How to implement refractions in recursive raytracer?

I am writing a recursive raytracer and have tried to implement refractions for over 3 weeks now with no success. I am trying to use

float generateTransmissionRay(Ray ray, HitRecord hit, float n, Ray &temp)
{
      vec3 N;
      if(dot(ray.direction,hit.normal)<0)
            N = -hit.normal;
      else
            N = hit.normal;
      float nt = hit.intersection.obj.mat.refractivity;
      float discriminant = 1-(pow(n,2)*(1-pow(dot(ray.direction,N),2)))/pow(nt,2);
      if(discriminant<=0)
      {
            return false;
      }
      temp.origin = EPSILON*hit.intersection.point;
      temp.direction = ((n*(ray.direction-(dot(ray.direction,N))*N))/nt)-sqrt(discriminant)*N;
      return true;
}
 
In the code above, temp corresponds to the refraction ray. the origin of the refraction ray (temp.origin) being the intersection point of the original ray. hit is an object which contains all the information from the object that was intersected by the primary ray (material properties, normal at point of intersection. etc). The call to that function is in my rayColor function, which is the function I recursively call to generate reflection and refraction rays. I've attached the code snippet related to reflections and refractions calculations in my rayColor function. rayColor takes a ray, a hit object corresponding to that ray, a depth, and a refraction_index) When I initially call rayColor, I pass it an index refraction of 1.0. Then during the recursive calls, I pass it the refraction indices of the object intersected by the ray.

I'm sure there's a number of things I'm doing wrong. I just can't pinpoint where or what. if I don't scale the refraction color by the transmittance coefficient (which I'm not even sure that I'm calculating right because I dont know if the way I'm calculating absorbance, which is denoted as "a" in the code, is correct, my scene still turns white, and doesn't look any different.) Part of the issue is that the color components for the ray are becoming >1 when I add the refracted color, and I'm not entirely sure how to fix that. When doing reflections I had gotten around that by setting a color component to 1 everytime it went over. But I dont think I'm supposed to do that.

I atteched two images, one of my scene with refractions enabled, one with refractions disabled. Perhaps the images might provide some insight to someone wiser than I.

ANy help in this matter would be greatly appreciated. I've been stuck on this for weeks!Start Free Trial

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RGBA rayColor(Ray ray, HitRecord hit, int depth, float n1)
{
       ....*Code that Calculates diffuse and specular components of each ray for every light in the scene*.....
.......
.....
 
	//Use Beer's law to claculate absorbance  and transmittance coefficient
	float dist = distanceBetweenPoints(ray.origin,hit.intersection.point);
	RGBA a =(ray.color*EPSILON)*(-dist);
	RGBA k;
	k.r = exp(a.r)*hit.intersection.obj.mat.refractivity;
	k.b = exp(a.b)*hit.intersection.obj.mat.refractivity;
	k.g = exp(a.g)*hit.intersection.obj.mat.refractivity;
	k.a = exp(a.a)*hit.intersection.obj.mat.refractivity;
	//Calculate reflectance
	float R_0 = (n1-hit.intersection.obj.mat.refractivity)/(n1+hit.intersection.obj.mat.refractivity);
	R_0 = pow(R_0,2);
	float cosTheta = dot(eye,hit.normal);
	float RTheta = R_0 + (1.0 - R_0) * pow(1.0 - cosTheta, 5.0);
	
	if (hit.intersection.obj.mat.material_specular.r != 0 ||
		hit.intersection.obj.mat.material_specular.g != 0 ||
		hit.intersection.obj.mat.material_specular.b != 0 ||
		hit.intersection.obj.mat.material_specular.a != 0) {
			//Get intersectionpoint 
			vec3 intersect;
			intersect.x = hit.intersection.point.x;
			intersect.y = hit.intersection.point.y;
			intersect.z = hit.intersection.point.z;
			vec3 refDirection = (ray.direction - 2 * (dot(hit.normal, ray.direction) * hit.normal));
			normalize(refDirection);
			refRay = generateRay(intersect + EPSILON * refDirection,refDirection);
						
			shootRay(refRay,refRecord);
			float objreflectivity = hit.intersection.obj.mat.reflectivity;
			float objrefractivity = hit.intersection.obj.mat.refractivity;
			
			ray.color = ray.color + hit.intersection.obj.mat.material_specular*rayColor(refRay,refRecord,depth + 1,1.0);
	
			
			if(hit.intersection.obj.mat.refractivity!=0)
			{
				bool notTotallyReflective = generateTransmissionRay(ray, hit, n1,transray);
							
				if(notTotallyReflective)
				{
					shootRay(transray,transRecord);	
					//ray.color = ray.color + k*rayColor(transray,transRecord,depth + 1,hit.intersection.obj.mat.refractivity);							
				}
			
			}
	}
 
	if (ray.color.r > 1)
		ray.color.r = 1;
	if (ray.color.b > 1)
		ray.color.b = 1;
	if (ray.color.g > 1)
		ray.color.g = 1;
	
	return ray.color;
}