import torch


def face_normals_packed(meshes):
    verts = meshes.verts_packed()
    faces = meshes.faces_packed()
    face_verts = verts[faces]
    normals = torch.cross(
        face_verts[:, 1] - face_verts[:, 0],
        face_verts[:, 2] - face_verts[:, 0],
        dim=1,
    )
    return normals / normals.norm(dim=1, keepdim=True).clamp_min(1e-12)


def vertex_normals_packed(meshes):
    verts = meshes.verts_packed()
    faces = meshes.faces_packed()
    face_normals = face_normals_packed(meshes)
    normals = torch.zeros_like(verts)
    normals.index_add_(0, faces[:, 0], face_normals)
    normals.index_add_(0, faces[:, 1], face_normals)
    normals.index_add_(0, faces[:, 2], face_normals)
    return normals / normals.norm(dim=1, keepdim=True).clamp_min(1e-12)