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How can you know if a vertex is visible to the camera, or is it obscured by some faces of the same mesh or a mesh of other objects?

I need a python solution for Blender 2.92 or above. At the input of the algorithm there is a Blender scene with objects (meshes) and a perspective camera, at the output I need to get a list of all the vertices of each object that got into the rendering.

This algorithm is needed for automatic preparation of 2D images with marking of visible parts of objects (for example, a person's face, which can be turned with the back of the head towards the camera, or wearing a helmet) for training neural networks.

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