When my brother first told me about it, the job seemed like an over-the-top challenge: installing a coffered ceiling in a barrel vault. But after some thought, we realized we could use the same techniques we've used on radius balustrades and countless curved walls. With a router, a trammel arm, and plenty of patience, we figured, we could take it on.

The plans called out a 134-inch radius for the barrel vault but didn't specify whether the measurement was from the framing or the drywall. So our first step was to check the actual radius at the drywall. To do this, we placed a 6-foot level against the ceiling, then measured perpendicular from the center of the level up to the drywall. Using a...

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