Fresnel

//Position, Incident, Normal, nt/ni
vec4 fresnel(vec3 P,vec3 I,vec3 N,number eta)
{
    number dNI=dot(N,I);//Compute once, use 5x
    vec3 R=I-2.0*dNI*N;//Reflected direction
    vec3 T=vec3(0.0);//Transmitted direction
    number k=1.0-eta*eta*(1.0-dNI*dNI);//Yolo
    if(k>=0.0)
        T=eta*I-(eta*dNI+sqrt(k))*N;//Swag

    number mag=dot(N,T)/dNI;//Magnification
    vec2 cd=vec2(1+mag*eta,mag+eta);//Common divisor
    vec2 r=vec2(1-mag*eta,mag-eta)/cd;//Reflected (S,P)
    vec2 t=vec2(2)/cd;//Transmitted (S,P)

    vec4 Colour_R=(r.x*r.x+r.y*r.y)*getColour(P,R);//getColour is some function that gets the colour along a ray at point P in direction R.
    if(k<0.0)
        return Colour_R;
    else
        return Colour_R+mag*eta*(t.x*t.x+t.y*t.y)*getColour(P,T);//Colour_T
    //Look maa, no trig! (Trig is a lie BTW.)
}