uniform sampler2D u_noiseTexture;
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uniform vec3 u_noiseTextureDimensions;
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uniform float u_noiseDetail;
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varying vec2 v_offset;
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varying vec3 v_maximumSize;
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varying float v_slice;
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varying float v_brightness;
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float wrap(float value, float rangeLength) {
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if(value < 0.0) {
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float absValue = abs(value);
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float modValue = mod(absValue, rangeLength);
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return mod(rangeLength - modValue, rangeLength);
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}
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return mod(value, rangeLength);
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}
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vec3 wrapVec(vec3 value, float rangeLength) {
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return vec3(wrap(value.x, rangeLength),
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wrap(value.y, rangeLength),
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wrap(value.z, rangeLength));
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}
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float textureSliceWidth = u_noiseTextureDimensions.x;
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float noiseTextureRows = u_noiseTextureDimensions.y;
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float inverseNoiseTextureRows = u_noiseTextureDimensions.z;
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float textureSliceWidthSquared = textureSliceWidth * textureSliceWidth;
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vec2 inverseNoiseTextureDimensions = vec2(noiseTextureRows / textureSliceWidthSquared,
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inverseNoiseTextureRows / textureSliceWidth);
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vec2 voxelToUV(vec3 voxelIndex) {
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vec3 wrappedIndex = wrapVec(voxelIndex, textureSliceWidth);
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float column = mod(wrappedIndex.z, textureSliceWidth * inverseNoiseTextureRows);
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float row = floor(wrappedIndex.z / textureSliceWidth * noiseTextureRows);
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float xPixelCoord = wrappedIndex.x + column * textureSliceWidth;
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float yPixelCoord = wrappedIndex.y + row * textureSliceWidth;
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return vec2(xPixelCoord, yPixelCoord) * inverseNoiseTextureDimensions;
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}
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// Interpolate a voxel with its neighbor (along the positive X-axis)
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vec4 lerpSamplesX(vec3 voxelIndex, float x) {
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vec2 uv0 = voxelToUV(voxelIndex);
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vec2 uv1 = voxelToUV(voxelIndex + vec3(1.0, 0.0, 0.0));
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vec4 sample0 = texture2D(u_noiseTexture, uv0);
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vec4 sample1 = texture2D(u_noiseTexture, uv1);
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return mix(sample0, sample1, x);
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}
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vec4 sampleNoiseTexture(vec3 position) {
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vec3 recenteredPos = position + vec3(textureSliceWidth / 2.0);
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vec3 lerpValue = fract(recenteredPos);
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vec3 voxelIndex = floor(recenteredPos);
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vec4 xLerp00 = lerpSamplesX(voxelIndex, lerpValue.x);
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vec4 xLerp01 = lerpSamplesX(voxelIndex + vec3(0.0, 0.0, 1.0), lerpValue.x);
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vec4 xLerp10 = lerpSamplesX(voxelIndex + vec3(0.0, 1.0, 0.0), lerpValue.x);
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vec4 xLerp11 = lerpSamplesX(voxelIndex + vec3(0.0, 1.0, 1.0), lerpValue.x);
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vec4 yLerp0 = mix(xLerp00, xLerp10, lerpValue.y);
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vec4 yLerp1 = mix(xLerp01, xLerp11, lerpValue.y);
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return mix(yLerp0, yLerp1, lerpValue.z);
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}
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// Intersection with a unit sphere with radius 0.5 at center (0, 0, 0).
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bool intersectSphere(vec3 origin, vec3 dir, float slice,
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out vec3 point, out vec3 normal) {
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float A = dot(dir, dir);
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float B = dot(origin, dir);
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float C = dot(origin, origin) - 0.25;
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float discriminant = (B * B) - (A * C);
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if(discriminant < 0.0) {
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return false;
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}
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float root = sqrt(discriminant);
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float t = (-B - root) / A;
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if(t < 0.0) {
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t = (-B + root) / A;
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}
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point = origin + t * dir;
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if(slice >= 0.0) {
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point.z = (slice / 2.0) - 0.5;
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if(length(point) > 0.5) {
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return false;
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}
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}
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normal = normalize(point);
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point -= czm_epsilon2 * normal;
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return true;
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}
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// Transforms the ray origin and direction into unit sphere space,
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// then transforms the result back into the ellipsoid's space.
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bool intersectEllipsoid(vec3 origin, vec3 dir, vec3 center, vec3 scale, float slice,
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out vec3 point, out vec3 normal) {
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if(scale.x <= 0.01 || scale.y < 0.01 || scale.z < 0.01) {
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return false;
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}
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vec3 o = (origin - center) / scale;
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vec3 d = dir / scale;
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vec3 p, n;
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bool intersected = intersectSphere(o, d, slice, p, n);
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if(intersected) {
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point = (p * scale) + center;
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normal = n;
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}
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return intersected;
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}
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// Assume that if phase shift is being called for octave i,
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// the frequency is of i - 1. This saves us from doing extra
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// division / multiplication operations.
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vec2 phaseShift2D(vec2 p, vec2 freq) {
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return (czm_pi / 2.0) * sin(freq.yx * p.yx);
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}
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vec2 phaseShift3D(vec3 p, vec2 freq) {
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return phaseShift2D(p.xy, freq) + czm_pi * vec2(sin(freq.x * p.z));
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}
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// The cloud texture function derived from Gardner's 1985 paper,
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// "Visual Simulation of Clouds."
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// https://www.cs.drexel.edu/~david/Classes/Papers/p297-gardner.pdf
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const float T0 = 0.6; // contrast of the texture pattern
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const float k = 0.1; // computed to produce a maximum value of 1
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const float C0 = 0.8; // coefficient
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const float FX0 = 0.6; // frequency X
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const float FY0 = 0.6; // frequency Y
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const int octaves = 5;
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float T(vec3 point) {
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vec2 sum = vec2(0.0);
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float Ci = C0;
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vec2 FXY = vec2(FX0, FY0);
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vec2 PXY = vec2(0.0);
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for(int i = 1; i <= octaves; i++) {
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PXY = phaseShift3D(point, FXY);
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Ci *= 0.707;
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FXY *= 2.0;
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vec2 sinTerm = sin(FXY * point.xy + PXY);
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sum += Ci * sinTerm + vec2(T0);
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}
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return k * sum.x * sum.y;
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}
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const float a = 0.5; // fraction of surface reflection due to ambient or scattered light,
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const float t = 0.4; // fraction of texture shading
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const float s = 0.25; // fraction of specular reflection
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float I(float Id, float Is, float It) {
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return (1.0 - a) * ((1.0 - t) * ((1.0 - s) * Id + s * Is) + t * It) + a;
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}
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const vec3 lightDir = normalize(vec3(0.2, -1.0, 0.7));
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vec4 drawCloud(vec3 rayOrigin, vec3 rayDir, vec3 cloudCenter, vec3 cloudScale, float cloudSlice,
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float brightness) {
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vec3 cloudPoint, cloudNormal;
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if(!intersectEllipsoid(rayOrigin, rayDir, cloudCenter, cloudScale, cloudSlice,
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cloudPoint, cloudNormal)) {
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return vec4(0.0);
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}
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float Id = clamp(dot(cloudNormal, -lightDir), 0.0, 1.0); // diffuse reflection
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float Is = max(pow(dot(-lightDir, -rayDir), 2.0), 0.0); // specular reflection
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float It = T(cloudPoint); // texture function
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float intensity = I(Id, Is, It);
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vec3 color = intensity * clamp(brightness, 0.1, 1.0) * vec3(1.0);
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vec4 noise = sampleNoiseTexture(u_noiseDetail * cloudPoint);
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float W = noise.x;
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float W2 = noise.y;
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float W3 = noise.z;
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// The dot product between the cloud's normal and the ray's direction is greatest
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// in the center of the ellipsoid's surface. It decreases towards the edge.
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// Thus, it is used to blur the areas leading to the edges of the ellipsoid,
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// so that no harsh lines appear.
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// The first (and biggest) layer of worley noise is then subtracted from this.
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// The final result is scaled up so that the base cloud is not too translucent.
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float ndDot = clamp(dot(cloudNormal, -rayDir), 0.0, 1.0);
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float TR = pow(ndDot, 3.0) - W; // translucency
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TR *= 1.3;
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// Subtracting the second and third layers of worley noise is more complicated.
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// If these layers of noise were simply subtracted from the current translucency,
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// the shape derived from the first layer of noise would be completely deleted.
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// The erosion of this noise should thus be constricted to the edges of the cloud.
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// However, because the edges of the ellipsoid were already blurred away, mapping
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// the noise to (1.0 - ndDot) will have no impact on most of the cloud's appearance.
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// The value of (0.5 - ndDot) provides the best compromise.
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float minusDot = 0.5 - ndDot;
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// Even with the previous calculation, subtracting the second layer of wnoise
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// erode too much of the cloud. The addition of it, however, will detailed
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// volume to the cloud. As long as the noise is only added and not subtracted,
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// the results are aesthetically pleasing.
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// The minusDot product is mapped in a way that it is larger at the edges of
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// the ellipsoid, so a subtraction and min operation are used instead of
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// an addition and max one.
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TR -= min(minusDot * W2, 0.0);
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// The third level of worley noise is subtracted from the result, with some
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// modifications. First, a scalar is added to minusDot so that the noise
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// starts affecting the shape farther away from the center of the ellipsoid's
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// surface. Then, it is scaled down so its impact is not too intense.
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TR -= 0.8 * (minusDot + 0.25) * W3;
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// The texture function's shading does not correlate with the shape of the cloud
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// produced by the layers of noise, so an extra shading scalar is calculated.
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// The darkest areas of the cloud are assigned to be where the noise erodes
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// the cloud the most. This is then interpolated based on the translucency
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// and the diffuse shading term of that point in the cloud.
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float shading = mix(1.0 - 0.8 * W * W, 1.0, Id * TR);
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// To avoid values that are too dark, this scalar is increased by a small amount
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// and clamped so it never goes to zero.
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shading = clamp(shading + 0.2, 0.3, 1.0);
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// Finally, the contrast of the cloud's color is increased.
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vec3 finalColor = mix(vec3(0.5), shading * color, 1.15);
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return vec4(finalColor, clamp(TR, 0.0, 1.0));
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}
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void main() {
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#ifdef DEBUG_BILLBOARDS
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gl_FragColor = vec4(0.0, 0.5, 0.5, 1.0);
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#endif
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// To avoid calculations with high values,
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// we raycast from an arbitrarily smaller space.
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vec2 coordinate = v_maximumSize.xy * v_offset;
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vec3 ellipsoidScale = 0.82 * v_maximumSize;
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vec3 ellipsoidCenter = vec3(0.0);
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float zOffset = max(ellipsoidScale.z - 10.0, 0.0);
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vec3 eye = vec3(0, 0, -10.0 - zOffset);
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vec3 rayDir = normalize(vec3(coordinate, 1.0) - eye);
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vec3 rayOrigin = eye;
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#ifdef DEBUG_ELLIPSOIDS
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vec3 point, normal;
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if(intersectEllipsoid(rayOrigin, rayDir, ellipsoidCenter, ellipsoidScale, v_slice,
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point, normal)) {
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gl_FragColor = v_brightness * vec4(1.0);
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}
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#else
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#ifndef DEBUG_BILLBOARDS
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vec4 cloud = drawCloud(rayOrigin, rayDir,
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ellipsoidCenter, ellipsoidScale, v_slice, v_brightness);
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if(cloud.w < 0.01) {
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discard;
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}
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gl_FragColor = cloud;
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#endif
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#endif
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}
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