Volume Slice Texture and Projection

Greetings! I’m writing a volume visualization program with Unity, and I’m trying to wrap my head around in how could I take a “slice” out of a volume (a Texture3D in Unity’s case), and project it onto a texture to be displayed somewhere else. Moreover, I’d also like to know how to project a given mesh onto this texture, but only the portion that is cut by the slice. Much like in a medical application’s case, this is what I’m going for:

As can be seen, there are two slice visualizations from different planes/views being displayed on the right. This visualization also shows the projection from the other slice plane (displayed as green) and the blue object. Notice how only the portion being cut by the plane is displayed.

Any help is appreciated, thank you very much!