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owerdraw artifacts

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Hello, im having some trouble with overdrawing when doing alpha blending in my software engine. The problem seems to be that due to rounding errors some pixels are drawn by more than one triangle that share vertices. The result is that when the next triangle is going to be drawn on that pixel and checks the color for determening alpha, the result is wrong since it has already been drawn once. I understand that i need to adopt some standard when it comes to shared vertices but i cant quite figure out what exactly to do. Anyone know? :/ screenshot: Thanks in advance.

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