Lunar Legend Tsukihime

After waking up in a hospital ward, Shiki Toono finds he can see invisible lines that, when severed, instantly destroy objects in Shingetsutan. He realizes that tracing these lines leads to the destruction of the traced object. Despite this unusual ability, Shiki aims to live his sophomore year in peace, keeping his supernatural vision a secret. However, his peace is disrupted when he meets a mysterious woman with bright red eyes on his way home from school. After experiencing a sudden psychotic episode, Shiki apparently kills the woman but collapses soon after. The next day, just as he’s about to be killed by demonic hounds, the woman he thought he killed saves him. She reveals herself as Arcueid Brunestud, a vampire princess. Together, Shiki and Arcueid decide to investigate their connected pasts and the recent murders in town.

[Adapted from MAL]