improve planet rings shaders (#5708)

* improve planet rings shaders

All rings are assumed to be icy

1) Each object in ring is darker depending of its phase
   (like Moon phases)
2) Each object shines brightly if sun is behind the ring
   (lot of low angle specular reflections)
3) Each object shines brightly if looking from the sun
   (simulating high geometric albedo > 1.0)

* Move phase functions into a library

* Fix black edges of planetary rings

data/shaders/opengl/lib.glsl

@@ -12,6 +12,25 @@ struct Surface {
 	float ambientOcclusion;
 };
 
+// Phase functions
+// https://www.scratchapixel.com/lessons/procedural-generation-virtual-worlds/simulating-sky/simulating-colors-of-the-sky.html
+float miePhaseFunction(const float g, const float mu)
+{
+	/*
+	 * Mie phase function:
+	 */
+	return 3.f / (8.f * 3.141592) * ((1.f - g * g) * (1.f + mu * mu)) / ((2.f + g * g) * pow(1.f + g * g - 2.f * g * mu, 1.5f));
+}
+
+float rayleighPhaseFunction(const float mu)
+{
+	/*
+	 * Rayleigh phase function:
+	 */
+	return 3.f / (16.f * 3.141592) * (1 + mu * mu);
+}
+
+
 // Currently used by: hopefully everything
 // Evaluates a standard blinn-phong diffuse+specular, with the addition of a
 // light intensity term to scale the lighting contribution based on (pre-calculated)

data/shaders/opengl/planetrings.frag

@@ -7,6 +7,7 @@
 uniform sampler2D texture0;
 in vec2 texCoord0;
 in vec4 texCoord1;
+in vec4 varyingEyepos;
 
 out vec4 frag_color;
 
@@ -16,10 +17,24 @@ void main(void)
 	vec4 col = vec4(0.0);
 	vec4 texCol = texture(texture0, texCoord0);
 
+	vec3 eyenorm = normalize(varyingEyepos.xyz);
+
 	for (int i=0; i<NUM_LIGHTS; ++i) {
 		float l = findSphereEyeRayEntryDistance(-vec3(texCoord1), vec3(uViewMatrixInverse * uLight[i].position), 1.0);
 		if (l <= 0.0) {
-			col = col + texCol*uLight[i].diffuse;
+			// first term: diffuse light phase (like in full/new moon)
+			float mu = dot(normalize(vec3(uLight[i].position)), eyenorm);
+			float diffuse = sqrt((1 - mu) / 2);
+
+			// second term: diffuse mie (scattering through ring)
+			float g = 0.76f;
+			float phaseThrough = miePhaseFunction(g, mu);
+
+			// third term: reflect mie (imitate albedo >= 1.0)
+			float muRev = dot(-normalize(vec3(uLight[i].position)), eyenorm);
+			float phaseReflect = miePhaseFunction(g, muRev);
+
+			col = col + texCol * (diffuse + phaseThrough + phaseReflect) * uLight[i].diffuse;
 		}
 	}
 	col.a = texCol.a;

data/shaders/opengl/planetrings.vert

@@ -6,11 +6,13 @@
 
 out vec2 texCoord0;
 out vec4 texCoord1;
+out vec4 varyingEyepos;
 
 void main(void)
 {
 	gl_Position = matrixTransform();
 
 	texCoord0 = a_uv0.xy;
 	texCoord1 = a_vertex;
+	varyingEyepos = uViewMatrix * a_vertex;
 }

src/Planet.cpp

@@ -156,9 +156,9 @@ void Planet::GenerateRings(Graphics::Renderer *renderer)
 	{
 		Color *row;
 		row = buf.get();
-		std::fill_n(row, RING_TEXTURE_WIDTH, Color::BLACK);
+		std::fill_n(row, RING_TEXTURE_WIDTH, Color::BLANK);
 		row = buf.get() + (RING_TEXTURE_LENGTH - 1) * RING_TEXTURE_WIDTH;
-		std::fill_n(row, RING_TEXTURE_WIDTH, Color::BLACK);
+		std::fill_n(row, RING_TEXTURE_WIDTH, Color::BLANK);
 	}
 
 	const vector3f texSize(RING_TEXTURE_WIDTH, RING_TEXTURE_LENGTH, 0.0f);