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sponge

I don't think I understood why exactly this would cause aliasing, could I get some clarification?

hubbahubba

Positions 4 and 5 are relatively far away compared to 1 and 2 right? So they represent a larger region in the texture space.

Now imagine that in the right image the region around position 5 are all different colors. For example, imagine all the colors around 5 are green but the color 5 is on is red. If you only take the square that 5 is inside and use that color to represent it in the original image (on the left), you're not accurately representing the color of 5.