Implementing soft shadows in a ray tracer

Question

what I am trying to do is implementing soft shadows in my simple ray tracer, developed in C++. The idea behind this, if I understood correctly, is to shoot multiple rays towards the light, instead of a single ray towards the center of the light, and average the results. The rays are therefore shot in different positions of the light. So far I am using random points, which I don't know if it is correct or if I should use points regularly distributed on the light surface. Assuming that I am doing right, I choose a random point on the light, which in my framework is implemented as a sphere. This is given by:

Vec3<T> randomPoint() const
{
    T x;
    T y;
    T z;

    // random vector in unit sphere
    std::random_device rd; //used for the new <random> library
    std::mt19937 gen(rd());
    std::uniform_real_distribution<> dis(-1, 1);

    do
    {
        x = dis(gen);
        y = dis(gen);
        z = dis(gen);


    } while (pow(x, 2) + pow(y, 2) + pow(z, 2) > 1);        // simple rejection sampling

    return center + Vec3<T>(x, y, z) * radius;
}

After this, I don't know how exactly I should move since my rendering equation (in my simple ray tracer) is defined as follows:

Vec3<float> surfaceColor = 0
for(int i < 0; i < lightsInTheScene.size(); i++){
    surfaceColor += obj->surfaceColor * transmission *
    std::max(float(0), nHit.dot(lightDirection)) * g_lights[i]->emissionColor;
}
return surfaceColor + obj->emissionColor;

where transmission is a simple float which is set to 0 in case the ray that goes from my hitPoint to the lightCenter used to find an object in the middle.

So, what I tried to do was:

creating multiple rays towards random points on the light
counting how many of them hit an object on their path and memorize this number

for simplicity: Let's imagine in my case that I shoot 3 shadow rays from my point towards random points on the light. Only 2 of 3 rays reach the light. Therefore the final color of my pixel will be = color * shadowFactor where shadowFactor = 2/3. In my equation then I delete the transmission factor (which is now wrong) and I use the shadowFactor instead. The problem is that in my equation I have:

 std::max(float(0), nHit.dot(lightDirection))

Which I don't know how to change since I don't have anymore a lightDirection which points towards the center of the light. Can you please help me understanding what should I do it and what's wrong so far? Thanks in advance!

You may wish to check this answer: stackoverflow.com/questions/31709332/ray-tracing-soft-shadow/… — Miloslaw Smyk

Nico Schertler Nico Schertler · Accepted Answer · 2015-07-27T18:00:53

You should evaluate the entire BRDF for the picked light samples. Then, you will also have the light direction (vector from object position to picked light sample). And you can average these results. Note that most area lights have a non-isotropic light emission characteristic (i.e. the amount of light emitted from a point varies by the outgoing direction).

Averaging the visibility does not produce correct results (although they are usually visually plausible).

Implementing soft shadows in a ray tracer

1 Answers