Does touching the penis invalidate ablution, and is the ruling on touching it through a barrier the same as direct touching?

Touching the male organ without a barrier invalidates ablution (wudu') according to many scholars, who cite the Hadith (definition): "Whoever touches his male organ must perform ablution." Others hold that it does not invalidate ablution. Some scholars have differentiated between touching with desire (which invalidates it) and without desire (which does not), and this view is very strong. As for touching from behind a barrier, it does not invalidate ablution.