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That does look normal. Remember we are essentially zooming way in on texture pages here with sprites like this. It is like in a 3D game when you get the camera as close as possible to some texture and see the actual pixels. 

One thing you can do to improve it is on the light_engine object in the variables tab, change the shadow_atlas_size and shadow_map_size.

The atlas size is the total size that will be used and you should simply use the biggest your platform supports. The shadow map size is the resolution for shadow maps and bigger will look better. The more you can fit into a single atlas, the faster performance is.

And again, the better aliasing the sprite has will help.

Another improvement is adding your own anti-aliasing as a post processing effect. As you know this is common and hides jagged edges in most games. You can use a post draw event somewhere after the game world is rendered and apply it (turn off automatic draw of application surface, etc.). 

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Increasing the shadow atlas and map help a lot and combined with display_reset's AA it looks pretty good now, but I'll probably have to keep performance in mind going forward. It's hard for me to judge it now since I don't have much on the screen visually yet but I'll see.

Thanks for the help! Additionally, would you happen to know any preferred AA systems (shaders or whatnot?) I should be able to find some on my own but if you have any recommendable ones that could help too.

Sorry I don't have any AA recommendation. You should generally be able to find something by asking around on the official GameMaker community forums. Usually Fast Approximate Anti-aliasing (FXAA) is cheap and all you should need.