Volume fog

#include "common.h"

sampler depthSampler : register(s0);
sampler noiseVolume : register(s1);

float4x4 invViewProj : register(c0);
float3 boundingBox[2] : register(c4);
float3 cameraPos : register(c6);
float3 fogColor : register(c7);
float fogDensity : register(c8);

// original code of ray-box intersection
// https://github.com/hpicgs/cgsee/wiki/Ray-Box-Intersection-on-the-GPU
struct Ray {
    float3 origin;
    float3 direction;
    float3 invDirection;
    int sign[3];
};

Ray MakeRay(float3 origin, float3 direction) {
    Ray ray;
    ray.origin = origin;
    ray.direction = direction;
    ray.invDirection = float3(1.0, 1.0, 1.0) / direction;
    ray.sign[0] = (ray.invDirection.x < 0) ? 1 : 0;
    ray.sign[1] = (ray.invDirection.y < 0) ? 1 : 0;
    ray.sign[2] = (ray.invDirection.z < 0) ? 1 : 0;
    return ray;
}

void RayBoxIntersection(in Ray ray, in float3 aabb[2],out float tmin, out float tmax) {
    float tymin, tymax, tzmin, tzmax;
    tmin = (aabb[ray.sign[0]].x - ray.origin.x) * ray.invDirection.x;
    tmax = (aabb[1-ray.sign[0]].x - ray.origin.x) * ray.invDirection.x;
    tymin = (aabb[ray.sign[1]].y - ray.origin.y) * ray.invDirection.y;
    tymax = (aabb[1-ray.sign[1]].y - ray.origin.y) * ray.invDirection.y;
    tzmin = (aabb[ray.sign[2]].z - ray.origin.z) * ray.invDirection.z;
    tzmax = (aabb[1-ray.sign[2]].z - ray.origin.z) * ray.invDirection.z;
    tmin = max(max(tmin, tymin), tzmin);
    tmax = min(min(tmax, tymax), tzmax);
    // post condition:
    // if tmin > tmax (in the code above this is represented by a return value of INFINITY)
    //     no intersection
    // else
    //     front intersection point = ray.origin + ray.direction * tmin (normally only this point matters)
    //     back intersection point  = ray.origin + ray.direction * tmax
}

float4 main( float2 texCoord : TEXCOORD0 ) : COLOR0 {
    float tmin, tmax;
    float4 outColor = float4(fogColor, 0);
    float3 p = RestorePositionFromDepth(texCoord, invViewProj, depthSampler);
    float3 direction = p - cameraPos;
    float distance = length(direction);
    Ray ray = MakeRay(cameraPos, direction);

    RayBoxIntersection(ray, boundingBox, tmin, tmax);

    // got intersection
    if(tmin <= tmax) {
        float3 pMin = cameraPos + tmin * direction;
        float3 pMax = cameraPos + tmax * direction;
        float3 v = cameraPos - pMin;
        if(distance > length(v) && dot(v, direction) < 0) {
            float thickness = length(pMax - pMin);
            float dTarget = length(p - pMin);
            outColor.a = fogDensity * (dTarget / thickness);
        }
    }

    return outColor;
};