determin direct messag arrow determin type arrow happen model chang updat arrow object me owner messag me layer object sender model facad sender me classifi role object receiv model facad receiv me classifi role fig sender port layer present sender fig receiv port layer present receiv sender port receiv port sx sender port sy sender port rx receiv port ry receiv port sx rx math ab sy ry math ab sx rx east set arrow east sx rx math ab sy ry math ab sx rx west set arrow west sy ry south set arrow south set arrow north 