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This is how the original Civ 1 does it: It separates the world into rectangles as you do, each rectangle's width and height is the same as the maximum width and height of a tile. When you click on the screen, it gets the relative position if the mouse from the current rectangle's top-left corner and gets the color from the following image with thise ...


Take a look at Viewports. Many of the Viewport subclasses take virtual height and width in their constructors. There are different flavors of viewport depending on how well you want Libgdx to keep to your desired aspect ratio.


A player can't exist at a location that isn't defined, because computers are discrete things. Bits in any representation of a number (integer or floating point) are either set or they are not set and the pattern they create defines a particular number which we interpret as location. That doesn't mean you can't have multiple coordinate systems though. Just ...

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