Eevee: Update LTC code

Main change are:
- the fresnel LUT is separated from the main GGX LUT.
- LUTs use sqrt(1.0 - NV) as roughness remapping. Improving precision and
  removes needs for acos().
- LTC LUT is normalized by matrix middle component. Improving precision.

source/blender/draw/engines/eevee/eevee_materials.c

@@ -441,7 +441,7 @@ static void eevee_init_noise_texture(void)
 
 static void eevee_init_util_texture(void)
 {
-	const int layers = 3 + 16;
+	const int layers = 4 + 16;
 	float (*texels)[4] = MEM_mallocN(sizeof(float[4]) * 64 * 64 * layers, "utils texels");
 	float (*texels_layer)[4] = texels;
 
@@ -450,12 +450,12 @@ static void eevee_init_util_texture(void)
 	texels_layer += 64 * 64;
 
 	/* Copy bsdf_split_sum_ggx into 2nd layer red and green channels.
-	   Copy ltc_mag_ggx into 2nd layer blue channel. */
+	   Copy ltc_mag_ggx into 2nd layer blue and alpha channel. */
 	for (int i = 0; i < 64 * 64; i++) {
 		texels_layer[i][0] = bsdf_split_sum_ggx[i * 2 + 0];
 		texels_layer[i][1] = bsdf_split_sum_ggx[i * 2 + 1];
-		texels_layer[i][2] = ltc_mag_ggx[i];
-		texels_layer[i][3] = ltc_disk_integral[i];
+		texels_layer[i][2] = ltc_mag_ggx[i * 2 + 0];
+		texels_layer[i][3] = ltc_mag_ggx[i * 2 + 1];
 	}
 	texels_layer += 64 * 64;
 
@@ -468,13 +468,22 @@ static void eevee_init_util_texture(void)
 	}
 	texels_layer += 64 * 64;
 
-	/* Copy Refraction GGX LUT in layer 4 - 20 */
+	/* Copy ltc_disk_integral in 4th layer  */
+	for (int i = 0; i < 64 * 64; i++) {
+		texels_layer[i][0] = ltc_disk_integral[i];
+		texels_layer[i][1] = 0.0; /* UNUSED */
+		texels_layer[i][2] = 0.0; /* UNUSED */
+		texels_layer[i][3] = 0.0; /* UNUSED */
+	}
+	texels_layer += 64 * 64;
+
+	/* Copy Refraction GGX LUT in layer 5 - 21 */
 	for (int j = 0; j < 16; ++j) {
 		for (int i = 0; i < 64 * 64; i++) {
 			texels_layer[i][0] = btdf_split_sum_ggx[j * 2][i];
-			texels_layer[i][1] = btdf_split_sum_ggx[j * 2][i];
-			texels_layer[i][2] = btdf_split_sum_ggx[j * 2][i];
-			texels_layer[i][3] = btdf_split_sum_ggx[j * 2][i];
+			texels_layer[i][1] = 0.0; /* UNUSED */
+			texels_layer[i][2] = 0.0; /* UNUSED */
+			texels_layer[i][3] = 0.0; /* UNUSED */
 		}
 		texels_layer += 64 * 64;
 	}

source/blender/draw/engines/eevee/shaders/bsdf_common_lib.glsl

@@ -272,6 +272,14 @@ vec2 lut_coords(float cosTheta, float roughness)
 	return coords * (LUT_SIZE - 1.0) / LUT_SIZE + 0.5 / LUT_SIZE;
 }
 
+vec2 lut_coords_ltc(float cosTheta, float roughness)
+{
+	vec2 coords = vec2(roughness, sqrt(1.0 - cosTheta));
+
+	/* scale and bias coordinates, for correct filtered lookup */
+	return coords * (LUT_SIZE - 1.0) / LUT_SIZE + 0.5 / LUT_SIZE;
+}
+
 /* -- Tangent Space conversion -- */
 vec3 tangent_to_world(vec3 vector, vec3 N, vec3 T, vec3 B)
 {
@@ -572,11 +580,9 @@ vec3 F_schlick(vec3 f0, float cos_theta)
 /* Fresnel approximation for LTC area lights (not MRP) */
 vec3 F_area(vec3 f0, vec2 lut)
 {
-	vec2 fac = normalize(lut.xy); /* XXX FIXME this does not work!!! */
-
 	/* Unreal specular matching : if specular color is below 2% intensity,
 	 * treat as shadowning */
-	return saturate(50.0 * dot(f0, vec3(0.3, 0.6, 0.1))) * fac.y + fac.x * f0;
+	return saturate(50.0 * dot(f0, vec3(0.3, 0.6, 0.1))) * lut.y + lut.x * f0;
 }
 
 /* Fresnel approximation for IBL */

source/blender/draw/engines/eevee/shaders/lit_surface_frag.glsl

@@ -198,12 +198,12 @@ void CLOSURE_NAME(
 	/* ---------------------------------------------------------------- */
 
 #ifdef CLOSURE_GLOSSY
-	vec2 lut_uv = lut_coords(dot(N, V), roughness);
+	vec2 lut_uv = lut_coords_ltc(dot(N, V), roughness);
 	vec4 ltc_mat = texture(utilTex, vec3(lut_uv, 0.0)).rgba;
 #endif
 
 #ifdef CLOSURE_CLEARCOAT
-	vec2 lut_uv_clear = lut_coords(dot(C_N, V), C_roughness);
+	vec2 lut_uv_clear = lut_coords_ltc(dot(C_N, V), C_roughness);
 	vec4 ltc_mat_clear = texture(utilTex, vec3(lut_uv_clear, 0.0)).rgba;
 	vec3 out_spec_clear = vec3(0.0);
 #endif
@@ -241,13 +241,13 @@ void CLOSURE_NAME(
 	}
 
 #ifdef CLOSURE_GLOSSY
-	vec3 brdf_lut_lights = texture(utilTex, vec3(lut_uv, 1.0)).rgb;
-	out_spec *= F_area(f0, brdf_lut_lights.xy) * brdf_lut_lights.z;
+	vec2 brdf_lut_lights = texture(utilTex, vec3(lut_uv, 1.0)).ba;
+	out_spec *= F_area(f0, brdf_lut_lights.xy);
 #endif
 
 #ifdef CLOSURE_CLEARCOAT
-	vec3 brdf_lut_lights_clear = texture(utilTex, vec3(lut_uv_clear, 1.0)).rgb;
-	out_spec_clear *= F_area(vec3(0.04), brdf_lut_lights_clear.xy) * brdf_lut_lights_clear.z;
+	vec2 brdf_lut_lights_clear = texture(utilTex, vec3(lut_uv_clear, 1.0)).ba;
+	out_spec_clear *= F_area(vec3(0.04), brdf_lut_lights_clear.xy);
 	out_spec += out_spec_clear * C_intensity;
 #endif
 

source/blender/draw/engines/eevee/shaders/ltc_lib.glsl

@@ -15,17 +15,18 @@ uniform sampler2DArray utilTex;
 #endif /* UTIL_TEX */
 
 /* Diffuse *clipped* sphere integral. */
-float diffuse_sphere_integral_lut(float avg_dir_z, float form_factor)
+float diffuse_sphere_integral(float avg_dir_z, float form_factor)
 {
+#if 1
+	/* use tabulated horizon-clipped sphere */
 	vec2 uv = vec2(avg_dir_z * 0.5 + 0.5, form_factor);
 	uv = uv * (LUT_SIZE - 1.0) / LUT_SIZE + 0.5 / LUT_SIZE;
 
-	return texture(utilTex, vec3(uv, 1.0)).w;
-}
-
-float diffuse_sphere_integral_cheap(float avg_dir_z, float form_factor)
-{
+	return texture(utilTex, vec3(uv, 3.0)).x;
+#else
+	/* Cheap approximation. Less smooth and have energy issues. */
 	return max((form_factor * form_factor + avg_dir_z) / (form_factor + 1.0), 0.0);
+#endif
 }
 
 /**
@@ -143,9 +144,9 @@ mat3 ltc_matrix(vec4 lut)
 {
 	/* load inverse matrix */
 	mat3 Minv = mat3(
-		vec3(  1,   0, lut.y),
-		vec3(  0, lut.z,   0),
-		vec3(lut.w,   0, lut.x)
+		vec3(lut.x, 0, lut.y),
+		vec3(    0, 1,     0),
+		vec3(lut.z, 0, lut.w)
 	);
 
 	return Minv;
@@ -185,12 +186,7 @@ float ltc_evaluate_quad(vec3 corners[4], vec3 N)
 
 	float form_factor = length(avg_dir);
 	float avg_dir_z = dot(N, avg_dir / form_factor);
-
-#if 1 /* use tabulated horizon-clipped sphere */
-	return form_factor * diffuse_sphere_integral_lut(avg_dir_z, form_factor);
-#else /* Less accurate version, a bit cheaper. */
-	return form_factor * diffuse_sphere_integral_cheap(avg_dir_z, form_factor);
-#endif
+	return form_factor * diffuse_sphere_integral(avg_dir_z, form_factor);
 }
 
 /* If disk does not need to be transformed and is already front facing. */
@@ -199,12 +195,7 @@ float ltc_evaluate_disk_simple(float disk_radius, float NL)
 	float r_sqr = disk_radius * disk_radius;
 	float one_r_sqr = 1.0 + r_sqr;
 	float form_factor = r_sqr * inversesqrt(one_r_sqr * one_r_sqr);
-
-#if 1 /* use tabulated horizon-clipped sphere */
-	return form_factor * diffuse_sphere_integral_lut(NL, form_factor);
-#else /* Less accurate version, a bit cheaper. */
-	return form_factor * diffuse_sphere_integral_cheap(NL, form_factor);
-#endif
+	return form_factor * diffuse_sphere_integral(NL, form_factor);
 }
 
 /* disk_points are WS vectors from the shading point to the disk "bounding domain" */
@@ -315,10 +306,5 @@ float ltc_evaluate_disk(vec3 N, vec3 V, mat3 Minv, vec3 disk_points[3])
 
 	/* Find the sphere and compute lighting. */
 	float form_factor = max(0.0, L1 * L2 * inversesqrt((1.0 + L1 * L1) * (1.0 + L2 * L2)));
-
-#if 1 /* use tabulated horizon-clipped sphere */
-	return form_factor * diffuse_sphere_integral_lut(avg_dir.z, form_factor);
-#else /* Less accurate version, a bit cheaper. */
-	return form_factor * diffuse_sphere_integral_cheap(avg_dir.z, form_factor);
-#endif
+	return form_factor * diffuse_sphere_integral(avg_dir.z, form_factor);
 }