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Optimized GGX G function for GLES2.
Also changed the mapping of anisotropy to match the common definition.
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@ -934,6 +934,7 @@ varying highp float dp_clip;
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// E. Heitz, "Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs", J. Comp. Graph. Tech. 3 (2) (2014).
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// Eqns 71-72 and 85-86 (see also Eqns 43 and 80).
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/*
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float G_GGX_2cos(float cos_theta_m, float alpha) {
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// Schlick's approximation
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// C. Schlick, "An Inexpensive BRDF Model for Physically-based Rendering", Computer Graphics Forum. 13 (3): 233 (1994)
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@ -946,6 +947,15 @@ float G_GGX_2cos(float cos_theta_m, float alpha) {
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// float sin2 = (1.0 - cos2);
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// return 1.0 / (cos_theta_m + sqrt(cos2 + alpha * alpha * sin2));
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}
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*/
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// This approximates G_GGX_2cos(cos_theta_l, alpha) * G_GGX_2cos(cos_theta_v, alpha)
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// See Filament docs, Specular G section.
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float V_GGX(float cos_theta_l, float cos_theta_v, float alpha) {
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float v = cos_theta_l * (cos_theta_v * (1.0 - alpha) + alpha);
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float l = cos_theta_v * (cos_theta_l * (1.0 - alpha) + alpha);
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return 0.5 / (v + l);
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}
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float D_GGX(float cos_theta_m, float alpha) {
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float alpha2 = alpha * alpha;
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@ -953,6 +963,7 @@ float D_GGX(float cos_theta_m, float alpha) {
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return alpha2 / (M_PI * d * d);
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}
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/*
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float G_GGX_anisotropic_2cos(float cos_theta_m, float alpha_x, float alpha_y, float cos_phi, float sin_phi) {
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float cos2 = cos_theta_m * cos_theta_m;
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float sin2 = (1.0 - cos2);
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@ -960,14 +971,30 @@ float G_GGX_anisotropic_2cos(float cos_theta_m, float alpha_x, float alpha_y, fl
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float s_y = alpha_y * sin_phi;
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return 1.0 / max(cos_theta_m + sqrt(cos2 + (s_x * s_x + s_y * s_y) * sin2), 0.001);
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}
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*/
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float D_GGX_anisotropic(float cos_theta_m, float alpha_x, float alpha_y, float cos_phi, float sin_phi) {
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float cos2 = cos_theta_m * cos_theta_m;
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// This approximates G_GGX_anisotropic_2cos(cos_theta_l, ...) * G_GGX_anisotropic_2cos(cos_theta_v, ...)
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// See Filament docs, Anisotropic specular BRDF section.
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float V_GGX_anisotropic(float alpha_x, float alpha_y, float TdotV, float TdotL, float BdotV, float BdotL, float NdotV, float NdotL) {
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float Lambda_V = NdotL * length(vec3(alpha_x * TdotV, alpha_y * BdotV, NdotV));
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float Lambda_L = NdotV * length(vec3(alpha_x * TdotL, alpha_y * BdotL, NdotL));
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return 0.5 / (Lambda_V + Lambda_L);
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}
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float D_GGX_anisotropic(float cos_theta_m, float alpha_x, float alpha_y, float cos_phi, float sin_phi, float NdotH) {
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float alpha2 = alpha_x * alpha_y;
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highp vec3 v = vec3(alpha_y * cos_phi, alpha_x * sin_phi, alpha2 * NdotH);
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highp float v2 = dot(v, v);
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float w2 = alpha2 / v2;
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float D = alpha2 * w2 * w2 * (1.0 / M_PI);
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return D;
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/* float cos2 = cos_theta_m * cos_theta_m;
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float sin2 = (1.0 - cos2);
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float r_x = cos_phi / alpha_x;
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float r_y = sin_phi / alpha_y;
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float d = cos2 + sin2 * (r_x * r_x + r_y * r_y);
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return 1.0 / max(M_PI * alpha_x * alpha_y * d * d, 0.001);
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return 1.0 / max(M_PI * alpha_x * alpha_y * d * d, 0.001); */
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}
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float SchlickFresnel(float u) {
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@ -1113,7 +1140,11 @@ LIGHT_SHADER_CODE
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if (roughness > 0.0) {
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// D
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#if defined(SPECULAR_SCHLICK_GGX)
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vec3 specular_brdf_NL = vec3(0.0);
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#else
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float specular_brdf_NL = 0.0;
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#endif
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#if defined(SPECULAR_BLINN)
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@ -1125,7 +1156,7 @@ LIGHT_SHADER_CODE
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float shininess = exp2(15.0 * (1.0 - roughness) + 1.0) * 0.25;
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float blinn = pow(cNdotH, shininess);
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blinn *= (shininess + 8.0) / (8.0 * 3.141592654);
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float specular_brdf_NL = (blinn) / max(4.0 * cNdotV * cNdotL, 0.75);
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specular_brdf_NL = (blinn) / max(4.0 * cNdotV * cNdotL, 0.75);
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#elif defined(SPECULAR_PHONG)
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@ -1134,7 +1165,7 @@ LIGHT_SHADER_CODE
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float shininess = exp2(15.0 * (1.0 - roughness) + 1.0) * 0.25;
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float phong = pow(cRdotV, shininess);
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phong *= (shininess + 8.0) / (8.0 * 3.141592654);
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float specular_brdf_NL = (phong) / max(4.0 * cNdotV * cNdotL, 0.75);
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specular_brdf_NL = (phong) / max(4.0 * cNdotV * cNdotL, 0.75);
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#elif defined(SPECULAR_TOON)
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@ -1142,11 +1173,10 @@ LIGHT_SHADER_CODE
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float RdotV = dot(R, V);
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float mid = 1.0 - roughness;
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mid *= mid;
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float specular_brdf_NL = smoothstep(mid - roughness * 0.5, mid + roughness * 0.5, RdotV) * mid;
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specular_brdf_NL = smoothstep(mid - roughness * 0.5, mid + roughness * 0.5, RdotV) * mid;
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#elif defined(SPECULAR_DISABLED)
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// none..
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float specular_brdf_NL = 0.0;
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#elif defined(SPECULAR_SCHLICK_GGX)
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// shlick+ggx as default
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@ -1156,28 +1186,28 @@ LIGHT_SHADER_CODE
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float cLdotH = max(dot(L, H), 0.0);
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#if defined(LIGHT_USE_ANISOTROPY)
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float alpha = roughness * roughness;
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float aspect = sqrt(1.0 - anisotropy * 0.9);
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float rx = roughness / aspect;
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float ry = roughness * aspect;
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float ax = rx * rx;
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float ay = ry * ry;
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float XdotH = dot(T, H);
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float YdotH = dot(B, H);
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float D = D_GGX_anisotropic(cNdotH, ax, ay, XdotH, YdotH);
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float G = G_GGX_anisotropic_2cos(cNdotL, ax, ay, XdotH, YdotH) * G_GGX_anisotropic_2cos(cNdotV, ax, ay, XdotH, YdotH);
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float ax = alpha / aspect;
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float ay = alpha * aspect;
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//float XdotH = dot(T, H);
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//float YdotH = dot(B, H);
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float D = D_GGX_anisotropic(cNdotH, ax, ay, XdotH, YdotH, cNdotH);
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//float G = G_GGX_anisotropic_2cos(cNdotL, ax, ay, XdotH, YdotH) * G_GGX_anisotropic_2cos(cNdotV, ax, ay, XdotH, YdotH);
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float G = V_GGX_anisotropic(ax, ay, dot(T, V), dot(T, L), dot(B, V), dot(B, L), cNdotV, cNdotL))
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#else
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float alpha = roughness * roughness;
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float D = D_GGX(cNdotH, alpha);
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float G = G_GGX_2cos(cNdotL, alpha) * G_GGX_2cos(cNdotV, alpha);
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//float G = G_GGX_2cos(cNdotL, alpha) * G_GGX_2cos(cNdotV, alpha);
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float G = V_GGX(cNdotL, cNdotV, alpha);
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#endif
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// F
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vec3 f0 = F0(metallic, specular, diffuse_color);
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float cLdotH5 = SchlickFresnel(cLdotH);
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vec3 F = mix(vec3(cLdotH5), vec3(1.0), f0);
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vec3 specular_brdf_NL = cNdotL * D * F * G;
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specular_brdf_NL = cNdotL * D * F * G;
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#endif
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@ -1196,11 +1226,12 @@ LIGHT_SHADER_CODE
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#endif
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float Dr = GTR1(cNdotH, mix(.1, .001, clearcoat_gloss));
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float Fr = mix(.04, 1.0, cLdotH5);
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float Gr = G_GGX_2cos(cNdotL, .25) * G_GGX_2cos(cNdotV, .25);
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//float Gr = G_GGX_2cos(cNdotL, .25) * G_GGX_2cos(cNdotV, .25);
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float Gr = V_GGX(cNdotL, cNdotV, 0.25);
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float specular_brdf_NL = 0.25 * clearcoat * Gr * Fr * Dr * cNdotL;
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float clearcoat_specular_brdf_NL = 0.25 * clearcoat * Gr * Fr * Dr * cNdotL;
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specular_light += specular_brdf_NL * light_color * specular_blob_intensity * attenuation;
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specular_light += clearcoat_specular_brdf_NL * light_color * specular_blob_intensity * attenuation;
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}
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#endif
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}
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@ -1070,11 +1070,10 @@ LIGHT_SHADER_CODE
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#if defined(LIGHT_USE_ANISOTROPY)
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float alpha = roughness * roughness;
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float aspect = sqrt(1.0 - anisotropy * 0.9);
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float rx = roughness / aspect;
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float ry = roughness * aspect;
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float ax = rx * rx;
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float ay = ry * ry;
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float ax = alpha / aspect;
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float ay = alpha * aspect;
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float XdotH = dot(T, H);
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float YdotH = dot(B, H);
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float D = D_GGX_anisotropic(cNdotH, ax, ay, XdotH, YdotH);
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