Visibility functions with different levels of exactness. (#9)

Engine/BuiltInShaders/common/BRDF.sh

@@ -13,17 +13,36 @@ float DistributionGGX(float NdotH, float rough) {
 	return a2 * CD_PI_INV * denom_inv * denom_inv;
 }
 
-// Geometry
-float Visibility(float NdotV, float NdotL, float rough) {
-	// Specular BRDF = (F * D * G) / (4 * NdotV * NdotL)
-	// = (F * D * (NdotV / (NdotV * (1 - K) + K)) * (NdotL / (NdotL * (1 - K) + K))) / (4 * NdotV * NdotL)
-	// = (F * D * (1 / (NdotV * (1 - K) + K)) * (1 / (NdotL * (1 - K) + K))) / 4
-	// = F * D * Vis
-	// Vis = 1 / (NdotV * (1 - K) + K) / (NdotL * (1 - K) + K) / 4
+float Visibility_HighQuality(float NdotV, float NdotL, float rough) {
+	// BRDF = (F * D * G) / (4 * NdotV * NdotL) = F * D * V
+	// V = G / (4 * NdotV * NdotL)
+	// = 0.5 / (NdotL * sqrt(a2 + (1 - a2) * NdotV^2) + NdotV * sqrt(a2 + (1 - a2) * NdotL^2))
+
+	// rough = (rough + 1) / 2, by Disney
+	// a = rough^2
+	float a2 = pow((rough + 1.0) * 0.5, 4);
+	float lambda_v = NdotL * sqrt(a2 + (1.0 - a2) * NdotV * NdotV);
+	float lambda_l = NdotV * sqrt(a2 + (1.0 - a2) * NdotL * NdotL);
+	
+	return 0.5 / (lambda_v + lambda_l);
+}
+
+float Visibility_LowQuality(float NdotV, float NdotL, float rough) {
+	// BRDF = (F * D * G) / (4 * NdotV * NdotL) = F * D * V
+	// V = G / (4 * NdotV * NdotL)
+	// = 1 / ((NdotV * (2 - a) + a) * (NdotL * (2 - a) + a))
+
+	// rough = (rough + 1) / 2, by Disney
+	// a = rough^2
+	float a = (rough + 1.0) * (rough + 1.0) * 0.25;
+	float g1_v_inv = NdotV * (2.0 - a) + a;
+	float g1_l_inv = NdotL * (2.0 - a) + a;
 
-	float f = rough + 1.0;
-	float k = f * f * 0.125;
-	float ggxV  = 1.0 / (NdotV * (1.0 - k) + k);
-	float ggxL  = 1.0 / (NdotL * (1.0 - k) + k);
-	return ggxV * ggxL * 0.25;
+	return 1.0 / (g1_v_inv * g1_l_inv);
 }
+
+// Geometry
+float Visibility(float NdotV, float NdotL, float rough) {
+	// TODO : Wrap them in macros after we've collected enough approximate / exact formulas.
+	return Visibility_LowQuality(NdotV, NdotL, rough);
+}