Lunar Legend Tsukihime

Shiki Toono wakes up in a hospital ward with the ability to see invisible lines. These thin threads, which make up all matter in Shingetsutan, instantly destroy an object when severed. Shiki discovers that if he traces the lines of something, its destruction soon follows. While keeping his supernatural vision a secret, Shiki proceeds to live his sophomore life in peace. However, this peace is short-lived when Shiki encounters a mysterious woman with bright red eyes on his way back from school. Following a sudden psychotic lapse, he appears to kill the woman, and passes out shortly after. As if things couldn't get any worse, Shiki is assailed by a pair of demonic hounds the next day—facing certain death, Shiki is saved by the timely arrival of the same woman from yesterday. She introduces herself as Arcueid Brunestud, a vampire princess. Deciding to team up, Shiki and Arcueid embark on a journey to uncover the truth behind their lineage and the recent string of murders around town.

(Source: MAL)