I need help converting this 2D sky shader to 3D

Question

I found this shader function on github and managed to get it working in GameMaker Studio 2, my current programming suite of choice. However this is a 2D effect that doesn't take into account the camera up vector, nor fov. Is there anyway that can be added into this? I'm only intermediate skill level when it comes to shaders so I'm not sure exactly what route to take, or whether it would even be considered worth it at this point, or if I should start with a different example.

uniform vec3 u_sunPosition;
varying vec2 v_vTexcoord;
varying vec4 v_vColour;
varying vec3 v_vPosition;

#define PI 3.141592
#define iSteps 16
#define jSteps 8

vec2 rsi(vec3 r0, vec3 rd, float sr) {
    // ray-sphere intersection that assumes
    // the sphere is centered at the origin.
    // No intersection when result.x > result.y
    float a = dot(rd, rd);
    float b = 2.0 * dot(rd, r0);
    float c = dot(r0, r0) - (sr * sr);
    float d = (b*b) - 4.0*a*c;
    if (d < 0.0) return vec2(1e5,-1e5);
    return vec2(
        (-b - sqrt(d))/(2.0*a),
        (-b + sqrt(d))/(2.0*a)
    );
}

vec3 atmosphere(vec3 r, vec3 r0, vec3 pSun, float iSun, float rPlanet, float rAtmos, vec3 kRlh, float kMie, float shRlh, float shMie, float g) {
    // Normalize the sun and view directions.
    pSun = normalize(pSun);
    r = normalize(r);

    // Calculate the step size of the primary ray.
    vec2 p = rsi(r0, r, rAtmos);
    if (p.x > p.y) return vec3(0,0,0);
    p.y = min(p.y, rsi(r0, r, rPlanet).x);
    float iStepSize = (p.y - p.x) / float(iSteps);

    // Initialize the primary ray time.
    float iTime = 0.0;

    // Initialize accumulators for Rayleigh and Mie scattering.
    vec3 totalRlh = vec3(0,0,0);
    vec3 totalMie = vec3(0,0,0);

    // Initialize optical depth accumulators for the primary ray.
    float iOdRlh = 0.0;
    float iOdMie = 0.0;

    // Calculate the Rayleigh and Mie phases.
    float mu = dot(r, pSun);
    float mumu = mu * mu;
    float gg = g * g;
    float pRlh = 3.0 / (16.0 * PI) * (1.0 + mumu);
    float pp = 1.0 + gg - 2.0 * mu * g;
    float pMie = 3.0 / (8.0 * PI) * ((1.0 - gg) * (mumu + 1.0)) / (sign(pp)*pow(abs(pp), 1.5) * (2.0 + gg));

    // Sample the primary ray.
    for (int i = 0; i < iSteps; i++) {

        // Calculate the primary ray sample position.
        vec3 iPos = r0 + r * (iTime + iStepSize * 0.5);

        // Calculate the height of the sample.
        float iHeight = length(iPos) - rPlanet;

        // Calculate the optical depth of the Rayleigh and Mie scattering for this step.
        float odStepRlh = exp(-iHeight / shRlh) * iStepSize;
        float odStepMie = exp(-iHeight / shMie) * iStepSize;

        // Accumulate optical depth.
        iOdRlh += odStepRlh;
        iOdMie += odStepMie;

        // Calculate the step size of the secondary ray.
        float jStepSize = rsi(iPos, pSun, rAtmos).y / float(jSteps);

        // Initialize the secondary ray time.
        float jTime = 0.0;

        // Initialize optical depth accumulators for the secondary ray.
        float jOdRlh = 0.0;
        float jOdMie = 0.0;

        // Sample the secondary ray.
        for (int j = 0; j < jSteps; j++) {

            // Calculate the secondary ray sample position.
            vec3 jPos = iPos + pSun * (jTime + jStepSize * 0.5);

            // Calculate the height of the sample.
            float jHeight = length(jPos) - rPlanet;

            // Accumulate the optical depth.
            jOdRlh += exp(-jHeight / shRlh) * jStepSize;
            jOdMie += exp(-jHeight / shMie) * jStepSize;

            // Increment the secondary ray time.
            jTime += jStepSize;
        }

        // Calculate attenuation.
        vec3 attn = exp(-(kMie * (iOdMie + jOdMie) + kRlh * (iOdRlh + jOdRlh)));

        // Accumulate scattering.
        totalRlh += odStepRlh * attn;
        totalMie += odStepMie * attn;

        // Increment the primary ray time.
        iTime += iStepSize;

    }

    // Calculate and return the final color.
    return iSun * (pRlh * kRlh * totalRlh + pMie * kMie * totalMie);
}

vec3 ACESFilm( vec3 x )
{
    float tA = 2.51;
    float tB = 0.03;
    float tC = 2.43;
    float tD = 0.59;
    float tE = 0.14;
    return clamp((x*(tA*x+tB))/(x*(tC*x+tD)+tE),0.0,1.0);
}

void main() {
    vec3 color = atmosphere(
        normalize( v_vPosition ),           // normalized ray direction
        vec3(0,6372e3,0),               // ray origin
        u_sunPosition,                        // position of the sun
        22.0,                           // intensity of the sun
        6371e3,                         // radius of the planet in meters
        6471e3,                         // radius of the atmosphere in meters
        vec3(5.5e-6, 13.0e-6, 22.4e-6), // Rayleigh scattering coefficient
        21e-6,                          // Mie scattering coefficient
        8e3,                            // Rayleigh scale height
        1.2e3,                          // Mie scale height
        0.758                           // Mie preferred scattering direction
    );

    // Apply exposure.
    color = ACESFilm( color );

    gl_FragColor = vec4(color, 1.0);
}

Answer 1

However this is a 2D effect that doesn't take into account the camera up vector, nor fov.

If you want to draw a sky in 3D, then you have to draw the on the back plane of the normalized device space. The normalized device space is is a cube with the left, bottom near of (-1, -1, -1) and the right, top, f ar of (1, 1, 1).
The back plane is the quad with:

bottom left:  -1, -1, 1
bottom right:  1, -1, 1
top right:    -1, -1, 1
top left:     -1, -1, 1

Render this quad. Note, the vertex coordinates have not to be transformed by any matrix, because the are normalized device space coordinates. But you have to transform the ray which is used for the sky (the direction which is passed to atmosphere).
This ray has to be a direction in world space, from the camera position to the the sky. By the vertex coordinate of the quad you can get a ray in normalized device space. You have tor transform this ray to world space. The inverse projection matrix (MATRIX_PROJECTION) transforms from normalized devices space to view space and the inverse view matrix (MATRIX_VIEW) transforms form view space to world space. Use this matrices in the vertex shader:

attribute vec3 in_Position;
varying   vec3 v_world_ray;

void main()
{
    gl_Position = vec4(inPos, 1.0);

    vec3 proj_ray = vec3(inverse(gm_Matrices[MATRIX_PROJECTION]) * vec4(inPos.xyz, 1.0));
    v_world_ray   = vec3(inverse(gm_Matrices[MATRIX_VIEW]) * vec4(proj_ray.xyz, 0.0));
}

In the fragment shader you have to rotate the ray by 90° around the x axis, but that is just caused by the way the ray is interpreted by function atmosphere:

varying vec3 v_world_ray;

// [...]

void main() {

    vec3 world_ray = vec3(v_world_ray.x, v_world_ray.z, -v_world_ray.y);

    vec3 color = atmosphere(
        normalize( world_ray.xyz ),     // normalized ray direction
        vec3(0,6372e3,0),               // ray origin
        u_sunPosition,                  // position of the sun
        22.0,                           // intensity of the sun
        6371e3,                         // radius of the planet in meters
        6471e3,                         // radius of the atmosphere in meters
        vec3(5.5e-6, 13.0e-6, 22.4e-6), // Rayleigh scattering coefficient
        21e-6,                          // Mie scattering coefficient
        8e3,                            // Rayleigh scale height
        1.2e3,                          // Mie scale height
        0.758                           // Mie preferred scattering direction
    );

    // Apply exposure.
    color = ACESFilm( color );

    fragColor = vec4(color.rgb, 1.0);
}