/* Amplitude reflection coefficient (s-polarized) */ float rs(float n1, float n2, float cosI, float cosT) { return (n1 * cosI - n2 * cosT) / (n1 * cosI + n2 * cosT); } /* Amplitude reflection coefficient (p-polarized) */ float rp(float n1, float n2, float cosI, float cosT) { return (n2 * cosI - n1 * cosT) / (n1 * cosT + n2 * cosI); } /* Amplitude transmission coefficient (s-polarized) */ float ts(float n1, float n2, float cosI, float cosT) { return 2 * n1 * cosI / (n1 * cosI + n2 * cosT); } /* Amplitude transmission coefficient (p-polarized) */ float tp(float n1, float n2, float cosI, float cosT) { return 2 * n1 * cosI / (n1 * cosT + n2 * cosI); } // cosI is the cosine of the incident angle, that is, cos0 = dot(view angle, normal) // lambda is the wavelength of the incident light (e.g. lambda = 510 for green) // From http://www.gamedev.net/page/resources/_/technical/graphics-programming-and-theory/thin-film-interference-for-computer-graphics-r2962 float thinFilmReflectance(float cos0, float lambda, float thickness, float n0, float n1, float n2) { float PI=3.1415926535897932384626433832795; // compute the phase change term (constant) float d10 = (n1 > n0) ? 0 : PI; float d12 = (n1 > n2) ? 0 : PI; float delta = d10 + d12; // now, compute cos1, the cosine of the reflected angle float sin1 = pow(n0 / n1, 2) * (1 - pow(cos0, 2)); if (sin1 > 1) return 1.0; // total internal reflection float cos1 = sqrt(1 - sin1); // compute cos2, the cosine of the final transmitted angle, i.e. cos(theta_2) // we need this angle for the Fresnel terms at the bottom interface float sin2 = pow(n0 / n2, 2) * (1 - pow(cos0, 2)); if (sin2 > 1) return 1.0; // total internal reflection float cos2 = sqrt(1 - sin2); // get the reflection transmission amplitude Fresnel coefficients float alpha_s = rs(n1, n0, cos1, cos0) * rs(n1, n2, cos1, cos2); // rho_10 * rho_12 (s-polarized) float alpha_p = rp(n1, n0, cos1, cos0) * rp(n1, n2, cos1, cos2); // rho_10 * rho_12 (p-polarized) float beta_s = ts(n0, n1, cos0, cos1) * ts(n1, n2, cos1, cos2); // tau_01 * tau_12 (s-polarized) float beta_p = tp(n0, n1, cos0, cos1) * tp(n1, n2, cos1, cos2); // tau_01 * tau_12 (p-polarized) // compute the phase term (phi) float phi = (2 * PI / lambda) * (2 * n1 * thickness * cos1) + delta; // finally, evaluate the transmitted intensity for the two possible polarizations float ts = pow(beta_s, 2) / (pow(alpha_s, 2) - 2 * alpha_s * cos(phi) + 1); float tp = pow(beta_p, 2) / (pow(alpha_p, 2) - 2 * alpha_p * cos(phi) + 1); // we need to take into account conservation of energy for transmission float beamRatio = (n2 * cos2) / (n0 * cos0); // calculate the average transmitted intensity (if you know the polarization distribution of your // light source, you should specify it here. if you don't, a 50%/50% average is generally used) float t = beamRatio * (ts + tp) / 2; // and finally, derive the reflected intensity return 1 - t; } shader irridescenceTex [[ string description = "Thin film coating shader. Use as reflection color for the material, with Fresnel for the material OFF (this texture computes its own Fresnel)" ]] ( float thicknessMin = 250 [[ string description = "Minimum thickness of the film, in nm" ]], float thicknessMax = 400 [[ string description = "Maximum thickness of the film, in nm" ]], string thickness = "test.png" [[ string description = "Texture map (usually noise) that determines the thickness of the film as fraction between the min and max" ]], float nmedium = 1 [[ string description = "Refractive index of the outer medium (typically air)" ]], // approximate refractive index of air float nfilm = 1.5 [[ string description = "Refractive index of the thin film itself" ]] , // approximate refractive index of water float ninternal = 1 [[ string description = "Refractive index of the material below the film" ]], // approximate refractive index of the lower material output color result = 0 ) { float cos0 = abs(dot(I , N)); color thickTex=texture(thickness, u, v); float t=(thickTex[0]+thickTex[1]+thickTex[2])/3.0; float thick=thicknessMin*(1.0-t)+thicknessMax*t; float red=thinFilmReflectance(cos0, 650, thick, nmedium, nfilm, ninternal); float green=thinFilmReflectance(cos0, 510, thick, nmedium, nfilm, ninternal); float blue=thinFilmReflectance(cos0, 475, thick, nmedium, nfilm, ninternal); result=color(red, green, blue); }