Say I have a map of the World that I want to use for a risk type game. What would be an efficient way to make all the countries into independent pieces?
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You can actually get individual vector maps of countries. It'd might be more efficient to get a map that's split already, rather than trying to cut them out yourself.
Yes, I think tss0004 is correct. You should split the countries manually in your image editor, then import them as separate frames or sprites and arrange them yourself.
I can say another way, just use masks, make effects over them, so, if you wanna hide one part of your map, just play with the effects ^^
It's like World of Warcraft used on the map, you discover the area and it hide the overlapping image ^^