Is it permissible to urinate standing up, provided one is certain that no impurity will touch the body or clothes?

There is no harm in urinating while standing when there is a need, provided the place is secluded and no one can see the urinating person's 'awrah (private parts), and no splash of urine gets on him. This is based on the action of the Prophet (peace beellations upon him). However, it is preferable to urinate while sitting, as this was the more common practice of the Prophet, it is more concealing of the 'awrah, and further removes one from urine splashes.