Disclaimer: I don't own SNK or Rivaille, sadly.
Rivaille had never had a conventional view of beauty. He looked at flowers and saw nothing. A palatial room was just the same as a plain one, so long as both were clean. Jewelry, flashy clothes, a song, a poem, a smile, a glance, a whisper in moonlight - they held no importance to him.
He gazed upon the beautiful women that practically threw themselves at him and thought worthless.
When he saw Eren's Titan form rising from the ashes, the dust; rising past the sun; rising towards something so indefinable and so large, so vital and right –
It is humanity's turn.
-when he saw all this, Lance Corporal Rivaille thought for the first time in his life, how beautiful.
(It is only later when Rivaille sees the same beauty in Eren's eyes that he pledges his body to protecting this man. For humanity's sake. For the sake of his comrades who had fallen in battle, and for the sake of those who had fallen needlessly. For the sake of the soundless voices who screamed their terror still.
…for his own sake.)