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?
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.
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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 ^^