All perfect praise be to Allah. Blessings and peace be upon Prophet Mohammad.
Asking permission is an Islamic etiquette, whether with one`s parents, or others. Almighty Allah Says (What means): “O ye who believe! let those whom your right hands possess, and the (children) among you who have not come of age ask your permission (before they come to your presence), on three occasions: before morning prayer; the while ye doff your clothes for the noonday heat; and after the late-night prayer: these are your three times of undress: outside those times it is not wrong for you or for them to move about attending to each other: Thus does God make clear the Signs to you: for God is full of knowledge and wisdom.” {An-Nur/58}.
This etiquette is to be observed whether the door was open, or closed since the above verse was sent down at a time when rooms had no doors unlike nowadays; still, asking permission was an obligation. Ibn Abbas said: “Allah is Most Forbearing, Most Merciful to believers and loves covering up. People used not to have doors for their homes…..so, Allah ordered them to ask permission at the three times of undress mentioned in the above verse, and bestowed upon them cover up and all that is good.” Please refer to “Taffseer Al-Qourtobi.” Therefore, it is imperative that you ask permission before you come to your parents presence, or wake them up for prayer by any means that attract their attention without entering their room since you may see them in a state that you aren`t allowed t see them in. It was reported that Prophet Mohammad (PBUH) was asked by a man who said: ”Oh, Messenger of Allah: Should I ask for my mother`s permission before I come to her presence? He replied: yes. The man said: I live with her ! The Prophet said: ask for her permission before you come to her presence. The man said: I`m her servant. The Prophet said: Ask for her permission before you come to her presence, would you want to see her undressed ?The man said: no. The Prophet said: Ask for her permission.“ {Narrated by Malik In his ”Moatta`].
Al-Khateeb Ash-Shirbini (May Allah bless his soul) said: “It is impermissible to enter another person`s house before seeking his permission, whether that person was an owner, a tenant, or a borrower. If he was a non-Mahram (Marriageable), or a non-Mahram kin, then asking permission is mandatory, whether the door was closed, or not. If he was a Mahram living in the house with the owner, then it isn`t mandatory that he asks permission, but he has to make him notice his presence by making a hem, or hitting the ground with his feet so that the undressed would have time to cover up. If he wasn`t a resident of the house, then it is impermissible for him to enter, except after asking permission, even if the door was open” {Moghni Al-Mohtajj, vol.5/pp.535}. And Allah Knows Best.