[Add] Atmospheric scattering and improved clouds.

assets/shaders/cloud.frag

@@ -4,30 +4,82 @@ out vec4 FragColor;
 in vec3 TexCoords;
 
 uniform sampler2D u_CloudTexture;
-uniform vec3 u_LightDir;
+uniform vec3 u_SunPos;
 
 const float PI = 3.14159265359;
 
+/* Atmosphere parameters. */
+const float ATMOSPHERE_RADIUS     = 6520275.0;
+const float PLANET_RADIUS         = 6371000.0;
+const float RAYLEIGH_SCALE_HEIGHT = 8000.0;
+const float MIE_SCALE_HEIGHT      = 1200.0;
+
+/* Scattering coefficients. */
+const vec3 RAYLEIGH_SCATTERING_COEFF  = vec3(0.0000058, 0.0000135, 0.0000331);
+const vec3 MIE_SCATTERING_COEFF       = vec3(0.00002);
+
+/* Mie scattering parameters. */
+const float MIE_G = 0.76;
+
+/* Number of samples for ray marching. */
+const int SAMPLES = 16;
+const int LIGHT_SAMPLES = 8;
+
+float ray_sphere_intersect(vec3 origin, vec3 dir, float radius) {
+  float a = dot(dir, dir);
+  float b = 2.0 * dot(origin, dir);
+  float c = dot(origin, origin) - radius * radius;
+  float d = b * b - 4.0 * a * c;
+  if (d < 0.0) {
+    return -1.0;
+  }
+  return (-b + sqrt(d)) / (2.0 * a);
+}
+
+vec3 get_sky_color(vec3 dir) {
+  vec3 eye = vec3(0.0, PLANET_RADIUS + 1.0, 0.0);
+  float dist = ray_sphere_intersect(eye, dir, ATMOSPHERE_RADIUS);
+  vec3 totalRayleigh = vec3(0.0);
+  vec3 totalMie = vec3(0.0);
+  float stepSize = dist / float(SAMPLES);
+  for (int i = 0; i < SAMPLES; i++) {
+    vec3 p = eye + dir * (float(i) + 0.5) * stepSize;
+    float h = length(p) - PLANET_RADIUS;
+    float rayleighDensity = exp(-h / RAYLEIGH_SCALE_HEIGHT);
+    float mieDensity = exp(-h / MIE_SCALE_HEIGHT);
+    float lightDist = ray_sphere_intersect(p, normalize(u_SunPos), ATMOSPHERE_RADIUS);
+    float lightStepSize = lightDist / float(LIGHT_SAMPLES);
+    float opticalDepthLight = 0.0;
+    for (int j = 0; j < LIGHT_SAMPLES; j++) {
+      vec3 lp = p + normalize(u_SunPos) * (float(j) + 0.5) * lightStepSize;
+      float lh = length(lp) - PLANET_RADIUS;
+      opticalDepthLight += exp(-lh / RAYLEIGH_SCALE_HEIGHT) * lightStepSize;
+    }
+    vec3 transmittance = exp(-(opticalDepthLight * RAYLEIGH_SCATTERING_COEFF
+          + opticalDepthLight * MIE_SCATTERING_COEFF));
+    totalRayleigh += rayleighDensity * stepSize * transmittance;
+    totalMie += mieDensity * stepSize * transmittance;
+  }
+
+  float mu = dot(dir, normalize(u_SunPos));
+  float rayleighPhase = 3.0 / (16.0 * PI) * (1.0 + mu * mu);
+  float miePhase = 3.0 / (8.0 * PI) * ((1.0 - MIE_G * MIE_G)
+      * (1.0 + mu * mu)) / ((2.0 + MIE_G * MIE_G) * pow(1.0 + MIE_G
+      * MIE_G - 2.0 * MIE_G * mu, 1.5));
+  return 20.0 * (totalRayleigh * RAYLEIGH_SCATTERING_COEFF * rayleighPhase
+      + totalMie * MIE_SCATTERING_COEFF * miePhase);
+}
+
 void main() {
-  /* Convert 3D texture coords to 2D using spherical mapping. */
   float u = atan(TexCoords.z, TexCoords.x) / (2.0 * PI) + 0.5;
   float v = asin(TexCoords.y) / PI + 0.5;
+  float cloudAlpha = texture(u_CloudTexture, vec2(u,v)).r;
 
-  /* Sample noise value from cloud texture. */
+  vec3 skyColor = get_sky_color(normalize(TexCoords));
-  float noise = texture(u_CloudTexture, vec2(u, v)).r;
+  vec3 cloudColor = mix(skyColor, vec3(1.0), smoothstep(0.5, 0.8, cloudAlpha));
 
-  /* Create soft-edged clouds from the noise. */
-  float cloudAlpha = smoothstep(0.5, 0.8, noise);
-
-  /* Some simple lighting. */
-  vec3 normal = normalize(TexCoords);
-  float diffuse = max(dot(normal, -u_LightDir), 0.0);
-  vec3 cloudColor = vec3(1.0) * (diffuse * 0.5 + 0.5); /* Add some ambient light. */
-
-  /* Fade out clouds at the poles to hide pinching. */
   float poleFade = 1.0 - abs(TexCoords.y);
-  cloudAlpha *= smoothstep(0.0, 0.2, poleFade);
+  float finalAlpha = smoothstep(0.0, 0.2, poleFade) * smoothstep(0.5, 0.8, cloudAlpha);
 
-  /* Cloud colour is white. it's transparency is determined by alpha. */
+  FragColor = vec4(pow(cloudColor, vec3(1.0/2.2)), finalAlpha);
-  FragColor = vec4(cloudColor, cloudAlpha);
 }

assets/shaders/sky.frag

@@ -1,17 +1,80 @@
 #version 330 core
 out vec4 FragColor;
 
-in vec3 WorldPos;
+in vec3 v_WorldPos;
+
+uniform vec3 u_SunPos;
+
+const float PI = 3.14159265359;
+
+/* Atmosphere parameters. */
+const float ATMOSPHERE_RADIUS     = 6520275.0;
+const float PLANET_RADIUS         = 6371000.0;
+const float RAYLEIGH_SCALE_HEIGHT = 8000.0;
+const float MIE_SCALE_HEIGHT      = 1200.0;
+
+/* Scattering coefficients. */
+const vec3 RAYLEIGH_SCATTERING_COEFF = vec3(0.0000058, 0.0000135, 0.0000331);
+const vec3 MIE_SCATTERING_COEFF      = vec3(0.00002);
+
+/* Mie scattering parameters. */
+const float MIE_G = 0.76;
+
+/* Number of samples for ray marching. */
+const int SAMPLES       = 16;
+const int LIGHT_SAMPLES = 8;
+
+float ray_sphere_intersect(vec3 origin, vec3 dir, float radius) {
+  float a = dot(dir, dir);
+  float b = 2.0 * dot(origin, dir);
+  float c = dot(origin, origin) - radius * radius;
+  float d = b * b - 4.0 * a * c;
+  if (d < 0.0) {
+    return -1.0;
+  }
+  return (-b + sqrt(d)) / (2.0 * a);
+}
 
 void main() {
-  /* Define colours for the top and bottom of the sky. */
+  vec3 dir = normalize(v_WorldPos);
-  vec3 zenithColor = vec3(0.3, 0.5, 0.8);
+  vec3 eye = vec3(0.0, PLANET_RADIUS + 1.0, 0.0);
-  vec3 horizonColor = vec3(0.7, 0.85, 1.0);
 
-  float blendFactor = (normalize(WorldPos).y + 1.0) / 2.0;
+  float dist = ray_sphere_intersect(eye, dir, ATMOSPHERE_RADIUS);
 
-  /* Blend the two colours. */
+  vec3 totalRayleigh = vec3(0.0);
-  vec3 finalColor = mix(horizonColor, zenithColor, blendFactor);
+  vec3 totalMie = vec3(0.0);
 
-  FragColor = vec4(finalColor, 1.0);
+  float stepSize = dist / float(SAMPLES);
+  for(int i = 0; i < SAMPLES; i++) {
+    vec3 p = eye + dir * (float(i) + 0.5) * stepSize;
+    float h = length(p) - PLANET_RADIUS;
+
+    float rayleighDensity = exp(-h / RAYLEIGH_SCALE_HEIGHT);
+    float mieDensity = exp(-h / MIE_SCALE_HEIGHT);
+
+    float lightDist = ray_sphere_intersect(p, normalize(u_SunPos), ATMOSPHERE_RADIUS);
+    float lightStepSize = lightDist / float(LIGHT_SAMPLES);
+    float opticalDepthLight = 0.0;
+    for(int j = 0; j < LIGHT_SAMPLES; j++) {
+      vec3 lp = p + normalize(u_SunPos) * (float(j) + 0.5) * lightStepSize;
+      float lh = length(lp) - PLANET_RADIUS;
+      opticalDepthLight += exp(-lh / RAYLEIGH_SCALE_HEIGHT) * lightStepSize;
+    }
+
+    vec3 transmittance = exp(-(opticalDepthLight * RAYLEIGH_SCATTERING_COEFF
+          + opticalDepthLight * MIE_SCATTERING_COEFF));
+      totalRayleigh += rayleighDensity * stepSize * transmittance;
+      totalMie += mieDensity * stepSize * transmittance;
+    }
+
+    float mu = dot(dir, normalize(u_SunPos));
+    float rayleighPhase = 3.0 / (16.0 * PI) * (1.0 + mu * mu);
+    float miePhase = 3.0 / (8.0 * PI) * ((1.0 - MIE_G * MIE_G)
+        * (1.0 + mu * mu)) / ((2.0 + MIE_G * MIE_G)
+        * pow(1.0 + MIE_G * MIE_G - 2.0 * MIE_G * mu, 1.5));
+
+    vec3 finalColor = 20.0 * (totalRayleigh * RAYLEIGH_SCATTERING_COEFF
+        * rayleighPhase + totalMie * MIE_SCATTERING_COEFF * miePhase);
+
+    FragColor = vec4(pow(finalColor, vec3(1.0/2.2)), 1.0);
 }

assets/shaders/sky.vert

@@ -1,17 +1,13 @@
 #version 330 core
 layout (location = 0) in vec3 aPos;
 
-out vec3 WorldPos;
-
 uniform mat4 view;
 uniform mat4 projection;
 
-void main() {
+out vec3 v_WorldPos;
-  WorldPos = aPos;
 
-  /* Force depth value to 1.0 after perspective division
+void main() {
-   * to ensure the skybox is always rendered behind everythig else.
+  v_WorldPos = aPos;
-   */
+  vec4 pos = projection * view * vec4(aPos, 1.0);
-  vec4 pos = projection * view * vec4(WorldPos, 1.0);
   gl_Position = pos.xyww;
 }

src/graphics/renderer.cpp

@@ -265,6 +265,7 @@ void Renderer::_render_sky(const Camera& camera) {
  
   _sky_shader.set_mat4("view", view);
   _sky_shader.set_mat4("projection", _projection);
+  _sky_shader.set_vec3("u_SunPos", {0.0f, 1.0f, 0.0f});
 
   glBindVertexArray(_sky_vao);
   glDrawElements(GL_TRIANGLES, _sky_indices_count, GL_UNSIGNED_INT, 0);
@@ -288,6 +289,7 @@ void Renderer::_render_clouds(const Camera& camera) {
   _cloud_shader.set_mat4("projection", _projection);
   _cloud_shader.set_mat4("view", cloud_view);
   _cloud_shader.set_vec3("u_LightDir", {-0.5f, -1.0f, -0.5f});
+  _cloud_shader.set_vec3("u_SunPos", {0.0f, 1.0f, 0.0f});
 
   glBindVertexArray(_sky_vao);
   glActiveTexture(GL_TEXTURE0);