I have a 3D bounding box defined by 8 vertices (values might vary from positive to negative etc), and I want to get the pose of the center of the box to be aligned with the left (y_max), bottom (z_min), nearest (x_min) corner edges of the bounding box (in the given example here, it should be corner 0, but y axis is flipped):

I have tried this:

#!/usr/bin/env python3

import numpy as np
import open3d as o3d
import matplotlib.pyplot as plt


def create_frame(
    translation: np.ndarray = np.zeros((3, 1), dtype=np.float32),
    orientation: np.ndarray = np.eye(3, dtype=np.float32),
    frame_size=0.1,
) -> o3d.geometry.TriangleMesh:
    frame_pose = o3d.geometry.TriangleMesh.create_coordinate_frame(
        size=frame_size, origin=translation
    )
    frame_pose.rotate(orientation)
    return frame_pose


def plot_box(vertices: np.ndarray) -> None:
    # Define the edges of the cuboid
    edges_ = [[0, 1],[0, 2],[0, 3],[1, 6],[1, 7],[2, 5],[2, 7],[3, 5],[3, 6],[4, 5],[4, 6],[4, 7],]

    # Create a 3D plot
    fig = plt.figure()
    ax = fig.add_subplot(111, projection="3d")

    ax.scatter(0.0, 0.0, 0.0, color="r")

    # Plot the vertices
    ax.scatter(vertices[:, 0], vertices[:, 1], vertices[:, 2], color="b")

    # Draw the edges
    for edge in edges_:
        ax.plot(vertices[edge, 0], vertices[edge, 1], vertices[edge, 2], color="c")

    # Annotate each vertex with its index
    for i, (x, y, z) in enumerate(vertices):
        ax.text(x, y, z, f"{i}", size=20, zorder=1, color="k")

    # Set labels
    ax.set_xlabel("X")
    ax.set_ylabel("Y")
    ax.set_zlabel("Z")

    plt.show()


def pose_from_points(vertices: np.ndarray) -> np.ndarray:
    # # Define edges of the cube
    edges = {
        0: [(0, 1), (0, 2), (0, 3)],
        1: [(0, 1), (1, 6), (1, 7)],
        2: [(0, 2), (2, 5), (2, 7)],
        3: [(0, 3), (3, 5), (3, 6)],
        4: [(4, 5), (4, 6), (4, 7)],
        5: [(2, 5), (3, 5), (4, 5)],
        6: [(6, 1), (6, 3), (6, 4)],
        7: [(1, 7), (2, 7), (4, 7)],
    }

    # Max X, Max Y, Min Z
    zero_corner_idx = np.argmin(vertices[:, 0] - vertices[:, 1] + vertices[:, 2])
    zero_edges = edges[zero_corner_idx]

    # Calculate edge lengths
    edge_lengths = np.linalg.norm(
        vertices[np.array(zero_edges)[:, 0]] - vertices[np.array(zero_edges)[:, 1]],
        axis=1,
    )

    print(f"zero corner ({zero_corner_idx}): {vertices[zero_corner_idx]}")
    print("edge lenghts ", edge_lengths)

    # Find longest and shortest edges
    longest_edge_idx = np.argmax(edge_lengths)
    shortest_edge_idx = np.argmin(edge_lengths)

    # Define x-axis direction vector
    x_axis = (
        vertices[zero_edges[longest_edge_idx][1]]
        - vertices[zero_edges[longest_edge_idx][0]]
    )
    x_axis = x_axis / np.linalg.norm(x_axis)
    if x_axis[0] < 0:
        print("--- Negative X axis! ---")
        x_axis = -x_axis
    # Define z-axis direction vector
    z_axis = (
        vertices[zero_edges[shortest_edge_idx][1]]
        - vertices[zero_edges[shortest_edge_idx][0]]
    )
    z_axis = z_axis / np.linalg.norm(z_axis)
    if z_axis[2] < 0:
        print("--- Negative Z axis! ---")
        z_axis = -z_axis
    # Calculate y-axis direction vector
    y_axis = np.cross(z_axis, x_axis)
    y_axis = y_axis / np.linalg.norm(y_axis)

    # Build transformation matrix
    center = np.mean(vertices, axis=0)

    pose = np.eye(4)
    # Translation
    pose[:3, 3] = center
    # Rotation
    pose[:3, 0] = x_axis
    pose[:3, 1] = y_axis
    pose[:3, 2] = z_axis

    return pose


if __name__ == "__main__":

    root_frame = create_frame(frame_size=0.08)

    # Vertices of the cuboid
    vertices = np.array(
        [
            [0.758587, 0.219573, 0.227423],
            [0.642588, -0.175735, 0.221591],
            [1.06273, 0.129976, 0.251165],
            [0.737332, 0.221676, 0.50764],
            [0.925473, -0.26323, 0.52555],
            [1.04147, 0.132079, 0.531382],
            [0.621333, -0.173633, 0.501808],
            [0.946728, -0.265333, 0.245333],
        ]
    )

    obbox = o3d.geometry.OrientedBoundingBox.create_from_points(
        o3d.utility.Vector3dVector(vertices)
    )
    obbox.color = [0.5, 0.2, 0.8]

    pose = pose_from_points(vertices=vertices)

    pose_frame = create_frame(
        translation=pose[:3, 3],
        orientation=pose[:3, :3],
    )
    # print(obbox.extent)
    # pose_frame.translate(-obbox.extent / 2, relative=True)

    o3d.visualization.draw_geometries([root_frame, pose_frame, obbox])
    plot_box(vertices=vertices)