Godot perspecive projection shaders

Camera.gd

extends TextureRect

export var sensitivity: Vector3 = Vector3(0.005, 0.005, TAU/4)
var euler: Vector3 = Vector3.ZERO

func _init() -> void:
	sensitivity.x *= -1

func _input(event: InputEvent) -> void:
	if event.is_action_pressed("ui_cancel"):
		if Input.get_mouse_mode() == Input.MOUSE_MODE_VISIBLE:
			Input.set_mouse_mode(Input.MOUSE_MODE_CAPTURED)
		else:
			Input.set_mouse_mode(Input.MOUSE_MODE_VISIBLE)

	if event.is_action_pressed("camera_reset_roll"):
		euler.z = 0

	if Input.get_mouse_mode() == Input.MOUSE_MODE_CAPTURED:
		if event is InputEventMouseMotion:
			euler.x += event.relative.y * sensitivity.y
			euler.x = clamp(euler.x, -TAU/4, TAU/4)
			euler.y += event.relative.x * sensitivity.x
			euler.y = fmod(euler.y, TAU)

func _process(delta: float) -> void:
	if Input.is_action_pressed("camera_roll_counterclockwise"):
		euler.z -= delta * sensitivity.z
	if Input.is_action_pressed("camera_roll_clockwise"):
		euler.z += delta * sensitivity.z
	euler.z = clamp(euler.z, -TAU/4, TAU/4)

	material.set_shader_param("rotation", Basis(euler))

Cylindrical.shader

shader_type canvas_item;

const float PI = 3.14159265358979;
const float TAU = PI * 2.0;
const float HALF_PI = PI / 2.0;

uniform mat3 rotation;
uniform float fov: hint_range(10, 90) = 90;
uniform float cylinder_height = 1;

void fragment() {
	vec2 resolution = 1.0 / SCREEN_PIXEL_SIZE;
	
	float theta = (PI / 180.0) * (fov / 2.0);
	vec2 pixel = (SCREEN_UV * 2.0 - 1.0) * tan(theta);
	pixel.y *= - resolution.y / resolution.x;
	vec3 towards_pixel = rotation * vec3(pixel, -1);
	
	float y_angle = atan(towards_pixel.x, towards_pixel.z);
	float x_angle = atan(towards_pixel.y, length(towards_pixel.xz));
	
	vec2 coords;
	coords.x = mod(y_angle, TAU) / TAU;
	coords.y = (tan(x_angle) + HALF_PI) / PI;
	
	if (coords.y >= 0.0 && coords.y <= 1.0) {
		COLOR = texture(TEXTURE, coords);
	} else {
		// Tiled "transparency" background
		vec2 screen_pos = SCREEN_UV * resolution;
		vec2 square = floor(screen_pos / 12.0);
		if (mod(square.x + square.y, 2.0) > 0.5) {
			COLOR.rgb = vec3(0.3)
		} else {
			COLOR.rgb = vec3(0.4);
		}
	}
}

Equirectangular.shader

shader_type canvas_item;

const float PI = 3.14159265358979;
const float TAU = PI * 2.0;
const float HALF_PI = PI / 2.0;

uniform mat3 rotation;
uniform float fov: hint_range(10, 90) = 90;

void fragment() {
	vec2 resolution = 1.0 / SCREEN_PIXEL_SIZE;
	
	float theta = (PI / 180.0) * (fov / 2.0);
	vec2 pixel = (SCREEN_UV * 2.0 - 1.0) * tan(theta);
	pixel.y *= - resolution.y / resolution.x;
	vec3 towards_pixel = rotation * vec3(pixel, -1);
	
	float y_angle = atan(towards_pixel.x, towards_pixel.z);
	float x_angle = atan(towards_pixel.y, length(towards_pixel.xz));
	
	vec2 coords;
	coords.x = mod(y_angle, TAU) / TAU;
	coords.y = (x_angle + HALF_PI) / PI;
	
	COLOR = texture(TEXTURE, coords);
}

Setup.md

1. Create a new scene with a Control
2. Add a TextureRect with the source image
   1. Set the TextureRect layout to Full Rect
   2. Add the Camera.gd script to the TextureRect
   3. Add the perspective shader to the TextureRect
3. Set the following actions in the project settings: camera_roll_clockwise, camera_roll_counterclockwise, camera_reset_roll
4. Launch the scene and enjoy :)