes here as cylinder. (They can be complicated.)

Lets combine the meshes $A$ and $B$ into one mesh (say $AB$). For each point $P_0$ on $C$, I calculated their closest distances - $d_{AB}$ (and the corresponding faces $F_{AB}$) from the mesh $AB$. I also calculated and stored the translation vector of each point of $AB$ from its initial and final points positions.

Since for each $P_0$, I have the face $F_{AB}$, and for each of its vertices, I have a translation vector; I averaged these translation vectors for the face $F_{AB}$. Now, I have a translation vector $T_{{P}_0}$ for each point $P_0$ of $C$.

Now I created a translation vector $T$ for each $P_0$ as a function of $d_{AB}$ and $T_{{P}_0}$ such that $\lvert{T}\rvert \propto d_{AB} T_{{P}_0}$.

This is a very naive solution and didn't work and also cannot work for more complicated meshes of such kind. I am starting to learn some geometrical algorithms. I am working with VTK (Visualization Toolkit Library) to work with the meshes.

It will be very helpful if I get some resources for solving this problem. Also, can we get point to point correspondences between the meshes? If yes, then how can we approach the problem with that ?

Since, I have only started learning computer graphics, please let me know if the solution I have is utterly wrong. Thanks in advance. Following are the sample images for initial and desired orientations.

Initial Orientation

Final Desired Orientation

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