Making the arch on the viola is the most difficult job for a luthier. It has the distinction of being the only task that requires you to work in three dimensions. Perhaps carving the scroll is a bit of a three-dimensional affair, but to no-where-near the scale of the arch. And it has virtually no bearing on sound.
Understanding three-dimensional shapes is something humans don’t seem to be adept at doing. It stands to reason, though. The organs we have to interpret spatial data don’t see in three dimensions. Our eyes see two different two-dimensional pictures and then our brain extrapolates a third dimension. Essentially, we guess what the third dimension really looks like. Coincidentally, this interpretation by the brain is why artists are able to simulate a three dimensional space on a two dimensional canvas. Our brains are unable to tell the difference between a fake and something real!
Poor conception or execution of the arch is devastating to sound quality, particularly in a Strad model instrument. Conversely, arching well done will facilitate beautiful sounds for hundreds of years.
I try to develop the arch as a whole, working on the part least finished, but I find it useful to finalize (or very nearly so) the channel—the recurve around the perimeter of each plate.
With finger planes, I work quickly to shape the viola. Keeping the three-dimensional shape in my head is tiring. I finish the arching in one session while the image in my mind is fresh.
Because direct sight does not yield good information, less direct methods must be used. I like to quickly run my fingers across these areas; a slight increase in pressure in the fingertips tells me it’s too full.
Shadows are also useful. The clues are subtle, but you can tell when a shadow “catches” on a bump or high spot.