Lesson 3 of 10 · The Solar System in GLSL
Venus
Sulfuric acid clouds. They lap the planet in four days; the planet takes 243.
Mercury turned as one piece. Venus does not: its clouds lap it in about 4 days, the planet takes 243, and backwards. That is called superrotation. The trick: latitude, asin(n.y), decides how far each point turns: the equator more, the poles less.
lap is each latitude's angle. cos(lat)*cos(lat) is 1 at the equator and 0 at the poles, so shear pulls the speeds apart. A shape that spans latitudes stretches into streaks and Vs. The clouds are Domain Warp's warp over a 3D noise, stretched in y to make bands.
Venus reflects 76% of the light, and below it is 465 °C. The air is so thick that light wraps around: soft pushes the terminator into the night. Below: Speed, Shear and Soft.
A cappuccino seen from above. At 465 °C.
asin(n.y) = latitude. A spin that depends on latitude = differential rotation. (dot(n, sun) + soft)/(1.0 + soft) = light that wraps around.shear to 0.0: it spins like a top. Raise it to 1.5 and wait a minute: streaks. Take soft to 0.8: almost no night.The code
precision highp float;
// The exact sphere: how far along the ray it is hit, or -1 if the ray misses
float sphere(vec3 ro, vec3 rd, float r){
float b = dot(ro, rd), c = dot(ro, ro) - r*r, h = b*b - c;
return h < 0.0 ? -1.0 : -b - sqrt(h);
}
// WoGL close: knee at 0.70, sRGB, chroma 1.3
vec3 wogl(vec3 c){
float l = dot(c, vec3(0.2126, 0.7152, 0.0722)), k = max(l - 0.7, 0.0);
c *= l > 0.0 ? (l - k + k/(1.0 + k))/l : 0.0;
c = pow(clamp(c, 0.0, 1.0), vec3(0.4545));
l = dot(c, vec3(0.2126, 0.7152, 0.0722));
return clamp(mix(vec3(l), c, 1.3), 0.0, 1.0);
}
// Noise in 3D: the usual fb with one more dimension. On a globe it leaves no seam.
float h3(vec3 p){ return h2(p.xy + p.z*vec2(37.0, 17.0)); }
float n3(vec3 p){
vec3 i = floor(p), f = fract(p);
f = f*f*(3.0 - 2.0*f);
return mix(mix(mix(h3(i), h3(i + vec3(1,0,0)), f.x), mix(h3(i + vec3(0,1,0)), h3(i + vec3(1,1,0)), f.x), f.y),
mix(mix(h3(i + vec3(0,0,1)), h3(i + vec3(1,0,1)), f.x), mix(h3(i + vec3(0,1,1)), h3(i + vec3(1,1,1)), f.x), f.y), f.z);
}
float f3(vec3 p){
float v = 0.0, a = 0.5;
for (int i = 0; i < 5; i++){ v += a*n3(p); p = p*2.03 + vec3(1.7, 9.2, 4.1); a *= 0.5; }
return v;
}
// A 2D turn (to spin the globe about its axis)
mat2 turn(float a){ float c = cos(a), s = sin(a); return mat2(c, -s, s, c); }
// The background: black, with a star now and then
vec3 sky(vec2 f){
float s = h2(floor(f));
return vec3(0.0002, 0.0003, 0.0006) + vec3(0.7, 0.7, 0.8)*step(0.9982, s)*h2(floor(f) + 3.1);
}
float speed = 0.25; // the clouds' lap
float shear = 0.9; // how much faster the equator goes than the poles
float soft = 0.25; // the light that wraps around through the air
void main(){
vec2 p = (gl_FragCoord.xy*2.0 - R)/min(R.x, R.y);
vec3 ro = vec3(0.0, 0.0, 3.2), rd = normalize(vec3(p, -2.4)); // the camera looks at the center
vec3 sun = normalize(vec3(M.x*4.0 - 3.8, M.y*3.0 - 1.0, 1.0)); // you move the sun: it is the pointer
vec3 col = sky(gl_FragCoord.xy);
float t = sphere(ro, rd, 1.0);
if (t > 0.0){
vec3 n = normalize(ro + rd*t);
float lat = asin(n.y); // latitude: -1.57 at the south pole, 1.57 at the north
float lap = T*speed*(1.0 + shear*cos(lat)*cos(lat)); // the equator laps more
vec3 q = n; q.xz = turn(lap)*q.xz;
float cloud = f3(q*vec3(2.2, 5.5, 2.2) + f3(q*3.0)*1.2); // bands: y stretched, and a warp (04)
vec3 cream = vec3(0.95, 0.83, 0.58), ochre = vec3(0.62, 0.46, 0.24);
vec3 albedo = mix(ochre, cream, smoothstep(0.30, 0.70, cloud))*0.76; // Venus reflects 76%
float light = max((dot(n, sun) + soft)/(1.0 + soft), 0.0);
col = albedo*light*2.4;
}
gl_FragColor = vec4(wogl(col), 1.0);
}