def METHOD_NAME(self, sd_start: float = 0, sd_end: float = 0) -> Optional[AbstractGeometricPath]:
    """Compute the resulting joint trajectory and auxilliary trajectory.
    This is a convenient method if only the final output is wanted.
    Parameters
    ----------
    sd_start:
        Starting path velocity.
    sd_end:
        Goal path velocity.
    return_data:
        If true, return a dict containing the internal data.
    Returns
    -------
    :
        Time-parameterized joint position trajectory or
        None If unable to parameterize. 
    """
    t0 = time.time()
    self.compute_parameterization(sd_start, sd_end)
    if self.problem_data.return_code != ParameterizationReturnCode.Ok:
        logger.warning("Fail to parametrize path. Return code: %s", self.problem_data.return_code)
        return None
    outputtraj = self.parametrizer(self.path, self.problem_data.gridpoints, self.problem_data.sd_vec)
    logger.info("Successfully parametrize path. Duration: %.3f, previously %.3f)",
                outputtraj.path_interval[1], self.path.path_interval[1])
    logger.info("Finish parametrization in %.3f secs", time.time() - t0)
    return outputtraj