The Shulhan Aruch (Orah Haim 55:13), based on the ruling of numerous Rishonim, writes that ten men cannot combine to form a Minyan if they are not together in the same room. For ten men to comprise a Minyan, they must be in one room. If ten or more people are together in the same room, then men in an adjoining room, or outside in the hallway, can pray with them and thereby be considered as praying with a Minyan.
A number of Rishonim maintained that people in different rooms can combine to form a Minyan if they can see each other. Thus, according to this opinion, if five men are in one room and five other men are in an adjoining room with an open door, or with just an arch without a door, they can form a Minyan since they can all see one another. This is the view taken by the Abi Ezri (Rav Eliezer Ben Yoel Ha'levi, Germany, 12th century) and the Rashba (Rav Shlomo Ben Aderet of Barcelona, Spain, 1235-1310). These Rishonim compare the laws regarding a Minyan to those that apply to a Zimun for Birkat Ha'mazon. Just as people seated in different room can nevertheless combine to form a Zimun if they can see each other, the same is true of ten men who wish to form a Minyan.
By contrast, the Or Zarua (Rav Yishak of Vienna, 13th century), based on the ruling of the Rashbash (Rav Shlomo Duran, Algiers, 1400-1467), maintained that visibility does not affect the status of men situated in different rooms. Even if they can see each other, they cannot form a Minyan if they are not together in the same room. The Hida (Rav Haim Yosef David Azulai, 1724-1806) understood the Bet Yosef as siding with this stringent view, and, indeed, this is the opinion accepted as Halacha. Therefore, ten men in two separate rooms cannot form a Minyan even if they can see each other.
This Halacha becomes very relevant at Shiba homes, Heaven forbid. Sometimes, if the living room is small, some of the men stand in other rooms, such as the kitchen, or in the hallway. Minyanim held in offices, too, often lack space, and the participants thus do not always stand in the same room. It must be assured that at least ten men are situated in the same room, and then the others can spread out into the hall or into other rooms.
If ten men are in the same room, then they form a Minyan even if they do not all see each other. If there are pillars or pieces of furniture that obstruct their view, they still form a Minyan, since they are all situated in the same room.
The Minhat Yishak (Rav Yishak Weiss, 1902-1989) addresses the case of a synagogue that expanded its sanctuary by removing a wall, combining it with the room next to it, but support pillars needed to be left in place, and they form what resembles a doorway. He ruled that since the pillars were not intended to form a separation, the resulting large room may be considered a single room with respect to the formation of a Minyan. Hence, a Minyan can be formed by ten men in the large room even if they are interspersed throughout the area that appears as two separate rooms.
The Minhat Yishak also addressed the common situation of a synagogue that was planned from the outset to have a portable divider that is sometimes put in place to separate the sanctuary into two separate areas. Since the initial plan was for the area to be occasionally separated, the Minhat Yishak writes, the two sections are treated as separate rooms. Therefore, when a Minyan is formed there, at least ten men must gather in one section, and then the others can position themselves in the other section.
Summary: For a Minyan to be formed, ten men must be situated together in the same room. If they are in separate rooms, they do not form a Minyan even if they can see each other. Once ten men are together in one room, others who are in the hallway or in a different room can join them and thus be considered as praying in a Minyan.