def project_onto_planes(planes, coordinates):
    """
    Does a projection of a 3D point onto a batch of 2D planes,
    returning 2D plane coordinates.

    Takes plane axes of shape n_planes, 3, 3
    # Takes coordinates of shape N, M, 3
    # returns projections of shape N*n_planes, M, 2
    """
    N, M, C = coordinates.shape
    n_planes, _, _ = planes.shape
    coordinates = coordinates.unsqueeze(1).expand(-1, n_planes, -1, -1).reshape(N*n_planes, M, 3)
    inv_planes = torch.linalg.inv(planes).unsqueeze(0).expand(N, -1, -1, -1).reshape(N*n_planes, 3, 3)
    projections = torch.bmm(coordinates, inv_planes)
    return projections

    Does a projection of a 3D point onto a batch of 2D planes,
    returning 2D plane coordinates.

    Takes plane axes of shape n_planes, 3, 3
    # Takes coordinates of shape N, M, 3
    # returns projections of shape N*n_planes, M, 2
    
training/volumetric_rendering/renderer.py