Filling the cut section made with Three-mesh-bvh

Hello, I have a thing I want to create and would appreciate any recommendations on how to go about it, maybe even @gkjohnson would have some input.
So basically, I took the code from this example - [fervent-frost-fb3id - CodeSandbox](https://Code sandbox). Here I would like to fill the gaps of the cut section like this example -
image
now in the Code Sandbox example we only have an outline of the cut section, how could I create some plane/mesh there so that it covers the cut section?

The only difference in my actual project is that my model is complex and has a lot of meshes with different materials which I am cutting through, unlike the provided example with the torus.

If there are any recommendations on how to go about it I would really appreciate it.