Well, I suppose it all goes to show you there's more than one way to skin a Maru (Though do pardon the sheer irony if you're a fan of everyone's favorite box-sliding Scottish Fold.) What I meant when I initially mentioned geometric approaches was much more related to on-the-fly solutions like vector analysis rather than the methodical approaches wrought with terrible, initimidating things like theories and axioms.
I suppose I ultimately view the TDC moreso as a tool to gather data, rather than the means by which a final firing solution is calculated. It can certainly do some very impressive things for its time. The PK is the thing that really stands out most to me-- its capability to combine several inputs from devices like the periscope and stadimeter (which I can only presume were all analog) and manage them in unison with movement compensation really is nothing short of extraordinary for period technology. But even with that said, when it comes time to take an approach track and compute a firing solution, I find most of those impressive features to be extraneous when I can put pen to paper and come with an equally effective firing solution as I could fumbling around with all the dials, bells, and whistles while still grappling with ensuring device accuracy for all the data I've manually fed into the equation (Speed, etc.)
Maybe I'm just the nerdy sort that has faith in the fact numbers don't lie, and it's significantly easier to verify a calculation than it is to cycle through all of your data at-hand, make sure it's timely and up to date, then double-check that it's all been entered correctly. Perhaps I've thus far just been siding with vanity in assuming that cranking out a good null-gyro shot was equally simple for most folks as feeding everything into the TDC, but my curiosity is still piqued about how WWII skippers viewed it... I suppose I'll just have to bite the bullet and go pick up the chronicles of the
Wahoo to start my library!