ISF - Shadertoy - Quasi Infinite Zoom Voronoi XlBXWw
/*{
"IMPORTED": [],
"CATEGORIES": [
"Automatically Converted",
"Shadertoy"
],
"DESCRIPTION": "Automatically converted from https://www.shadertoy.com/view/XlBXWw by Shane. This was inspired by Fabrice Neyret's \"Infinite Fall\" shader.",
"INPUTS": []
}
*/
/*
Quasi Infinite Zoom Voronoi
---------------------------
The infinite zoom effect has been keeping me amused for years.
This one is based on something I wrote some time ago, but was inspired by Fabrice Neyret's
"Infinite Fall" shader. I've aired on the side of caution and called it "quasi infinite,"
just in case it doesn't adhere to his strict infinite zoom standards. :)
Seriously though, I put together a couple of overly optimized versions a couple of days ago,
just for fun, and Fabrice's comments were pretty helpful. I also liked the way he did the
layer rotation in his "Infinite Fall" version, so I'm using that. The rest is stock standard
infinite zoom stuff that has been around for years.
Most people like to use noise for this effect, so I figured I'd do something different
and use Voronoi. I've also bump mapped it, added specular highlights, etc. It was
tempting to add a heap of other things, but I wanted to keep the example relatively simple.
By the way, most of the code is basic bump mapping and lighting. The infinite zoom code
takes up just a small portion.
Fabrice Neyret's versions:
infinite fall - short
https://www.shadertoy.com/view/ltjXWW
infinite fall - FabriceNeyret2
https://www.shadertoy.com/view/4sl3RX
Other examples:
Fractal Noise - mu6k
https://www.shadertoy.com/view/Msf3Wr
Infinite Sierpinski - gleurop
https://www.shadertoy.com/view/MdfGR8
Infinite Zoom - fizzer
https://www.shadertoy.com/view/MlXGW7
Private link to a textured version of this.
Bumped Infinite Zoom Texture - Shane
https://www.shadertoy.com/view/Xl2XWw
*/
vec2 hash22(vec2 p) {
// Faster, but doesn't disperse things quite as nicely. However, when framerate
// is an issue, and it often is, this is a good one to use. Basically, it's a tweaked
// amalgamation I put together, based on a couple of other random algorithms I've
// seen around... so use it with caution, because I make a tonne of mistakes. :)
float n = sin(dot(p, vec2(41, 289)));
return fract(vec2(262144, 32768)*n);
// Animated.
//p = fract(vec2(262144, 32768)*n);
//return sin( p*6.2831853 + time )*0.5 + 0.5;
}
// One of many 2D Voronoi algorithms getting around, but all are based on IQ's
// original. I got bored and roughly explained it. It was a slow day. :) The
// explanations will be obvious to many, but not all.
float Voronoi(vec2 p)
{
// Partitioning the 2D space into repeat cells.
vec2 ip = floor(p); // Analogous to the cell's unique ID.
p -= ip; // Fractional reference point within the cell (fract(p)).
// Set the minimum distance (squared distance, in this case, because it's
// faster) to a maximum of 1. Outliers could reach as high as 2 (sqrt(2)^2)
// but it's being capped to 1, because it covers a good portion of the range
// (basically an inscribed unit circle) and dispenses with the need to
// normalize the final result.
//
// If you're finding that your Voronoi patterns are a little too contrasty,
// you could raise "d" to something like "1.5." Just remember to divide
// the final result by the same amount, clamp, or whatever.
float d = 1.;
// Put a "unique" random point in the cell (using the cell ID above), and it's 8
// neighbors (using their cell IDs), then check for the minimum squared distance
// between the current fractional cell point and these random points.
for (int i = -1; i <= 1; i++){
for (int j = -1; j <= 1; j++){
vec2 cellRef = vec2(i, j); // Base cell reference point.
vec2 offset = hash22(ip + cellRef); // 2D offset.
// Vector from the point in the cell to the offset point.
vec2 r = cellRef + offset - p;
float d2 = dot(r, r); // Squared length of the vector above.
d = min(d, d2); // If it's less than the previous minimum, store it.
}
}
// In this case, the distance is being returned, but the squared distance
// can be used too, if preferred.
return sqrt(d);
}
/*
// 2D 2nd-order Voronoi: Obviously, this is just a rehash of IQ's original. I've tidied
// up those if-statements. Since there's less writing, it should go faster. That's how
// it works, right? :)
//
float Voronoi2(vec2 p){
vec2 g = floor(p), o;
p -= g;// p = fract(p);
vec2 d = vec2(1); // 1.4, etc.
for(int y = -1; y <= 1; y++){
for(int x = -1; x <= 1; x++){
o = vec2(x, y);
o += hash22(g + o) - p;
float h = dot(o, o);
d.y = max(d.x, min(d.y, h));
d.x = min(d.x, h);
}
}
//return sqrt(d.y) - sqrt(d.x);
return (d.y - d.x); // etc.
}
*/
void main() {
// Screen coordinates.
vec2 uv = (gl_FragCoord.xy - RENDERSIZE.xy*.5)/RENDERSIZE.y;
// Variable setup, plus rotation.
float t = TIME, s, a, b, e;
// Rotation the canvas back and forth.
float th = sin(TIME*.1)*sin(TIME*.13)*4.;
float cs = cos(th), si = sin(th);
uv *= mat2(cs, -si, si, cs);
// Setup: I find 2D bump mapping more intuitive to pretend I'm raytracing, then lighting a bump mapped plane
// situated at the origin. Others may disagree. :)
vec3 sp = vec3(uv, 0); // Surface posion. Hit point, if you prefer. Essentially, a screen at the origin.
vec3 ro = vec3(0, 0, -1); // Camera position, ray origin, etc.
vec3 rd = normalize(sp-ro); // Unit direction vector. From the origin to the screen plane.
vec3 lp = vec3(cos(TIME)*.375, sin(TIME)*0.1, -1); // Light position - Back from the screen.
// The number of layers. More gives you a more continous blend, but is obviously slower.
// If you change the layer number, you'll proably have to tweak the "gFreq" value.
const float L = 8.;
// Global layer frequency, or global zoom, if you prefer.
const float gFreq = .5;
float sum = 0.; // Amplitude sum, of sorts.
// Setting up the layer rotation matrix, used to rotate each layer.
// Not completely necessary, but it helps mix things up. It's standard practice, but
// this one is based on Fabrice's example.
th = 3.14159265*.7071/L;
cs = cos(th), si = sin(th);
mat2 M = mat2(cs, -si, si, cs);
// The overall scene color. Initiated to zero.
vec3 col = vec3(0);
// Setting up the bump mapping variables and initiating them to zero.
// f - Function value
// fx - Change in "f" in in the X-direction.
// fy - Change in "f" in in the Y-direction.
float f = 0., fx = 0., fy = 0.;
vec2 eps = vec2(4./RENDERSIZE.y, 0);
// I've had to off-center this just a little to avoid an annoying white speck right
// in the middle of the canvas. If anyone knows how to get rid of it, I'm all ears. :)
vec2 offs = vec2(.1);
// Infinite Zoom.
//
// The first three lines are a little difficult to explain without describing what infinite
// zooming is in the first place. A lot of it is analogous to fBm. Sum a bunch of increasing
// frequencies with decreasing amplitudes.
//
// Anyway, the effect is nothing more than a series of layers being expanded from an initial
// size to a final size, then being snapped back to its original size to repeat the process
// again. However, each layer is doing it at diffent incremental stages in time, which tricks
// the brain into believing the process is continuous. If you wish to spoil the illusion,
// simply reduce the layer count. If you wish to completely ruin the effect, set it to one.
// Infinite zoom loop.
for (float i = 0.; i<L; i++){
// Fractional time component. Obviously, incremented by "1./L" and ranging from
// zero to one, whilst on a repeat cycle.
s = fract((i - t*2.)/L);
// Using the fractional time component to determine the layer frequency. It increases
// with time, then snaps back to one in a cyclic fashion.
// Note that exp2(t) is just another way to write pow(2., s). The latter is more
// intuitive, but slower... Well, I assume it is.
e = exp2(s*L)*gFreq; // Range (approx): [ 1, pow(2., L)*gFreq ]
// Layer ampltude component. Inversely propotional to the frequency, which makes sense.
// Because the layers are finite, you need to smoothly interpolate between them,
// and the "cos" setup below is just one of many ways to do it.
a = (1. - cos(s*6.2831))/e; // Smooth transition.
//a = (1. - abs(s-.5)*2.)/e; // Alternative linear fade. Not as smooth, or accurate.
//a = (1. - abs(s-.5)*2.); a *= a*(3.-2.*a)/e; // Smooth linear fade, if so desired.
// Accumulating each layer.
// I had to have a bit of a think as to how to bump map this. Normally, you'd write a function
// then call it three times, but that'd be too expensive, so it's all being done simultaneously.
//
// Either way, it's still pretty simple. In addition to accumulating the pixel value, accumulate
// sample values just to the left of it and above. The X-gradient and Y-gradient can then be
// determined outside the loop.
//
f += Voronoi(M*sp.xy*e + offs)*a; // Sample value multiplied by the amplitude.
fx += Voronoi(M*(sp.xy - eps.xy)*e + offs)*a; // Same for the nearby sample in the X-direction.
fy += Voronoi(M*(sp.xy - eps.yx)*e + offs)*a; // Same for the nearby sample in the Y-direction.
// Sum each amplitude. Used to normalize the results once the loop is complete.
sum += a;
// Rotating each successive layer is pretty standard, but this is the way Fabrice does
// it.
M *= M;
}
// I doubt it'd happen, but just in case sum is zero.
sum = max(sum, .001);
// Normalizing the three Voronoi samples.
f /= sum;
fx /= sum;
fy /= sum;
// Common bump mapping stuff.
float bumpFactor = .2;
// Using the above to determine the dx and dy function gradients.
fx = (fx - f)/eps.x; // Change in X
fy = (fy - f)/eps.x; // Change in Y.
// Using the gradient vector, "vec3(fx, fy, 0)," to perturb the XY plane normal ",vec3(0, 0, -1)."
vec3 n = normalize( vec3(0, 0, -1) + vec3(fx, fy, 0)*bumpFactor );
// Determine the light direction vector, calculate its distance, then normalize it.
vec3 ld = lp - sp;
float lDist = max(length(ld), .001);
ld /= lDist;
// Light attenuation.
float atten = 1.25/(1. + lDist*0.15 + lDist*lDist*0.15);
//float atten = min(1./(dist*dist*2.), 1.);
// Diffuse value.
float diff = max(dot(n, ld), 0.);
// Enhancing the diffuse value a bit. Made up.
diff = pow(diff, 2.)*.66 + pow(diff, 4.)*.34;
// Specular highlighting.
float spec = pow(max(dot( reflect(-ld, n), -rd), 0.), 16.);
// Using the infinite Voronoi value to produce a purplish color.
vec3 objCol = vec3(f*f, pow(f, 5.)*.05, f*f*.36);
// Blood... ruby red.
//vec3 objCol = vec3(f*f, pow(f, 16.), pow(f, 8.)*.5);
// Using the values above to produce the final color.
col = (objCol*(diff + .5) + vec3(.4, .6, 1)*spec*1.5)*atten;
// Done.
gl_FragColor = vec4(sqrt(min(col, 1.)), 1);
}