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me working during the day with the gf doing an exercise video in my peripheral vision while my 3d printer whirrs away noisily in the background printing and having my collection of expensive board games and gaming table covered in dust from the workshop is 0 for 3 on my list of wants.
my current study is a meter shorter but the same width as my new office and lacks a south facing skylight, the gym has a patio doors for lighting and just needs room for an exercise bike and enough room for my gf to lay out flat with all lumbs extended, the workshop extends out into the wide alcove so its bigger than the rest of the rooms and I don't want any windows for the local crackheads to be looking in through anyways (but could remove the black covering from the alcove windows). the games room will have dimmed room lighting and powerful lights over the gaming table and my painting table will use daylight lamps so sunlight is never gonna be a factor. if it wasnt a games room it would be rows of shelving for storage which still works.
I'll hang sheets up to simulate the walls before I start to check it feels ok but as is none of it feels like a compromise to me.
you will surely regret dividing up the space, leading to four cramped boxy rooms with poor lighting.
the activities you have suggested coexist happily together.