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Can someone explain what is happening here? How is it possible for the frames to be doing this?
There is no resizing with TEXTURES or HI_ going on. I've seen this before on other sprites too and it's quite annoying to say the least. In SLADE, they appear to be lined up perfectly but in-game I get that.
Not sure which renderer you are using, or how many sprites there are on that picture. I'm assuming the green fire effect is its own sprite. If so, you could see this effect in:
* OpenGL if the sampling mode is set to linear. What is happening is that the sampler grabs a little bit of the black transparent pixel next to it in the sprite. It could be fixed by using premultiplied alpha in the textures along with a glBlendMode taking premultiplied input. But this is unlikely to be changed because some mods use broken images for some of the textures where the alpha channel has to be ignored. The various upscalers might also have trouble with a premultiplied approach.
* The software renderer still draws some of its masked stuff using span ranges. There could be a rounding issue that makes it grab just a little bit from a transparent black pixel next to where the sprite begins. You probably only see that for player sprites on Linux, though, because vid_hw2d would have drawn that weapon on the GPU.