About the spherify poses!

[dwangxxx]

Hello, now I have more questions. Could you tell me how to generate the spherify poses? I cannot understand the following code.

def spherify_poses(poses, bds):
    def add_row_to_homogenize_transform(p):
        r"""Add the last row to homogenize 3 x 4 transformation matrices."""
        return np.concatenate(
            [p, np.tile(np.reshape(np.eye(4)[-1, :], [1, 1, 4]), [p.shape[0], 1, 1])], 1
        )

    # p34_to_44 = lambda p: np.concatenate(
    #     [p, np.tile(np.reshape(np.eye(4)[-1, :], [1, 1, 4]), [p.shape[0], 1, 1])], 1
    # )

    p34_to_44 = add_row_to_homogenize_transform

    rays_d = poses[:, :3, 2:3]
    rays_o = poses[:, :3, 3:4]

    def min_line_dist(rays_o, rays_d):
        A_i = np.eye(3) - rays_d * np.transpose(rays_d, [0, 2, 1])
        b_i = -A_i @ rays_o
        pt_mindist = np.squeeze(
            -np.linalg.inv((np.transpose(A_i, [0, 2, 1]) @ A_i).mean(0)) @ (b_i).mean(0)
        )
        return pt_mindist

    pt_mindist = min_line_dist(rays_o, rays_d)

    center = pt_mindist
    up = (poses[:, :3, 3] - center).mean(0)

    vec0 = normalize(up)
    vec1 = normalize(np.cross([0.1, 0.2, 0.3], vec0))
    vec2 = normalize(np.cross(vec0, vec1))
    pos = center
    c2w = np.stack([vec1, vec2, vec0, pos], 1)

    poses_reset = np.linalg.inv(p34_to_44(c2w[None])) @ p34_to_44(poses[:, :3, :4])

    rad = np.sqrt(np.mean(np.sum(np.square(poses_reset[:, :3, 3]), -1)))

    sc = 1.0 / rad
    poses_reset[:, :3, 3] *= sc
    bds *= sc
    rad *= sc

    centroid = np.mean(poses_reset[:, :3, 3], 0)
    zh = centroid[2]
    radcircle = np.sqrt(rad ** 2 - zh ** 2)
    new_poses = []

    for th in np.linspace(0.0, 2.0 * np.pi, 120):

        camorigin = np.array([radcircle * np.cos(th), radcircle * np.sin(th), zh])
        up = np.array([0, 0, -1.0])

        vec2 = normalize(camorigin)
        vec0 = normalize(np.cross(vec2, up))
        vec1 = normalize(np.cross(vec2, vec0))
        pos = camorigin
        p = np.stack([vec0, vec1, vec2, pos], 1)

        new_poses.append(p)

    new_poses = np.stack(new_poses, 0)

    new_poses = np.concatenate(
        [new_poses, np.broadcast_to(poses[0, :3, -1:], new_poses[:, :3, -1:].shape)], -1
    )
    poses_reset = np.concatenate(
        [
            poses_reset[:, :3, :4],
            np.broadcast_to(poses[0, :3, -1:], poses_reset[:, :3, -1:].shape),
        ],
        -1,
    )

    return poses_reset, new_poses, bds

Could you provide me some details? Maybe I should read some articles about this, but I dont know what I should read. Could you provide me some information? Thank you very much!