Gemara

(R. Aba brei d'R. Chiya bar Aba): One may urinate in public.

Support (Beraisa): One may urinate in public. A case occurred in which a man needed to urinate, but he delayed. His stomach swelled.

Once, Shmuel needed to urinate while he was teaching. They spread a sheet to give him privacy.

His father: I will pay you 400 Zuz to reverse what you did. You were able to urinate with privacy, but your Talmidim would not be able to (while you are teaching). Perhaps they will endanger themselves!

Mar bar Rav Ashi was crossing a bridge. He needed to urinate. They told him that his mother-in-law was coming.

Mar bar Rav Ashi: Even if I had to urinate in her ear (some explain - right next to her), I would do so and not endanger myself!

Question: The Beraisa said that once, a man's stomach swelled because he needed to urinate, but he delayed. Perhaps it swelled because he drank a leech!

Answer: Afterwards, he could not urinate normally. Only drops would come out.

(Beraisa): There are two holes in the Ever. One of them is for urine, and the other is for semen. They are separated by the thickness of a garlic peel;

If a man delays urinating, the separation could be broken, and make him sterile.

(Reish Lakish): "Lo Yihyeh Vecha Akar v'Akarah uvi'Vhemtecha" teaches that you will not be sterile if you are like an animal (unashamed to urinate in public if necessary).

Shabbos 62b (R. Yosi b'Rebbi Chanina): "Ha'Shochvim Al Mitos Shen u'Sruchim Al Arsosam" - they would urinate naked in front of their beds. (They would not bother to go outside.)

Objection (R. Avahu): We cannot say that for this "Yiglu b'Rosh Golim (they will be the first to be exiled)"! Rather, they would stick their beds together and swap wives.

(R. Avahu): Urinating in front of one's bed while naked causes poverty.

(Rava): It is problematic only if he faces the bed. If he turns away, it is fine;

Even facing the bed is problematic only if he urinates on the ground. If he urinates into a Kli, it is fine.

Nidah 17a (Beraisa - R. Shimon): Hash-m hates one who urinates in front of his bed while he is naked. I do not love him.

Makos 16b (Rav Achai): If one urgently needs to relieve himself and holds it in, he transgresses "v'Lo Seshaktzu (do not make yourselves detestable)."

Rishonim

The Rif and Rosh (Shabbos 28b and 6:12) bring the teachings of R. Avahu and Rava.

Rashi (44b DH Ahadar): Shmuel's father offered him 400 Zuz to teach that one may not delay until he can urinate with privacy.

R. Gershom (44b DH Amar): He offered him 400 Zuz to urinate in front of his Talmidim, to teach them not to hold it in and endanger themselves.

Tosfos (Nidah 17a DH u'Mashtin): It says in Shabbos that urinating in front of one's bed while naked causes poverty. Here, some texts say that he has relations naked, for one must be modest during relations.

Poskim

Shulchan Aruch (OC 3:12): One eliminates modestly at night in the same way he does during the day.

Mishnah Berurah (22): One may urinate even during the day in front of many people, if necessary, e.g. he has no other place. It is permitted even in front of a woman, if there is no other place, for there is danger if one refrains.

Aruch ha'Shulchan (9): One may urinate even during the day in front of many people, if necessary, for there is danger if one delays greatly, like it says in Bechoros. If one will need to pray or bless Birkas ha'Mazon there, which is forbidden within four Amos of urine perhaps he may (delay until he can) find a modest place.

Kaf ha'Chayim (36): One who must urinate in front of many people should go to the side.

Shulchan Aruch (241:1): Hash-m hates one who urinates in front of his bed while naked.

Beis Yosef (DH Arum): The same applies if he was clothed. We discuss a typical case, i.e. because he is naked he does not go outside to urinate.

Prishah (1): Hash-m hates him because he brings himself to poverty. Tosfos connotes like this.

Mishnah Berurah (1): Hash-m hates him because He wants people to act with cleanliness and Kedushah, and this man acts in a repulsive, filthy way, and Hash-m cannot put His Shechinah on him.

Shulchan Aruch (ibid.): This causes poverty. This is only if he faces the bed. If he turns away, it is fine. Even facing the bed is problematic only if he urinates on the ground. If he urinates into a Kli, it is fine.

Magen Avraham (4): A Chacham must cover the urine, for he cannot avoid thinking about Torah.

Kaf ha'Chayim (7): Alternatively, he can add a Revi'is of water to be Mevatel the urine. Everyone, not only Chacham must learn Torah at night. There is a great reward for this!

Mishnah Berurah (2): All the more so one may not urinate in front of other places, such as a table. One must conduct more cleanliness with them!

Aruch ha'Shulchan (YD 116:20): One who delays moving his bowels transgressed 'Bal Teshaktzu.' Regarding urinating, it is also dangerous. Also, it can cause sterility. If one holds it in too much, the thin membrane between the conduits for urine and semen can break. If one holds it in and the urine returns to the body, this brings jaundice.

Igros Moshe (YD 3 47:5): The Gemara forbids being modest about urinating, due to concern for danger. This is why in many places there are many urinals in one room. Even though it is all in the house and one need not go outside, it could be made with walls for modesty without concern for danger. They relied on the fact that Chachamim never enacted modesty for this, and it was impossible for previous generations. Even nowadays, in some countries one must go outside. One cannot say that it is forbidden to do so, but it is proper to urinate in a bathroom made for excrement, which has walls, since it is easy to do so. It is as if there is no need (to be immodest), for he has a modest place. Letter of the law he should be modest in such a case. One with Yir'as Shamayim should do so when there is a (modest) place. When there is no place with walls, he should not wait for one, due to danger. When they build, it is good to build walls also for urinals.

Tzitz Eliezer (6:49 Isur Yichud 15:12): Chachamim said that two men may not accompany a woman on the road in the field, lest one man need to relieve himself, and the other will be secluded with her. This does not apply to traveling in a car or taxi, for the walls of the car suffice for modesty. One can urinate on the other side.

Bi'ur Halachah (92:1 DH Hayah): If a Shali'ach Tzibur needs to relieve himself before Chazaras ha'Shatz, if he could withhold himself for the time to walk a Parsah (about four kilometers; most say that this is 72 minutes), since b'Di'eved his Tefilah is valid, for Kavod ha'Briyos he may rely on the Rif, who permits l'Chatchilah. It seems that even those who are stringent admit here. However, if he cannot wait this time (it is forbidden, for), all agree that his Tefilah is an abomination.