Godot shader bending a flat 2d world (e.g. a platformer) to a tiny planet.

curved_fragment.shader

shader_type canvas_item;

uniform sampler2D screen_texture : hint_screen_texture, filter_nearest;
uniform float radius = 3.0;

void fragment() {
	vec2 uv = SCREEN_UV;
	uv.y = 1.0 - uv.y; // seems like the origin changed in Godot 4.
	vec2 surface = vec2(0.5, 0.2);
	vec2 center = surface - vec2(0, radius);
	float base = length(uv - center);
	float height = base - radius;
	float xdiff = (uv.x - surface.x) / base * height;
	uv = clamp(vec2 (uv.x - xdiff, surface.y + height), vec2(0.0, 0.0), vec2(1.0, 1.0));
	uv.y = 1.0 - uv.y; // flip back after all calculations
	COLOR.rgb = textureLod(screen_texture, uv, 0.0).rgb;
}

Regarding the project setup / implementation: I never actually used this shader in an own project, but only wrote it as an answer for a request in some forum years ago. The screenshot you see above is taken from https://github.com/godotengine/godot-demo-projects/tree/master/2d/screen_space_shaders , where I just added the curved fragment shader in my local copy. So I cannot say much about practical implementation issues.

Regarding the origin change - let's ask an expert. :-) @Calinou: Do you know why I had to flip the Y-axis of SCREEN_UV for this shader to work in Godot 4? (The code was working perfectly fine without lines 8 and 15 in Godot 3.x)

@Calinou: Do you know why I had to flip the Y-axis of SCREEN_UV for this shader to work in Godot 4? (The code was working perfectly fine without lines 8 and 15 in Godot 3.x)

Godot 3.x used flipped viewports (it followed OpenGL convention), but this is no longer required in Godot 4 as we could break compatibility to make it the right way around.

Thanks for the confirmation/clarification! Since neither Maik nor myself were able to find this info, I just proposed to add it to the official migration tutorial: godotengine/godot-docs#7833