icosa medusa

turtling is fun... :-)
spherical tiling based on icosahedron (reminds me of medusa's hairdo - hence the name)
based on https://www.shaderoo.org/?shader=IkKuv9
and again using reinder's occlusion methods from "Cubic space division #2"

Created by flockaroo on 2018/12/4
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// created by florian berger (flockaroo) - 2018
// License Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

// derived from  "medusas hairdo" https://www.shaderoo.org/?shader=IkKuv9
// using reinder's occlusion magic from  "Cubic space division #2"

Canvas.setpenopacity(1.);

// Global code will be evaluated once.
const turtle = new Turtle();
const polygonList = [];
const quads = [];

const PI2 = Math.PI*2.0;

function mcos(x) {
    return Math.cos(x);
}

function msin(x) {
    return Math.sin(x);
}

function cos2(x) {
    return [Math.cos(x[0]),Math.cos(x[1])];
}

function sin2(x) {
    return [Math.sin(x[0]),Math.sin(x[1])];
}

function SC(x) {
    return [Math.sin(x),Math.cos(x)];
}

function add2(a,b) {
    return [a[0]+b[0],a[1]+b[1]];
}

function add3(a,b) {
    return [a[0]+b[0],a[1]+b[1],a[2]+b[2]];
}

function sub3(a,b) {
    return [a[0]-b[0],a[1]-b[1],a[2]-b[2]];
}

function dot3(a,b) {
    return a[0]*b[0]+a[1]*b[1]+a[2]*b[2];
}

function scale2(a,b) {
    return [a[0]*b,a[1]*b];
}

function scale3(a,b) {
    return [a[0]*b,a[1]*b,a[2]*b];
}

function scale4(a,b) {
    return [a[0]*b,a[1]*b,a[2]*b,a[3]*b];
}

function mul4(a,b) {
    return [a[0]*b[0],a[1]*b[1],a[2]*b[2],a[3]*b[3]];
}

function mymix(a,b,f) {
    return a*(1.0-f)+b*f;
}

function mymix22(a,b,f) {
    return [a[0]*(1.0-f[0])+b[0]*f[0],a[1]*(1.0-f[1])+b[1]*f[1]];
}

function mix3(a,b,f) {
    return add3(scale3(a,(1.0-f)),scale3(b,f));
}

function length2(a) {
    return Math.sqrt(a[0]*a[0]+a[1]*a[1]);
}

function length3(a) {
    return Math.sqrt(a[0]*a[0]+a[1]*a[1]+a[2]*a[2]);
}

function normalize3(a) {
    return scale3(a,1.0/length3(a));
}

function cross(a,b) {
    return [
        a[1]*b[2]-b[1]*a[2],
        a[2]*b[0]-b[2]*a[0],
        a[0]*b[1]-b[0]*a[1]
    ];
}

const G=(.5+Math.sqrt(5./4.));
//const PI2=(3.141592653*2.);
const PI=3.141592653;

function fract(a) {return a-Math.floor(a);}
function floor2(a) { return [Math.floor(a[0]),Math.floor(a[1])];}
function fract2(a) { return [fract(a[0]),fract(a[1])];}

// noise funcs by Morgan McGuire
https://www.shadertoy.com/view/4dS3Wd

function hash(n) { return fract(Math.sin(n) * 1.0e4); }
function hash2(p) { return fract(1.0e4 * Math.sin(17.0 * p[0] + p[1] * 0.1) * (0.1 + Math.abs(Math.sin(p[1] * 13.0 + p[0])))); }

function noise(x) {
    var i = Math.floor(x);
    var f = fract(x);
    var u = f * f * (3.0 - 2.0 * f);
    return mymix(hash(i), hash(i + 1.0), u);
}

function noise2(x) {
    var i = floor2(x);
    var f = fract2(x);
    var r1=mymix(hash2(add2(i,[0,0])), hash2(add2(i,[1,0])), f[0]);
    var r2=mymix(hash2(add2(i,[0,1])), hash2(add2(i,[1,1])), f[0]);
    return mymix(r1, r2, f[1]);
}

function getRand01Sph(pos)
{
    var res = [1024,1024];
    //var texc=((pos.xy*123.+pos.z)*res+.5)/res;
    var texc=[ pos[0]*123.+pos[2]+.5/res[0],
               pos[1]*123.+pos[2]+.5/res[1] ];
    var n=1.0-noise2(scale2(texc,256.));
    return [0,0,0,0];
    return [n,n,n,n];
}

//const vec4 p0 = vec4( 1, G, -G ,0 )/length(vec2(1,G));

const pI = scale4([ 1, G, -G ,0 ],1.0/length2([1,G]));

/*vec3 icosaPosRaw[12] = vec3[] (
    -p0.xwz,  p0.xwy, -p0.xwy,  p0.xwz,
     p0.wyx, -p0.wzx,  p0.wzx, -p0.wyx,
     p0.yxw,  p0.zxw, -p0.zxw, -p0.yxw
);*/

const icosaPosRaw = [
    [-pI[0],-pI[3],-pI[2]/*.xwz*/],
    [ pI[0], pI[3], pI[1]/*.xwy*/],
    [-pI[0],-pI[3],-pI[1]/*.xwy*/],
    [ pI[0], pI[3], pI[2]/*.xwz*/],
    
    [ pI[3], pI[1], pI[0]/*.wyx*/],
    [-pI[3],-pI[2],-pI[0]/*.wzx*/],
    [ pI[3], pI[2], pI[0]/*.wzx*/],
    [-pI[3],-pI[1],-pI[0]/*.wyx*/],
     
    [ pI[1], pI[0], pI[3]/*.yxw*/],
    [ pI[2], pI[0], pI[3]/*.zxw*/],
    [-pI[2],-pI[0],-pI[3]/*.zxw*/],
    [-pI[1],-pI[0],-pI[3]/*.yxw*/]
];

const posIdx = [
0,  6, 1,
0, 11, 6,
1,  4, 0,
1,  8, 4,
1, 10, 8,
2,  5, 3,
2,  9, 5,
2, 11, 9,
3,  7, 2,
3, 10, 7,
4,  8, 5,
4,  9, 0,
5,  8, 3,
5,  9, 4,
6, 10, 1,
6, 11, 7,
7, 10, 6,
7, 11, 2,
8, 10, 3,
9, 11, 0
];

// get icosahedron triangle
function getIcosaTri(idx)
{
    var i1 = posIdx[(idx%20)*3+0];
    var i2 = posIdx[(idx%20)*3+1];
    var i3 = posIdx[(idx%20)*3+2];

    var p1=icosaPosRaw[i1];
    var p2=icosaPosRaw[i2];
    var p3=icosaPosRaw[i3];
    return [p1,p2,p3];
}


// subdivide 1 triangle into 4 triangles and give back closest triangle
function getTriSubDiv(idx, p1, p2, p3)
{
    var p4 = normalize3(add3(p1,p2));
    var p5 = normalize3(add3(p2,p3));
    var p6 = normalize3(add3(p3,p1));

    if     (idx==0) { p1=p1; p2=p4; p3=p6; }
    else if(idx==1) { p1=p6; p2=p5; p3=p3; }
    else if(idx==2) { p1=p6; p2=p4; p3=p5; }
    else if(idx==3) { p1=p4; p2=p2; p3=p5; }
    return [p1, p2, p3];
}


var triStripIndex = [0,1,2,1,3,2];

function mixSq3(a,b,f) { return mymix3(a,b,Math.cos(f*PI)*.5+.5); }

function geomTangentCurve(pos1, pos2, tan1, tan2, r1, r2, 
                          rSegNum, tSegNum, vIdx)
{
    var l = length3(sub3(pos1,pos2));
    l*=.4;
    var i=Math.floor(vIdx/3/2)%tSegNum;
    //{  // converted some loops into proper vertex index values
        var fact, fact2;
        fact=Math.max(0.,(i)/(tSegNum)); // force >=0 because of sqrt below
        fact=-Math.cos(fact*PI)*.5+.5; // more homogeneous steps
        var p1=mix3(add3(pos1,scale3(tan1,l*Math.sqrt(fact ))),sub3(pos2,scale3(tan2,l*Math.sqrt(1.-fact ))),fact );
        fact2=Math.max(0.,(i+1)/(tSegNum)); // force >=0 because of sqrt below
        fact2=-Math.cos(fact2*PI)*.5+.5; // more homogeneous steps
        var p2=mix3(add3(pos1,scale3(tan1,l*Math.sqrt(fact2))),sub3(pos2,scale3(tan2,l*Math.sqrt(1.-fact2))),fact2);

        var ta = mix3(tan1,tan2,fact);
        var tn = mix3(tan1,tan2,fact2);

        var dph=PI*2./(rSegNum);
        //vec3 b1=normalize(vec3(ta.x,-ta.y,0));
        var b1=normalize3(cross(ta,p1));
        var b2=normalize3(cross(ta,b1));
        //vec3 b3=normalize(vec3(tn.x,-tn.y,0));
        var b3=normalize3(cross(tn,p2));
        var b4=normalize3(cross(tn,b3));
        var r_1 = mymix(r1,r2,fact);
        var r_2 = mymix(r1,r2,fact2);
        var j=Math.floor(vIdx/3/2/tSegNum)%rSegNum;
        //{
            var ph  = (j)*dph;
            var ph2 = ph+dph;
            var v1 = add3(p1,scale3(add3(scale3(b1,mcos(ph )),scale3(b2,msin(ph ))),r_1));
            var v2 = add3(p1,scale3(add3(scale3(b1,mcos(ph2)),scale3(b2,msin(ph2))),r_1));
            var v3 = add3(p2,scale3(add3(scale3(b3,mcos(ph )),scale3(b4,msin(ph ))),r_2));
            var v4 = add3(p2,scale3(add3(scale3(b3,mcos(ph2)),scale3(b4,msin(ph2))),r_2));
            var v = [v1,v2,v3,v4];
            var pos = v[triStripIndex[vIdx%6]];
            var normal = normalize3(cross(sub3(v[1],v[0]),sub3(v[2],v[0])));
        //}
    //}
    return [pos,normal]
}

function calcAngle(v1, v2)
{
    return Math.acos(dot3(v1,v2)/length3(v1)/length3(v2));
}

// distance to 2 torus segments in a triangle
// each torus segment spans from the middle of one side to the middle of another side
function geomTruchet(p1, p2, p3, dz, rSegNum, tSegNum, trNum, 
                     radius, idx )
{

    if (radius<0.0) radius=.45*dz;
    var d = 10000.0;
    var rnd =getRand01Sph(add3(add3(p1,p2),p3))[0];
    var rnd2=getRand01Sph(add3(add3(p1,p2),p3))[1];
    // random rotation of torus-start-edges
    if      (rnd>.75) { var d=p1; p1=p2; p2=d; }
    else if (rnd>.50) { var d=p1; p1=p3; p3=d; }
    else if (rnd>.25) { var d=p2; p2=p3; p3=d; }
    
    var p4 = scale3(p1,(1.-dz));
    var p5 = scale3(p2,(1.-dz));
    var p6 = scale3(p3,(1.-dz));

    // FIXME: why is this necessary - very seldom actually!?
    var xchg=false;
    if(dot3(cross(sub3(p2,p1),sub3(p3,p1)),p1)>0.0) {
        var dummy;
        dummy=p2; p2=p3; p3=dummy;
        dummy=p5; p5=p6; p6=dummy;
        xchg=true;
    }

    var lp1 = length3(p1);
    var lp4 = length3(p4);
    
    var r,r1,r2,fact,ang,fullAng;
    var n = normalize3(cross(sub3(p2,p1),sub3(p3,p1)));

    // torus segments:
    // actually i have to fade from one torus into another
    // because not all triangles are equilateral
    var m;
//    std::vector <vec3> p;
    var v1,v2,v3,v4,v5,v6;
    var tubeNum=rSegNum*tSegNum*2*3;
    var i=Math.floor(idx/(tubeNum))%trNum;
    {
        if(i==0) { v1=p1; v2=p2; v3=p3; v4=p4; v5=p5; v6=p6; }
        if(i==1) { v1=p2; v2=p3; v3=p1; v4=p5; v5=p6; v6=p4; }
        if(i==2) { v1=p3; v2=p1; v3=p2; v4=p6; v5=p4; v6=p5; }
        //if(dot(cross(v2-v1,v3-v1),v1)>0.0) { vec3 dummy=v2; v2=v3; v3=dummy; }
        //if(dot(cross(v5-v4,v6-v4),v4)>0.0) { vec3 dummy=v5; v5=v6; v6=dummy; }

    	fullAng = calcAngle(sub3(v3,v1),sub3(v2,v1));
        //ang = calcAngle(pos2-v1,v2-v1);
        var dang=fullAng/(tSegNum);
        //if (fullAng<.001) break;

        //float r1, r2;
        //r1=length(v2-v1)*.5f; r1=length(v3-v1)*.5f;
        var pos1, pos2, pos3;
        pos1 = scale3(normalize3(add3(v2,v1)),lp1); 
        pos2 = scale3(normalize3(add3(v6,v4)),lp4);
        //pos3 = scale3(normalize3(add3(v2,v3)),lp4);
        // FIXME: why is this necessary - very seldom actually!? - see above
        if(xchg) {
            pos1 = scale3(normalize3(add3(v5,v4)),lp1); pos2 = scale3(normalize3(add3(v3,v1)),lp4);
        }
        if(rnd2>.25)
        {
            if(i==0) { pos1 = scale3(normalize3(add3(v5,v4)),lp4); pos2 = scale3(normalize3(add3(v6,v4)),lp4); }
            if(i==1) { pos1 = scale3(normalize3(add3(v2,v1)),lp1); pos2 = scale3(normalize3(add3(v3,v1)),lp1); }
        }
        var tan1 = normalize3(cross(sub3(v2,v1),v1));
        var tan2 = normalize3(cross(sub3(v3,v1),v1));
        var pn = geomTangentCurve(pos1,pos2,tan1,tan2,radius,radius,rSegNum,tSegNum,
                                  idx%tubeNum);
    
        return pn;
    }
}

// final shape
function geom_medusa(rNum, tNum, subdiv, idx)
{
    var p1,p2,p3;

    var icosaFaceNum = 20;
    var subDivNum = 4;
    
    var trNum = 3; // tubes per truchet segemnt
    var truchetNum=rNum*tNum*2*3*trNum; // 2 triangles * 3 vertices * trNum tubes
    
    //for(int i1=0;i1<icosaFaceNum;i1++)
    var idiv=truchetNum; for(var i=0;i<subdiv;i++) idiv*=subDivNum;
    var pi = getIcosaTri(Math.floor(idx/idiv));
    var p_subDivNum_i = 1;
    for(var i=0;i<subdiv;i++)
    {
        idiv=Math.floor(idiv/subDivNum);
        var isub = Math.floor(idx/idiv)%subDivNum;
        pi = getTriSubDiv(isub,pi[0],pi[1],pi[2]);
        p_subDivNum_i*=subDivNum;
    }
    var pn = geomTruchet(pi[0],pi[1],pi[2],0.12/(1+subdiv),rNum,tNum,trNum,-1.,idx%truchetNum);
    
    return pn;
}


function medusaTri(idx)
{
    var pos = [0,0,0];
    var normal = [0,0,0];
    var pn;
    pn=geom_medusa(8,6,0,idx);
    //pn=geomTangentCurve([-2,0,0], [0,0,2], [1,0,0], [0,0,-1], .1, .1, 10, 10, idx);
    pos=pn[0];
    //pn = getIcosaTri(Math.floor(idx/3));
    //pos=pn[idx%3];
    return pos;
}


function rotX(ph,v) {
    return [ v[0],v[1]*mcos(ph)+v[2]*msin(ph), v[2]*mcos(ph)-v[1]*msin(ph) ];
}

function rotY(ph,v) {
    return [ v[0]*mcos(ph)+v[2]*msin(ph), v[1], v[2]*mcos(ph)-v[0]*msin(ph) ];
}

function project(p)
{
    p[2]+=180;
    return [p[0]/p[2]*180.,p[1]/p[2]*180.,p[2]];
}

function insertQuad(p0,p1,p2,p3)
{
    var z = p0[2]+p1[2]+p2[2]+p3[2];
    var idx=0;
    for(idx=0;idx<quads.length && quads[idx+8]<z;idx+=9);
    
    // hmm, why is the one below not working... !?
    //for(var i=0;i<quads.length;i+=9) {
    //    if(quads[i+8]>z) { idx=i; break; }
    //}
    quads.splice(idx, 0, p0[0], p0[1], p1[0], p1[1], p2[0], p2[1], p3[0], p3[1], z);
}

function walk(i) {
    var num = 8*6*3*20;
    if(i==0){
        for(let j=0;j<num;j++) {
            var p0=medusaTri(j*6);
            var p1=medusaTri(j*6+1);
            var p2=medusaTri(j*6+2);
            var p3=medusaTri(j*6+4);
            p0=scale3(p0,70.0);
            p1=scale3(p1,70.0);
            p2=scale3(p2,70.0);
            p3=scale3(p3,70.0);
            p0=rotX(1.4,p0);
            p1=rotX(1.4,p1);
            p2=rotX(1.4,p2);
            p3=rotX(1.4,p3);
            p0=rotY(.1,p0);
            p1=rotY(.1,p1);
            p2=rotY(.1,p2);
            p3=rotY(.1,p3);
            p0=project(p0);
            p1=project(p1);
            p2=project(p2);
            p3=project(p3);
    
            if(cross(sub3(p1,p0),sub3(p2,p0))[2]<0.0)
            {
                insertQuad(p0,p2,p3,p1);
            }
        }
    }
    
    var p0=[quads[i*9+0],quads[i*9+1]];
    var p1=[quads[i*9+2],quads[i*9+3]];
    var p2=[quads[i*9+4],quads[i*9+5]];
    var p3=[quads[i*9+6],quads[i*9+7]];
    const p = new Polygon();
    p.cp.push([p0[0], p0[1]]);
    p.cp.push([p1[0], p1[1]]);
    p.cp.push([p2[0], p2[1]]);
    p.cp.push([p3[0], p3[1]]);
    p.addOutline(0);
    drawPolygon(turtle, p);
    /*turtle.penup();
    turtle.goto(p0);
    turtle.pendown();
    turtle.goto(p1);
    turtle.goto(p2);
    turtle.goto(p0);*/
    /*turtle.goto(p3);
    turtle.goto(p2);*/
    return i <= num/1.8;
}

////////////////////////////
// reinder's occlusion code parts from "Cubic space division #2"
////////////////////////////

function drawPolygon(turtle, p) {
    let vis = true;
    for (let j=0; j<polygonList.length; j++) {
        if(!p.boolean(polygonList[j])) {
            vis = false;
            break;
        }
    }
    if (vis) {
        p.draw(turtle, 0);
        polygonList.push(p);
    }
}

// polygon functions
function LineSegment(p1, p2) {
    this.p1 = p1;
    this.p2 = p2;
}
function Polygon() {
    this.cp = []; // clip path: array of [x,y] pairs
    this.dp = []; // 2d line to draw: array of linesegments
}
Polygon.prototype.addOutline = function(s=0) {
    for (let i=s, l=this.cp.length; i<l; i++) {
        this.dp.push(new LineSegment(this.cp[i], this.cp[(i+1)%l]));
    }
}
Polygon.prototype.createPoly = function(x,y,c,r,a) {
    this.cp = [];
    for (let i=0; i<c; i++) {
        this.cp.push( [x + Math.sin(i*Math.PI*2/c+a) * r, y + Math.cos(i*Math.PI*2/c+a) * r] );
    }
}
Polygon.prototype.draw = function(t, inp=0) {
    if (this.dp.length ==0) {
        return;
    }
    for (let i=0, l=this.dp.length; i<l; i++) {
        const d = this.dp[i];
        if (!vec2_equal(d.p1, t.pos())) {
            t.penup();
            t.goto([d.p1[0]+inp*(Math.random()-.5), d.p1[1]+inp*(Math.random()-.5)]);
            t.pendown();   
        }
        t.goto([d.p2[0]+inp*(Math.random()-.5), d.p2[1]+inp*(Math.random()-.5)]);
    }
}
Polygon.prototype.inside = function(p) {
    // find number of i ntersection points from p to far away
    // if even your outside
    const p1 = [0.1, -1000];
    let int = 0;
    for (let i=0, l=this.cp.length; i<l; i++) {
        if (vec2_find_segment_intersect(p, p1, this.cp[i], this.cp[(i+1)%l])) {
            int ++;
        }    
    }
    return int & 1;
}
Polygon.prototype.boolean = function(p, diff = true) {
    // very naive polygon diff algorithm - made this up myself
    const ndp = [];
    for (let i=0, l=this.dp.length; i<l; i++) {
        const ls = this.dp[i];
        
        // find all intersections with clip path
        const int = [];
        for (let j=0, cl=p.cp.length; j<cl; j++) {
            const pint = vec2_find_segment_intersect(ls.p1,ls.p2,p.cp[j],p.cp[(j+1)%cl]);
            if (pint) {
                int.push(pint);
            }
        }
        if (int.length == 0) { // 0 intersections, inside or outside?
            if (diff == !p.inside(ls.p1)) {
                ndp.push(ls);
            }
        } else {
            int.push(ls.p1);
            int.push(ls.p2);
            // order intersection points on line ls.p1 to ls.p2
            const cmp = [ls.p2[0]-ls.p1[0], ls.p2[1]-ls.p1[1]];
            int.sort( (a,b) => {
                const db = vec2_dot([b[0]-ls.p1[0], b[1]-ls.p1[1]], cmp);
                const da = vec2_dot([a[0]-ls.p1[0], a[1]-ls.p1[1]], cmp);
                return da - db;
            });
            for (let j=0; j<int.length-1; j++) {
                if (!vec2_equal(int[j], int[j+1])) {
                    if (diff == !p.inside([(int[j][0]+int[j+1][0])/2,(int[j][1]+int[j+1][1])/2])) {
                        ndp.push(new LineSegment(int[j], int[j+1]));
                    }
                }
            }
        }
    }
    this.dp = ndp;
    return this.dp.length > 0;
}

// vec functions
const vec2_equal = (a,b) => vec2_dist_sqr(a,b) < 0.01;
const vec2_dot = (a, b) => a[0]*b[0]+a[1]*b[1];
const vec2_dist_sqr = (a, b) => (a[0]-b[0])*(a[0]-b[0]) + (a[1]-b[1])*(a[1]-b[1]);
//port of http://paulbourke.net/geometry/pointlineplane/Helpers.cs
function vec2_find_segment_intersect(l1p1, l1p2, l2p1, l2p2) {
    const d = (l2p2[1] - l2p1[1]) * (l1p2[0] - l1p1[0]) - (l2p2[0] - l2p1[0]) * (l1p2[1] - l1p1[1]);
    const n_a = (l2p2[0] - l2p1[0]) * (l1p1[1] - l2p1[1]) - (l2p2[1] - l2p1[1]) * (l1p1[0] - l2p1[0]);
    const n_b = (l1p2[0] - l1p1[0]) * (l1p1[1] - l2p1[1]) - (l1p2[1] - l1p1[1]) * (l1p1[0] - l2p1[0]);
    if (d == 0) {
        return false;
    }
    const ua = n_a / d;
    const ub = n_b / d;
    if (ua >= 0 && ua <= 1 && ub >= 0 && ub <= 1) {
        return [l1p1[0] + (ua * (l1p2[0] - l1p1[0])), l1p1[1] + (ua * (l1p2[1] - l1p1[1])) ];
    }
    return false;  
}