Manual GLSL cubemap lookup. Hopefully correct maybe.

ManualGLSLCubemapLookup.cpp

#include <cstdio>
#include <cmath>

struct float2
{
    float x = 0.0f;
    float y = 0.0f;
    float2() {}
    float2( float _x, float _y ) { x = _x; y = _y; }
};

struct float3
{
    float x = 0.0f;
    float y = 0.0f;
    float z = 0.0f;
    float3() {}
    float3(float _x, float _y, float _z ) { x = _x; y = _y; z = _z; }
};

float3 normalize( float3 v )
{
    float length = sqrt( v.x * v.x + v.y * v.y + v.z * v.z );
    v.x /= length;
    v.y /= length;
    v.z /= length;
    return v;
}

// ref: https://www.gamedev.net/forums/topic/687535-implementing-a-cube-map-lookup-function/5337475/
float2 sampleCube( const float3 v, float& faceIndex )
{
	float3 vAbs = float3( fabs( v.x ), fabs( v.y ), fabs( v.z ) );
	float ma;
	float2 uv;

	if( vAbs.z >= vAbs.x && vAbs.z >= vAbs.y ) {
		faceIndex = v.z < 0.0 ? 5.0 : 4.0;
		ma = 0.5 / vAbs.z;
		uv = float2( v.z < 0.0 ? -v.x : v.x, -v.y );
	} else if( vAbs.y >= vAbs.x ) {
		faceIndex = v.y < 0.0 ? 3.0 : 2.0;
		ma = 0.5 / vAbs.y;
		uv = float2( v.x, v.y < 0.0 ? -v.z : v.z );
	} else {
		faceIndex = v.x < 0.0 ? 1.0 : 0.0;
		ma = 0.5 / vAbs.x;
		uv = float2( v.x < 0.0 ? v.z : -v.z, -v.y );
	}

	return float2(
        uv.x * ma + 0.5f,
        uv.y * ma + 0.5f
    );
}

float3 unsampleCube( float2 uv, int faceIndex )
{
    float3 v;
    float ma;

    uv.x -= 0.5f; uv.y -= 0.5f;
    
    if ( faceIndex == 0 || faceIndex == 1 ) {
        v.x = faceIndex == 0 ? 0.5f : -0.5f;
        v.z = faceIndex == 0 ? -uv.x : uv.x; v.y = -uv.y;
    } else if ( faceIndex == 2 || faceIndex == 3 ) {
        v.y = faceIndex == 2 ? 0.5f : -0.5f;
        v.z = faceIndex == 2 ? uv.y : -uv.y; v.x = uv.x;
    } else if ( faceIndex == 4 || faceIndex == 5 ) {
        v.z = faceIndex == 4 ? 0.5f : -0.5f;
        v.x = faceIndex == 4 ? uv.x : -uv.x; v.y = -uv.y;
    }

    return normalize( v );
}

int main() {
    for( float x = -1; x <= 1; x += 0.25f ) {
        for( float y = -1; y <= 1; y += 0.25f ) {
            for( float z = -1; z <= 1; z += 0.25f ) {
                float3 v = normalize( float3( x, y, z ) );

                float idx = 0;
                float2 uv = sampleCube( v, idx );
                float3 v2 = unsampleCube( uv, idx );
                bool ok = ( fabs( v2.x - v.x ) + fabs( v2.y - v.y ) + fabs( v2.y - v.y ) ) < 0.001f;
                printf(
                    "%.2f %.2f %.2f = %.2f %.2f, %.1f = %.2f %.2f %.2f, %s\n",
                    v.x, v.y, v.z,
                    uv.x, uv.y, idx,
                    v2.x, v2.y, v2.z,
                    ok ? "OK" : "WRONG"
                );
            }
        }
    }
}