#include <math.h>

class vec3{

public:
	double x;
	double y;
	double z;


	vec3()
	{
		x = 0;
		y = 0;
		z = 0;
	}

	vec3(double X, double Y, double Z)
	{
		x = X;
		y = Y;
		z = Z;
	}

	vec3 scale(double s)
	{
		return vec3(x*s, y*s, z*s);
	}

	void normalize()
	{
		double distance = x*x + y*y + z*z;
		distance = sqrt(distance);
		x = x/distance;
		y = y/distance;
		z = z/distance;
	}

	vec3 add(vec3 b)
	{
		return vec3(x + b.x, y + b.y, z + b.z);
	}

	vec3 crossProduct(vec3 b)
	{
		vec3 output;
		output.x = y*b.z - z*b.y;
		output.y = z*b.x - x*b.z;
		output.z = x*b.y - y*b.x;
		return output;
	}

	void negate()
	{
		x = -x;
		y = -y;
		z = -z;
	}

	float distance()
	{
		return (float)sqrt(x*x + y*y + z*z);
	}

	float dotProduct(vec3 b)
	{
		double output = x*b.x + y*b.y + z*b.z;
		return (float)output;		
	}

	vec3 reflection(vec3 normal)
	{
		vec3 R;
		float temp = normal.dotProduct(vec3(x, y, z)); //View(dot)normal
		R.x = -(2*normal.x*temp - x);
		R.y = -(2*normal.y*temp - y);
		R.z = -(2*normal.z*temp - z);
		return R;
	}

	//this function uses snells law to calculate the refraction of our ray through a transparent surface
	vec3 refraction(vec3 normal, double dielectric)
	{
		double cosTheta1 = normal.dotProduct( vec3(-x, -y, -z) );
		double cosTheta2 = sqrt( 1 - (dielectric*dielectric)*( 1 - (cosTheta1*cosTheta1)) );
		if(cosTheta1 > 0)
		{
			vec3 vRefract = vec3(dielectric*x, dielectric*y, dielectric*z);
			double temp = (dielectric*cosTheta1) - cosTheta2;
			vRefract = vec3(vRefract.x + (temp*normal.x), vRefract.y + (temp*normal.y), vRefract.z + (temp*normal.z) );
			vRefract.normalize();
			return vRefract;
		}
		else
		{
			vec3 vRefract = vec3(dielectric*x, dielectric*y, dielectric*z);
			double temp = cosTheta2 + (dielectric*cosTheta1);
			vRefract = vec3(vRefract.x - (temp*normal.x), vRefract.y - (temp*normal.y), vRefract.z - (temp*normal.z) );
			vRefract.normalize();
			return vRefract;
		}

	}

	vec3 betterRefraction(vec3 normal, double dielectric)
	{	
		normal.normalize();
		float cosI = -normal.dotProduct(vec3(x, y, z));

		if(cosI < 0)
			dielectric = 1.0/dielectric;

		float sin2T = dielectric*dielectric*(1.0 - cosI*cosI);
		if(sin2T < 1.0)
		{
			vec3 intRefrac = vec3(x*dielectric - (normal.x*(dielectric + sqrt(1.0-sin2T)) ), y*dielectric - (normal.y*(dielectric + sqrt(1.0-sin2T)) ), z*dielectric - (normal.z*(dielectric + sqrt(1.0-sin2T)) ) );
			intRefrac.normalize();
			return intRefrac;
		}

		return vec3(0,0,0);


	}

};