Currently, I have blending and depth testing turn on for a 2D game. When I draw my textures, the “upper” texture remove some portion of the lower textures if they intersect. Clearly, transparent pixels of the textures are taken into account of the depth test, and it clear out all the colors of the drawn lower textures if they intersect. Moreover, alpha blendings are incorrectly rendered. Are there any sort of functions that can tell OpenGL to not include transparent pixels into depth testing?
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No it’s not possible. This is true of all hardware depth testing.
GL (full or ES — and D3D) all have the same model — they paint in the order you specify polygons. If you draw polygon A in before polygon B, and logically polygon A should be in front on polygon B, polygon B won’t be painted (courtesy of the depth test).
The solution is to draw you polygons in order from farthest to nearest the current view origin. Happily in a 2D game this should just be a simple sort (one you probably won’t even need to do very often).
In 3D games BSPs are the basic solution to this issue.