The building in question is a shared computer research and teaching laboratory. Cambridge University and Microsoft are building it on the new science and technology site in West Cambridge.
The idea was to let the people who were going to use the building see and comment on the arrangement of space within it, and learn how it would function.
It was devised by researchers at Cambridge University, as part of a project on using electronic communication between buildings' architects and their eventual users.
Project leader Paul Richens, director of the university's Martin Centre for Architectural and Urban Studies, said: "The best way to learn about a building is to run around in it, and in a computer game that's just what you do."
The building in question is a shared computer research and teaching laboratory. Cambridge University and Microsoft are building it on the new science and technology site in West Cambridge.
"It's very difficult for people to read architectural plans," Mr Richens said.
"By making a computer game out of the building they can see much better what they are getting."
Weaponry
The point of Quake, though, is to go around blasting things with a collection of fearsome weaponry.
"They were doing that originally but we had to take the guns out - the head of the department didn't like that at all," Mr Richens said.
Initially they put into the game only the basic structure of the building, which looked more or less like the real thing does at the moment, halfway through construction.
Having found that the principle worked, they put in all of the building - except that at that stage the architect had not decided what its finishes would be so it had Quake's "grungy" textures.
There were some problems however.
Be careful in there
Mr Richens revealed that the lifts were a bit dangerous because "if you get in while it's upstairs, it comes down and hits you on the head, and you die.
"And we had to spend a lot of time putting handrails on all the landings because people kept falling off," he added.
Quake's code is such that both the scenery and the 3D animated characters are replaceable.
It means the architect in London, Geoff Cohen of RMJM, can take the sponsor, Microsoft's Bill Gates, in Seattle, on a virtual tour of the building watched by anyone who cares to join in - provided they surrender their guns at the door.
Cost advantage
It could now be done with other buildings but Mr Richens said the ideal is to find a way to turn any architectural drawing into a "game", which was technically not easy to do.
So this is a possible way forward, and potentially a money-spinning idea.
The chief advantage is cost. Established architectural virtual reality modelling systems tended to be very expensive, Mr Richens said.
"We get slightly better results using a £30 game running on a £150 graphics card. So it's extremely low-cost virtual reality."
Japan's Institute for Architects is interested and the Martin Centre has worked with a Japanese company which wants to be able to load something similar into the new Playstation.
The project has had about £80,000 in funding from the Engineering and Physical Sciences Research Council, with a similar amount from Microsoft.
Screenshots: Martin Centre