ice-and-fire.glsl

/* ice and fire, by mattz
   License Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

   Demonstrate triangulation of jittered triangular lattice.

*/
const float s3 = 1.7320508075688772;
const float i3 = 0.5773502691896258;

const mat2 tri2cart = mat2(1.0, 0.0, -0.5, 0.5*s3);
const mat2 cart2tri = mat2(1.0, 0.0, i3, 2.0*i3);

//////////////////////////////////////////////////////////////////////
// cosine based palette
// adapted from https://www.shadertoy.com/view/ll2GD3

vec3 pal( in float t ) {

    const vec3 a = vec3(0.5);
    const vec3 b = vec3(0.5);
    const vec3 c = vec3(0.8, 0.8, 0.5);
    const vec3 d = vec3(0, 0.2, 0.5);

    return clamp(a + b*cos( 6.28318*(c*t+d) ), 0.0, 1.0);

}

//////////////////////////////////////////////////////////////////////
// from https://www.shadertoy.com/view/4djSRW

#define HASHSCALE1 .1031
#define HASHSCALE3 vec3(443.897, 441.423, 437.195)

float hash12(vec2 p) {
    vec3 p3  = fract(vec3(p.xyx) * HASHSCALE1);
    p3 += dot(p3, p3.yzx + 19.19);
    return fract((p3.x + p3.y) * p3.z);
}

vec2 hash23(vec3 p3) {
	p3 = fract(p3 * HASHSCALE3);
    p3 += dot(p3, p3.yzx+19.19);
    return fract((p3.xx+p3.yz)*p3.zy);
}

//////////////////////////////////////////////////////////////////////
// compute barycentric coordinates from point differences
// adapted from https://www.shadertoy.com/view/lslXDf

vec3 bary(vec2 v0, vec2 v1, vec2 v2) {
    float inv_denom = 1.0 / (v0.x * v1.y - v1.x * v0.y);
    float v = (v2.x * v1.y - v1.x * v2.y) * inv_denom;
    float w = (v0.x * v2.y - v2.x * v0.y) * inv_denom;
    float u = 1.0 - v - w;
    return vec3(u,v,w);
}

//////////////////////////////////////////////////////////////////////
// distance to line segment from point differences

float dseg(vec2 xa, vec2 ba) {
    return length(xa - ba*clamp(dot(xa, ba)/dot(ba, ba), 0.0, 1.0));
}

//////////////////////////////////////////////////////////////////////
// generate a random point on a circle from 3 integer coords (x, y, t)

vec2 randCircle(vec3 p) {

    vec2 rt = hash23(p);

    float r = sqrt(rt.x);
    float theta = 6.283185307179586 * rt.y;

    return r*vec2(cos(theta), sin(theta));

}

//////////////////////////////////////////////////////////////////////
// make a time-varying cubic spline at integer coords p that stays
// inside a unit circle

vec2 randCircleSpline(vec2 p, float t) {

    // standard catmull-rom spline implementation
    float t1 = floor(t);
    t -= t1;

    vec2 pa = randCircle(vec3(p, t1-1.0));
    vec2 p0 = randCircle(vec3(p, t1));
    vec2 p1 = randCircle(vec3(p, t1+1.0));
    vec2 pb = randCircle(vec3(p, t1+2.0));

    vec2 m0 = 0.5*(p1 - pa);
    vec2 m1 = 0.5*(pb - p0);

    vec2 c3 = 2.0*p0 - 2.0*p1 + m0 + m1;
    vec2 c2 = -3.0*p0 + 3.0*p1 - 2.0*m0 - m1;
    vec2 c1 = m0;
    vec2 c0 = p0;

    return (((c3*t + c2)*t + c1)*t + c0) * 0.8;

}

//////////////////////////////////////////////////////////////////////
// perturbed point from index

vec2 triPoint(vec2 p) {
    float t0 = hash12(p);
    return tri2cart*p + 0.45*randCircleSpline(p, 0.45*iTime + t0);
}

//////////////////////////////////////////////////////////////////////
// main shading function. inputs:
//
//   p - current pixel location in scene
//
//   tfloor - integer grid coordinates of bottom-left triangle vertex
//
//   t0, t1, t2 - displaced cartesian coordinates (xy) and integer
//                grid offsets (zw) of triangle vertices, relative
//                to tfloor
//
//   scl - pixel size in scene units
//
//   cw - pixel accumulator. xyz are rgb color pre-multiplied by
//        weights, and w is total weight.
//

void tri_color(in vec2 p,
               in vec4 t0, in vec4 t1, in vec4 t2,
               in float scl,
               inout vec4 cw) {

    // get differences relative to vertex 0
    vec2 p0 = p - t0.xy;
    vec2 p10 = t1.xy - t0.xy;
    vec2 p20 = t2.xy - t0.xy;

    // get barycentric coords
    vec3 b = bary(p10, p20, p0);

    // distances to line segments
    float d10 = dseg(p0, p10);
    float d20 = dseg(p0, p20);
    float d21 = dseg(p - t1.xy, t2.xy - t1.xy);

    // unsigned distance to triangle boundary
    float d = min(min(d10, d20), d21);

    // now signed distance (negative inside, positive outside)
    d *= -sign(min(b.x, min(b.y, b.z)));

    // only wory about coloring if close enough
    if (d < 0.5*scl) {

        //////////////////////////////////////////////////
        // generate per-vertex palette entries

        // sum of all integer grid indices
        vec2 tsum = t0.zw + t1.zw + t2.zw;

        // generate unique random number in [0, 1] for each vertex of
        // this triangle
        vec3 h_tri = vec3(hash12(tsum + t0.zw),
                          hash12(tsum + t1.zw),
                          hash12(tsum + t2.zw));

        //////////////////////////////////////////////////
        // now set up the "main" triangle color:

        // get the cartesian centroid of this triangle
        vec2 pctr = (t0.xy + t1.xy + t2.xy) / 3.0;

        // angle of scene-wide color gradient
        float theta = 1.0 + 0.1*iTime;
        vec2 dir = vec2(cos(theta), sin(theta));

        // how far are we along gradient?
        float grad_input = dot(pctr, dir) - sin(0.5*iTime);

        // h0 varies smoothly from 0 to 1
        float h0 = sin(0.7*grad_input)*0.5 + 0.5;

        // now the per-vertex random numbers are all biased towards h
        // (still in [0, 1] range tho)
        h_tri = mix(vec3(h0), h_tri, 0.4);

        //////////////////////////////////////////////////
        // final color accumulation

        // barycentric interpolation of per-vertex palette indices
        float h = dot(h_tri, b);

        // color lookup
        vec3 c = pal(h);

        // weight for anti-aliasing is 0.5 at border, 0 just outside,
        // 1 just inside
        float w = smoothstep(0.5*scl, -0.5*scl, d);

        // add to accumulator
        cw += vec4(w*c, w);

    }

}

//////////////////////////////////////////////////////////////////////

void mainImage( out vec4 fragColor, in vec2 fragCoord ) {

    float scl = 6.0 / iResolution.x;

    // get 2D scene coords
    vec2 p = (fragCoord - 0.5 - 0.5*iResolution.xy) * scl;

    // get triangular base coords
    vec2 tfloor = floor(cart2tri * p + 0.5);

    // precompute 9 neighboring points
    vec2 pts[9];

    for (int i=0; i<3; ++i) {
        for (int j=0; j<3; ++j) {
            pts[3*i+j] = triPoint(tfloor + vec2(i-1, j-1));
        }
    }

    // color accumulator
    vec4 cw = vec4(0);

    // for each of the 4 quads:
    for (int i=0; i<2; ++i) {
        for (int j=0; j<2; ++j) {

            // look at lower and upper triangle in this quad
            vec4 t00 = vec4(pts[3*i+j  ], tfloor + vec2(i-1, j-1));
            vec4 t10 = vec4(pts[3*i+j+3], tfloor + vec2(i,   j-1));
            vec4 t01 = vec4(pts[3*i+j+1], tfloor + vec2(i-1, j));
            vec4 t11 = vec4(pts[3*i+j+4], tfloor + vec2(i,   j));

            // lower
            tri_color(p, t00, t10, t11, scl, cw);

            // upper
            tri_color(p, t00, t11, t01, scl, cw);

        }
    }


    // final pixel color
    fragColor = cw / cw.w;

}

// https://www.shadertoy.com/view/MdfBzl