--- title: trajectory ---

fastvideo.models.dits.hyworld.trajectory.rot_x

rot_x(theta)
Source
def rot_x(theta):
    c, s = np.cos(theta), np.sin(theta)
    return np.array([[1, 0, 0], [0, c, -s], [0, s, c]])

fastvideo.models.dits.hyworld.trajectory.rot_y

rot_y(theta)
Source
def rot_y(theta):
    c, s = np.cos(theta), np.sin(theta)
    return np.array([[c, 0, s], [0, 1, 0], [-s, 0, c]])

fastvideo.models.dits.hyworld.trajectory.rot_z

rot_z(theta)
Source
def rot_z(theta):
    c, s = np.cos(theta), np.sin(theta)
    return np.array([[c, -s, 0], [s, c, 0], [0, 0, 1]])

fastvideo.models.dits.hyworld.trajectory.generate_camera_trajectory_local

generate_camera_trajectory_local(motions)

list of dict

{"forward": 1.0}, {"yaw": np.pi/2}, {"pitch": np.pi/6}, {"right": 1.0} - forward: Translation (Forward or Backward) - yaw: Rotate (Left or Right) - pitch: Rotate (Up or Down) - right: Translation (Right or Left) - third_yaw: Third Perspective Rotate (Left or Right)

Source
def generate_camera_trajectory_local(motions):
    """
    motions: list of dict
             {"forward": 1.0}, {"yaw": np.pi/2}, {"pitch": np.pi/6}, {"right": 1.0}
             - forward: Translation (Forward or Backward)
             - yaw:   Rotate (Left or Right)
             - pitch: Rotate (Up or Down)
             - right: Translation (Right or Left)
             - third_yaw: Third Perspective Rotate (Left or Right)
    """

    poses = []
    T = np.eye(4)
    poses.append(T.copy())

    for move in motions:
        # Rotate (Left or Right)
        if "yaw" in move:
            R = rot_y(move["yaw"])
            T[:3, :3] = T[:3, :3] @ R

        # Rotate (Up or Down)
        if "pitch" in move:
            R = rot_x(move["pitch"])
            T[:3, :3] = T[:3, :3] @ R

        # Translation (Z-direction of the camera's local coordinate system)
        forward = move.get("forward", 0.0)
        if forward != 0:
            local_t = np.array([0, 0, forward])
            world_t = T[:3, :3] @ local_t
            T[:3, 3] += world_t

        # Translation (Z-direction of the camera's local coordinate system)
        right = move.get("right", 0.0)
        if right != 0:
            local_t = np.array([right, 0, 0])
            world_t = T[:3, :3] @ local_t
            T[:3, 3] += world_t

        # Third Perspective Rotate (Left or Right)
        third_yaw = move.get("third_yaw", 0.0)
        if third_yaw != 0:
            theta = -third_yaw
            C = np.array([[1, 0.0, 0, 0], [0, 1, 0, 0], [0, 0, 1, -1.0], [0, 0, 0, 1]])
            c_origin = C.copy()
            # Rotation around the Y-axis
            R_y = np.array([
                [np.cos(theta), 0, np.sin(theta)],
                [0, 1, 0],
                [-np.sin(theta), 0, np.cos(theta)],
            ])
            # Translation
            C[:3, :3] = C[:3, :3] @ R_y
            C[:3, 3] = R_y @ C[:3, 3]
            c_inv = np.linalg.inv(c_origin)
            c_relative = c_inv @ C
            T = T @ c_relative

        poses.append(T.copy())

    return poses