{ RCSid $Id: WalterBSDF.cal,v 1.1 2014/03/19 19:06:20 greg Exp $ }
{
	Isotropic BSDF model by Walter et al.
}
			{ BRDF parameters (change these) }
kdinr : 0.;
ksinr : 1.;
f0r : 0.277605834967475;
alpha_r : 0.077419771872748;
			{ BTDF parameters (change these) }
ksint : 0.126221381019119;
sigma_i : 1.434228082595141;
sigma_o : 1.656368055960319;
f0t : 0.2;
alpha_t : 0.149990535073450;

			{ Useful functions }
s(x) : x*x;
abs(x) : if(x, x, -x);
noneg(x) : if(x, x, 0);

			{ Reflection functions }
Gr(x) : 2/(1 + sqrt(1 + s(alpha_r)*(1-s(x))/s(x)));
Fr(w) : f0r + (1-f0r)*(1-w)^5;
Dr(htn) : s(alpha_r)/PI/s( s(htn)*(s(alpha_r)-1) + 1 );

lobe3r(wihr,win,won,htn) : Fr(wihr)*Dr(htn)*Gr(win)*Gr(won) / (4*win*won);
lobe2r(ix,iy,iz,ox,oy,oz,htx,hty,htz,nf) : lobe3r((ix*htx+iy*hty+iz*htz)*nf,
							iz, oz, htz*nf);
lobe1r(ix,iy,iz,ox,oy,oz,htx,hty,htz) : lobe2r(ix,iy,iz,ox,oy,oz,htx,hty,htz,
						1/sqrt(s(htx)+s(hty)+s(htz)));

			{ Transmission functions }
Gt(x) : 2/(1 + sqrt(1 + s(alpha_t)*(1-s(x))/s(x)));
Ft(w) : f0t + (1-f0t)*(1-w)^5;
Dt(htn) : s(alpha_t)/PI/s( s(htn)*(s(alpha_t)-1) + 1 );

lobe3t(wiht,woht,win,won,htn) : abs(wiht*woht/(win*won)) *
		s(sigma_o)*(1-Ft(wiht))*Dt(htn)*Gt(win)*Gt(won) /
			s(sigma_i*wiht + sigma_o*woht);

lobe2t(ix,iy,iz,ox,oy,oz,htx,hty,htz,nf) : lobe3t((ix*htx+iy*hty+iz*htz)*nf,
		(ox*htx+oy*hty+oz*htz)*nf, iz, oz, htz*nf);

lobe1t(ix,iy,iz,ox,oy,oz,htx,hty,htz) : lobe2t(ix,iy,iz,ox,oy,oz,htx,hty,htz,
						1/sqrt(s(htx)+s(hty)+s(htz)));

			{ Final function call - reflection & transmission }
			{ vectors normalized, pointing away from surface }
walter(ix,iy,iz,ox,oy,oz) : if(iz*oz, kdinr/PI +
					ksinr*lobe1r(ix,iy,iz,ox,oy,oz,
						ix+ox, iy+oy, iz+oz),
					ksint*noneg(lobe1t(ix,iy,iz,ox,oy,oz,
						-sigma_i*ix-sigma_o*ox,
						-sigma_i*iy-sigma_o*oy,
						-sigma_i*iz-sigma_o*oz)) );