Ray Tracer, shadow ray produces black circle? - c++

Question

As you can see in the image, I'm getting a black circle on the top of the spheres and the image appears grainy. It's supposed to be more sharp however there are these small black and white spots.
This is the code for the shadow ray
int pos = 0;
float intersect(const ray &r, vector<unique_ptr<object>> &obj)
{
//gives closest object hit point and position;
float closest = numeric_limits<float>::max();
for(int j = 0; j < obj.size(); j++)
{
float t = obj[j]->intersect(r);
if(t > 1e-6 && t < closest)
{
closest = t;
pos = j;
}
}
return closest;
}
vec color(const ray& r, vector<unique_ptr<object>> &shape, vector<unique_ptr<Light>> &lighting, int depth)
{
vec background_color( .678, .847, .902);
vec total{0.0, 0.0, 0.0};
vec ambient{0.125, 0.125, 0.125};
float t_near = intersect(r, shape);
if(t_near == numeric_limits<float>::max())
return background_color;
else
{
total += ambient;
for(int i = 0; i < lighting.size(); i++){
total += shape[pos]->shade(lighting[i]->position(), t_near, r);//gives specular + diffuse
vec shadow_dir = unit_vector(lighting[i]->position() - r.p_at_par(t_near));
ray shadowRay(r.p_at_par(t_near), shadow_dir);
float dist = shadow_dir.lenght();
float a = intersect(shadowRay, shape);
if(a != numeric_limits<float>::max())
return vec(0.0, 0.0, 0.0);
}
return total;
}
}

Answer 1

Okay, got it.
For the black circle, you have to test for the distance of the shadow ray to be less that the distance between the point and the light source. Also, for the distance, the shadow_dir shouldn't be normalised. And to deal with the black white spots, which is dude to shadow intersection, you have to add N*bias to the hit point where the bias is for example 1e-4. The bias shouldn't be too small
vec shadow_dir = lighting[i]->position() - r.p_at_par(t_near);
float dist = shadow_dir.lenght();
vec N = unit_vector(shape[pos]->normal(r, t_near));
shadow_dir = unit_vector(shadow_dir);
ray shadowRay(r.p_at_par(t_near) + N*1e-4, shadow_dir);
float a = intersect(shadowRay, shape);
if(a != numeric_limits<float>::max()){
float m = shadowRay.p_at_par(a).lenght();
if(a < dist)
return vec(0.0, 0.0, 0.0);
}
}