const turbulence = 1; //min=.01 max=5 step=.01
const stormDirection = 0; //min=0 max=360 step=1
const rings = 6; //min=1 max=10 step=1
const segmentsPerRing = 16; //min=2 max=40 step=2
const segmentMargin = 2; //min=0 max=5 step=.1
const squaresPerSegment = 8; //min=1 max=15 step=1

Canvas.setpenopacity(.8);

/*
// Seedable random number generator by David Bau: http://davidbau.com/archives/2010/01/30/random_seeds_coded_hints_and_quintillions.html
!function(a,b,c,d,e,f,g,h,i){function j(a){var b,c=a.length,e=this,f=0,g=e.i=e.j=0,h=e.S=[];for(c||(a=[c++]);d>f;)h[f]=f++;for(f=0;d>f;f++)h[f]=h[g=s&g+a[f%c]+(b=h[f])],h[g]=b;(e.g=function(a){for(var b,c=0,f=e.i,g=e.j,h=e.S;a--;)b=h[f=s&f+1],c=c*d+h[s&(h[f]=h[g=s&g+b])+(h[g]=b)];return e.i=f,e.j=g,c})(d)}function k(a,b){var c,d=[],e=typeof a;if(b&&"object"==e)for(c in a)try{d.push(k(a[c],b-1))}catch(f){}return d.length?d:"string"==e?a:a+"\0"}function l(a,b){for(var c,d=a+"",e=0;e<d.length;)b[s&e]=s&(c^=19*b[s&e])+d.charCodeAt(e++);return n(b)}function m(c){try{return o?n(o.randomBytes(d)):(a.crypto.getRandomValues(c=new Uint8Array(d)),n(c))}catch(e){return[+new Date,a,(c=a.navigator)&&c.plugins,a.screen,n(b)]}}function n(a){return String.fromCharCode.apply(0,a)}var o,p=c.pow(d,e),q=c.pow(2,f),r=2*q,s=d-1,t=c["seed"+i]=function(a,f,g){var h=[];f=1==f?{entropy:!0}:f||{};var o=l(k(f.entropy?[a,n(b)]:null==a?m():a,3),h),s=new j(h);return l(n(s.S),b),(f.pass||g||function(a,b,d){return d?(c[i]=a,b):a})(function(){for(var a=s.g(e),b=p,c=0;q>a;)a=(a+c)*d,b*=d,c=s.g(1);for(;a>=r;)a/=2,b/=2,c>>>=1;return(a+c)/b},o,"global"in f?f.global:this==c)};if(l(c[i](),b),g&&g.exports){g.exports=t;try{o=require("crypto")}catch(u){}}else h&&h.amd&&h(function(){return t})}(this,[],Math,256,6,52,"object"==typeof module&&module,"function"==typeof define&&define,"random");
Math.seedrandom(new Date().toDateString());
*/

init();
const turtle = new Turtle();
const sn = SquareTiledSimplex2D(Simplex().createNoise4D(), 200, turbulence);//new SimplexNoise((Math.random() * 100) | 0);
const sdm = V.rot2d(stormDirection * 2 * Math.PI / 360);

// The walk function will be called until it returns false.
function walk(i, t) {
    function samplePoint(pt) {
        return N.clamp(.1 + .9*(sn.sample(...V.rotateClamp(
            V.add(V.scale([200,0], t), V.trans(sdm, pt)),
            [-100, -100],
            [100, 100]
        )) / 2 + .5), 0, 1);
    }
    
    const ring = i / segmentsPerRing | 0;
    const segment = i % segmentsPerRing;
    
    const innerR = 17 + ring * squaresPerSegment * 3;
    const outerR = 17 + (ring + 1) * squaresPerSegment * 3 - segmentMargin;
    
    let useSegmentsPerRing = segmentsPerRing;
    while(innerR * 2 * Math.PI / useSegmentsPerRing < 10) {
        useSegmentsPerRing /= 2;
    }
    
    const [innerThetaPerSegment, outerThetaPerSegment, innerStartTheta, outerStartTheta] = getThetaBounds(segment, useSegmentsPerRing, innerR, outerR);

    function getThetaBounds(segment, segmentsPerRing, innerR, outerR) {
        const innerThetaMargin = segmentMargin / innerR;
        const outerThetaMargin = segmentMargin / outerR;
        const innerThetaPerSegment = 2 * Math.PI / segmentsPerRing - innerThetaMargin;
        const outerThetaPerSegment = 2 * Math.PI / segmentsPerRing - outerThetaMargin;
        return [
            innerThetaPerSegment,
            outerThetaPerSegment,
            innerThetaMargin / 2 + (innerThetaPerSegment + innerThetaMargin) * segment,
            outerThetaMargin / 2 + (outerThetaPerSegment + outerThetaMargin) * segment
        ];
    }

    const innerPts = PT.arc(innerR, innerThetaPerSegment, innerStartTheta, null, true);
    const outerPts = PT.arc(outerR, outerThetaPerSegment, outerStartTheta, null, true).reverse();
    PT.drawTour(turtle, innerPts.concat(outerPts));
    
    const rowR = (outerR - innerR) / squaresPerSegment;
    for(let row = 0; row < squaresPerSegment; row++) {
        const rInnerR = innerR + row * rowR;
        const rOuterR = innerR + (row+1) * rowR;

        const [cInnerThetaPerSegment, cOuterThetaPerSegment, cInnerStartTheta, cOuterStartTheta] = getThetaBounds(segment, useSegmentsPerRing, rInnerR, rOuterR);
        
        for(let isle = 0; isle < squaresPerSegment; isle++) {
            const midR = (rOuterR + rInnerR) / 2;
            const midTheta = (cOuterStartTheta + cInnerStartTheta)/2 + ((cOuterThetaPerSegment + cInnerThetaPerSegment) / 2)/squaresPerSegment * (isle + .5);
            const midPoint = [
                midR * Math.cos(midTheta),
                midR * Math.sin(midTheta)
            ];
            
            //PT.drawPoint(turtle, midPoint);
            
            const cv = samplePoint(midPoint)
            const rDiff = (rOuterR - rInnerR) * (1-cv) / 2;
            const srInnerR = rInnerR + rDiff;
            const srOuterR = rOuterR - rDiff;

            const [scInnerThetaPerSegment, scOuterThetaPerSegment, scInnerStartTheta, scOuterStartTheta] = getThetaBounds(segment, useSegmentsPerRing, srInnerR, srOuterR);

            const innerThetaDiff = scInnerThetaPerSegment / squaresPerSegment * (1-cv) / 2;
            const outerThetaDiff = scOuterThetaPerSegment / squaresPerSegment * (1-cv) / 2;

            const innerReach = scInnerThetaPerSegment / squaresPerSegment * cv;
            const outerReach = scOuterThetaPerSegment / squaresPerSegment * cv;
            const cellInnerPts = PT.arc(srInnerR, innerReach, Math.max(0, cInnerStartTheta + isle * cInnerThetaPerSegment / squaresPerSegment + innerThetaDiff), Math.max(3, innerThetaDiff * 2 * srInnerR * 10 | 0), true);
            const cellOuterPts = PT.arc(srOuterR, outerReach, Math.max(0, cOuterStartTheta + isle * cOuterThetaPerSegment / squaresPerSegment + outerThetaDiff), Math.max(3, outerThetaDiff * 2 * srOuterR * 10 | 0), true).reverse();
            PT.drawTour(turtle, cellInnerPts.concat(cellOuterPts));
        }
    }
    
    const SQRT3 = 3**.5;
    const SQRT3over2 = SQRT3/2;

    const hexR = 3.6;
    const baseHex = PT.circular(hexR, 6);
    for(let x = -5; x <= 5; x++) {
        for(let y = -10; y <= 10; y++) {
            const l = [
                (Math.abs(y) % 2 == 1? hexR * Math.SQRT2: 0) + hexR * x * 3,
                hexR * SQRT3over2 * y
            ];
            if(V.lenSq(l) > ((17-hexR)**2)*.9) continue;
            
            const v = samplePoint(l);
            PT.drawTour(turtle, baseHex.map(pt => V.add(V.scale(pt, .8), l)));
            PT.drawTour(turtle, baseHex.map(pt => V.add(V.scale(pt, .8 * v), l)));
            PT.drawTour(turtle, baseHex.map(pt => V.add(V.scale(pt, .4 * v), l)));
        }
    }
    
    return i < rings * segmentsPerRing - 1;
}

///////////////////////////////////////////////////////
// Port by Jurgen Westerhof 2024
// from https://www.skypack.dev/view/simplex-noise
//
// Usage:
// const noise = Simplex().createNoise2D(randomFunction); // or
//             = Simplex().createNoise3D(randomFunction); // or
//             = Simplex().createNoise4D(randomFunction);
// const simplexSample = noise(x, y[, z[, t]]);
///////////////////////////////////////////////////////
function Simplex(){const t=.5*(Math.sqrt(3)-1),e=(3-Math.sqrt(3))/6,n=1/6,r=(Math.sqrt(5)-1)/4,o=(5-Math.sqrt(5))/20,a=t=>0|Math.floor(t),l=new Float64Array([1,1,-1,1,1,-1,-1,-1,1,0,-1,0,1,0,-1,0,0,1,0,-1,0,1,0,-1]),s=new Float64Array([1,1,0,-1,1,0,1,-1,0,-1,-1,0,1,0,1,-1,0,1,1,0,-1,-1,0,-1,0,1,1,0,-1,1,0,1,-1,0,-1,-1]),c=new Float64Array([0,1,1,1,0,1,1,-1,0,1,-1,1,0,1,-1,-1,0,-1,1,1,0,-1,1,-1,0,-1,-1,1,0,-1,-1,-1,1,0,1,1,1,0,1,-1,1,0,-1,1,1,0,-1,-1,-1,0,1,1,-1,0,1,-1,-1,0,-1,1,-1,0,-1,-1,1,1,0,1,1,1,0,-1,1,-1,0,1,1,-1,0,-1,-1,1,0,1,-1,1,0,-1,-1,-1,0,1,-1,-1,0,-1,1,1,1,0,1,1,-1,0,1,-1,1,0,1,-1,-1,0,-1,1,1,0,-1,1,-1,0,-1,-1,1,0,-1,-1,-1,0]);function i(t){const e=512,n=new Uint8Array(e);for(let t=0;t<256;t++)n[t]=t;for(let e=0;e<255;e++){const r=e+~~(t()*(256-e)),o=n[e];n[e]=n[r],n[r]=o}for(let t=256;t<e;t++)n[t]=n[t-256];return n}return new class{buildPermutationTable(t){return i(t)}createNoise2D(n){return function(n=Math.random){const r=i(n),o=new Float64Array(r).map((t=>l[t%12*2])),s=new Float64Array(r).map((t=>l[t%12*2+1]));return function(n,l){let c=0,i=0,f=0;const u=(n+l)*t,m=a(n+u),w=a(l+u),y=(m+w)*e,A=n-(m-y),F=l-(w-y);let p,h;A>F?(p=1,h=0):(p=0,h=1);const M=A-p+e,d=F-h+e,q=A-1+2*e,D=F-1+2*e,N=255&m,b=255&w;let x=.5-A*A-F*F;if(x>=0){const t=N+r[b];x*=x,c=x*x*(o[t]*A+s[t]*F)}let P=.5-M*M-d*d;if(P>=0){const t=N+p+r[b+h];P*=P,i=P*P*(o[t]*M+s[t]*d)}let S=.5-q*q-D*D;if(S>=0){const t=N+1+r[b+1];S*=S,f=S*S*(o[t]*q+s[t]*D)}return 70*(c+i+f)}}(n)}createNoise3D(t){return function(t=Math.random){const e=i(t),r=new Float64Array(e).map((t=>s[t%12*3])),o=new Float64Array(e).map((t=>s[t%12*3+1])),l=new Float64Array(e).map((t=>s[t%12*3+2]));return function(t,s,c){let i,f,u,m;const w=.3333333333333333*(t+s+c),y=a(t+w),A=a(s+w),F=a(c+w),p=(y+A+F)*n,h=t-(y-p),M=s-(A-p),d=c-(F-p);let q,D,N,b,x,P;h>=M?M>=d?(q=1,D=0,N=0,b=1,x=1,P=0):h>=d?(q=1,D=0,N=0,b=1,x=0,P=1):(q=0,D=0,N=1,b=1,x=0,P=1):M<d?(q=0,D=0,N=1,b=0,x=1,P=1):h<d?(q=0,D=1,N=0,b=0,x=1,P=1):(q=0,D=1,N=0,b=1,x=1,P=0);const S=h-q+n,T=M-D+n,U=d-N+n,g=h-b+2*n,j=M-x+2*n,k=d-P+2*n,v=h-1+.5,z=M-1+.5,B=d-1+.5,C=255&y,E=255&A,G=255&F;let H=.6-h*h-M*M-d*d;if(H<0)i=0;else{const t=C+e[E+e[G]];H*=H,i=H*H*(r[t]*h+o[t]*M+l[t]*d)}let I=.6-S*S-T*T-U*U;if(I<0)f=0;else{const t=C+q+e[E+D+e[G+N]];I*=I,f=I*I*(r[t]*S+o[t]*T+l[t]*U)}let J=.6-g*g-j*j-k*k;if(J<0)u=0;else{const t=C+b+e[E+x+e[G+P]];J*=J,u=J*J*(r[t]*g+o[t]*j+l[t]*k)}let K=.6-v*v-z*z-B*B;if(K<0)m=0;else{const t=C+1+e[E+1+e[G+1]];K*=K,m=K*K*(r[t]*v+o[t]*z+l[t]*B)}return 32*(i+f+u+m)}}(t)}createNoise4D(t){return function(t=Math.random){const e=i(t),n=new Float64Array(e).map((t=>c[t%32*4])),l=new Float64Array(e).map((t=>c[t%32*4+1])),s=new Float64Array(e).map((t=>c[t%32*4+2])),f=new Float64Array(e).map((t=>c[t%32*4+3]));return function(t,c,i,u){let m,w,y,A,F;const p=(t+c+i+u)*r,h=a(t+p),M=a(c+p),d=a(i+p),q=a(u+p),D=(h+M+d+q)*o,N=t-(h-D),b=c-(M-D),x=i-(d-D),P=u-(q-D);let S=0,T=0,U=0,g=0;N>b?S++:T++,N>x?S++:U++,N>P?S++:g++,b>x?T++:U++,b>P?T++:g++,x>P?U++:g++;const j=S>=3?1:0,k=T>=3?1:0,v=U>=3?1:0,z=g>=3?1:0,B=S>=2?1:0,C=T>=2?1:0,E=U>=2?1:0,G=g>=2?1:0,H=S>=1?1:0,I=T>=1?1:0,J=U>=1?1:0,K=g>=1?1:0,L=N-j+o,O=b-k+o,Q=x-v+o,R=P-z+o,V=N-B+2*o,W=b-C+2*o,X=x-E+2*o,Y=P-G+2*o,Z=N-H+3*o,$=b-I+3*o,_=x-J+3*o,tt=P-K+3*o,et=N-1+4*o,nt=b-1+4*o,rt=x-1+4*o,ot=P-1+4*o,at=255&h,lt=255&M,st=255&d,ct=255&q;let it=.6-N*N-b*b-x*x-P*P;if(it<0)m=0;else{const t=at+e[lt+e[st+e[ct]]];it*=it,m=it*it*(n[t]*N+l[t]*b+s[t]*x+f[t]*P)}let ft=.6-L*L-O*O-Q*Q-R*R;if(ft<0)w=0;else{const t=at+j+e[lt+k+e[st+v+e[ct+z]]];ft*=ft,w=ft*ft*(n[t]*L+l[t]*O+s[t]*Q+f[t]*R)}let ut=.6-V*V-W*W-X*X-Y*Y;if(ut<0)y=0;else{const t=at+B+e[lt+C+e[st+E+e[ct+G]]];ut*=ut,y=ut*ut*(n[t]*V+l[t]*W+s[t]*X+f[t]*Y)}let mt=.6-Z*Z-$*$-_*_-tt*tt;if(mt<0)A=0;else{const t=at+H+e[lt+I+e[st+J+e[ct+K]]];mt*=mt,A=mt*mt*(n[t]*Z+l[t]*$+s[t]*_+f[t]*tt)}let wt=.6-et*et-nt*nt-rt*rt-ot*ot;if(wt<0)F=0;else{const t=at+1+e[lt+1+e[st+1+e[ct+1]]];wt*=wt,F=wt*wt*(n[t]*et+l[t]*nt+s[t]*rt+f[t]*ot)}return 27*(m+w+y+A+F)}}(t)}}}

function SquareTiledSimplex2D(noise4D, tileSize = 200, noiseZoom = 1) {
    class SquareTiledSimplex2D {
        constructor(noise4D, tileSize, noiseZoom) {
            this.noise4D = noise4D;
            this.tileSize = tileSize;
            this.noiseZoom = noiseZoom
        }
        sample(x, y) {
            const alpha = Math.PI * 2 / 200 * (200 / this.tileSize) * x;
            const beta = Math.PI * 2 / 200 * (200 / this.tileSize) * y;
    
            return this.noise4D(
                Math.cos(alpha) * this.noiseZoom,
                Math.sin(alpha) * this.noiseZoom,
                Math.cos(beta) * this.noiseZoom,
                Math.sin(beta) * this.noiseZoom
            );
        }
    }
    return new SquareTiledSimplex2D(noise4D, tileSize, noiseZoom);
}

function init() {
    ///////////////////////////////////////////////////////
    // Vector functions - Created by Jurgen Westerhof 2024
    // https://turtletoy.net/turtle/d068ad6040
    ///////////////////////////////////////////////////////
    class Vector {
        static add  (a,b) { return a.map((v,i)=>v+b[i]); }
        static sub  (a,b) { return a.map((v,i)=>v-b[i]); }
        static mul  (a,b) { return a.map((v,i)=>v*b[i]); }
        static div  (a,b) { return a.map((v,i)=>v/b[i]); }
        static scale(a,s) { return a.map(v=>v*s); }
    
        static det(m)                { return m.length == 1? m[0][0]: m.length == 2 ? m[0][0]*m[1][1]-m[0][1]*m[1][0]: m[0].reduce((r,e,i) => r+(-1)**(i+2)*e*this.det(m.slice(1).map(c => c.filter((_,j) => i != j))),0); }
        static angle(a)              { return Math.PI - Math.atan2(a[1], -a[0]); } //compatible with turtletoy heading
        static rot2d(angle)          { return [[Math.cos(angle), -Math.sin(angle)], [Math.sin(angle), Math.cos(angle)]]; }
        static rot3d(yaw,pitch,roll) { return [[Math.cos(yaw)*Math.cos(pitch), Math.cos(yaw)*Math.sin(pitch)*Math.sin(roll)-Math.sin(yaw)*Math.cos(roll), Math.cos(yaw)*Math.sin(pitch)*Math.cos(roll)+Math.sin(yaw)*Math.sin(roll)],[Math.sin(yaw)*Math.cos(pitch), Math.sin(yaw)*Math.sin(pitch)*Math.sin(roll)+Math.cos(yaw)*Math.cos(roll), Math.sin(yaw)*Math.sin(pitch)*Math.cos(roll)-Math.cos(yaw)*Math.sin(roll)],[-Math.sin(pitch), Math.cos(pitch)*Math.sin(roll), Math.cos(pitch)*Math.cos(roll)]]; }
        static trans(matrix,a)       { return a.map((v,i) => a.reduce((acc, cur, ci) => acc + cur * matrix[ci][i], 0)); }
        //Mirror vector a in a ray through [0,0] with direction mirror
        static mirror2d(a,mirror)    { return [Math.atan2(...mirror)].map(angle => this.trans(this.rot2d(angle), this.mul([-1,1], this.trans(this.rot2d(-angle), a)))).pop(); }

        static equals(a,b)   { return !a.some((e, i) => e != b[i]); }
        static approx(a,b,p) { return this.len(this.sub(a,b)) < (p === undefined? .001: p); }
        static norm  (a)     { return this.scale(a,1/this.len(a)); }
        static len   (a)     { return Math.hypot(...a); }
        static lenSq (a)     { return a.reduce((a,c)=>a+c**2,0); }
        static lerp  (a,b,t) { return a.map((v, i) => v*(1-t) + b[i]*t); }
        static dist  (a,b)   { return Math.hypot(...this.sub(a,b)); }
        
        static dot  (a,b)   { return a.reduce((a,c,i) => a+c*b[i], 0); }
        static cross(...ab) { return ab[0].map((e, i) => ab.map(v => v.filter((ee, ii) => ii != i))).map((m,i) => (i%2==0?-1:1)*this.det(m)); }
        
        static clamp(a,min,max) { return a.map((e,i) => Math.min(Math.max(e, min[i]), max[i])) };
        static rotateClamp(a,min,max) { return a.map((e,i) => {
            const d = max[i]-min[i];
            if(d == 0) return min[i];
            while(e < min[i]) { e+=d; }
            while(e > max[i]) { e-=d; }
            return e;
        });
        }
    }
    this.V = Vector;
    
    class Intersection2D {
        //a-start, a-direction, b-start, b-direction
        //returns false on no intersection or [[intersection:x,y], scalar a-direction, scalar b-direction
        static info(as, ad, bs, bd) { const d = V.sub(bs, as), det = -V.det([bd, ad]); if(det === 0) return false; const res = [V.det([d, bd]) / det, V.det([d, ad]) / det]; return [V.add(as, V.scale(ad, res[0])), ...res]; }
        static ray(a, b, c, d) { return this.info(a, b, c, d); }
        static segment(a,b,c,d, inclusiveStart = true, inclusiveEnd = true) { const i = this.info(a, V.sub(b, a), c, V.sub(d, c)); return i === false? false: ( (inclusiveStart? 0<=i[1] && 0<=i[2]: 0<i[1] && 0<i[2]) && (inclusiveEnd?   i[1]<=1 && i[2]<=1: i[1]<1 && i[2]<1) )?i[0]:false;}
        static tour(tour, segmentStart, segmentDirection) { return tour.map((e, i, a) => [i, this.info(e, V.sub(a[(i+1)%a.length], e), segmentStart, segmentDirection)]).filter(e => e[1] !== false && 0 <= e[1][1] && e[1][1] <= 1).filter(e => 0 <= e[1][2]).map(e => ({position: e[1][0],tourIndex: e[0],tourSegmentPortion: e[1][1],segmentPortion: e[1][2],}));}
        static inside(tour, pt) { return tour.map((e,i,a) => this.segment(e, a[(i+1)%a.length], pt, [Number.MAX_SAFE_INTEGER, 0], true, false)).filter(e => e !== false).length % 2 == 1; }
        static circles(centerA, radiusA, centerB, radiusB) {const result = {intersect_count: 0,intersect_occurs: true,one_is_in_other: false,are_equal: false,point_1: [null, null],point_2: [null, null],};const dx = centerB[0] - centerA[0];const dy = centerB[1] - centerA[1];const dist = Math.hypot(dy, dx);if (dist > radiusA + radiusB) {result.intersect_occurs = false;}if (dist < Math.abs(radiusA - radiusB) && !N.approx(dist, Math.abs(radiusA - radiusB))) {result.intersect_occurs = false;result.one_is_in_other = true;}if (V.approx(centerA, centerB) && radiusA === radiusB) {result.are_equal = true;}if (result.intersect_occurs) {const centroid = (radiusA**2 - radiusB**2 + dist * dist) / (2.0 * dist);const x2 = centerA[0] + (dx * centroid) / dist;const y2 = centerA[1] + (dy * centroid) / dist;const prec = 10000;const h = (Math.round(radiusA**2 * prec)/prec - Math.round(centroid**2 * prec)/prec)**.5;const rx = -dy * (h / dist);const ry = dx * (h / dist);result.point_1 = [x2 + rx, y2 + ry];result.point_2 = [x2 - rx, y2 - ry];if (result.are_equal) {result.intersect_count = null;} else if (result.point_1.x === result.point_2.x && result.point_1.y === result.point_2.y) {result.intersect_count = 1;} else {result.intersect_count = 2;}}return result;}
    }
    this.Intersection = Intersection2D;
    
    class PathTools {
        static bezier(p1, cp1, cp2, p2, steps = null) {steps = (steps === null? Math.max(3, (V.len(V.sub(cp1, p1)) + V.len(V.sub(cp2, cp1)) + V.len(V.sub(p2, cp2))) | 0): steps) - 1; return Array.from({length: steps + 1}).map((v, i, a, f = i/steps) => [[V.lerp(p1, cp1, f),V.lerp(cp1, cp2, f),V.lerp(cp2, p2, f)]].map(v => V.lerp(V.lerp(v[0], v[1], f), V.lerp(v[1], v[2], f), f))[0]);}
        // https://stackoverflow.com/questions/18655135/divide-bezier-curve-into-two-equal-halves#18681336
        static splitBezier(p1, cp1, cp2, p2, t=.5) {const e = V.lerp(p1, cp1, t);const f = V.lerp(cp1, cp2, t);const g = V.lerp(cp2, p2, t);const h = V.lerp(e, f, t);const j = V.lerp(f, g, t);const k = V.lerp(h, j, t);return [[p1, e, h, k], [k, j, g, p2]];}
        static circular(radius,verticeCount,rotation=0) {return Array.from({length: verticeCount}).map((e,i,a,f=i*2*Math.PI/verticeCount+rotation) => [radius*Math.cos(f),radius*Math.sin(f)])}
        static circle(r){return this.circular(r,Math.max(12, r*2*Math.PI|0));}
        static arc(radius, extend = 2 * Math.PI, clockWiseStart = 0, steps = null, includeLast = false) { return [steps == null? (radius*extend+1)|0: steps].map(steps => Array.from({length: steps}).map((v, i, a) => [radius * Math.cos(clockWiseStart + extend*i/(a.length-(includeLast?1:0))), radius * Math.sin(clockWiseStart + extend*i/(a.length-(includeLast?1:0)))])).pop(); }
        static draw(turtle, path) {path.forEach((pt, i) => turtle[i==0?'jump':'goto'](pt));}
        static drawTour(turtle, path) {this.draw(turtle, path.concat([path[0]]));}
        static drawPoint(turtle, pt, r = .1) {this.drawTour(turtle, this.circle(r).map(e => V.add(e, pt)));}
        static drawArrow(turtle, s, d, width = 6, length = 3) {turtle.jump(s);const arrowHeadBase = V.add(s,d);turtle.goto(arrowHeadBase);turtle.goto(V.add(arrowHeadBase, V.trans(V.rot2d(-V.angle(d)), [-length, width/2])));turtle.jump(V.add(arrowHeadBase, V.trans(V.rot2d(-V.angle(d)), [-length, -width/2])));turtle.goto(arrowHeadBase);}
        static circlesTangents(c1_center, c1_radius, c2_center, c2_radius, internal = false) {let middle_circle = [V.scale(V.sub(c1_center, c2_center), .5)].map(hwp => [V.add(c2_center, hwp), V.len(hwp)]).pop();if(!internal && c1_radius == c2_radius) {let target = V.sub(c2_center, c1_center);let scaledTarget = V.scale(target, c1_radius/V.len(target));let partResult = [V.add(c1_center, V.trans(V.rot2d(Math.PI/2), scaledTarget)),V.add(c1_center, V.trans(V.rot2d(Math.PI/-2), scaledTarget))];return [partResult,partResult.map(pt => V.add(pt, target))]}let swap = !internal && c2_radius > c1_radius;if(swap) {let t = [[...c1_center], c1_radius];c1_center = c2_center;c1_radius = c2_radius;c2_center = t[0];c2_radius = t[1];}let internal_waypoints = intersectCircles2(c1_center, c1_radius + (internal?c2_radius:-c2_radius), ...middle_circle);if(internal_waypoints.length == 0) return [];const circlePointAtDirection2 = (circle_center, radius, direction) => V.add(circle_center, V.scale(direction, radius/V.len(direction)));const result = [[circlePointAtDirection2(c1_center, c1_radius, V.sub(internal_waypoints[0], c1_center)),circlePointAtDirection2(c1_center, c1_radius, V.sub(internal_waypoints[1], c1_center))],[circlePointAtDirection2(c2_center, c2_radius, internal? V.sub(c1_center, internal_waypoints[0]): V.sub(internal_waypoints[0], c1_center)),circlePointAtDirection2(c2_center, c2_radius, internal? V.sub(c1_center, internal_waypoints[1]): V.sub(internal_waypoints[1], c1_center))]];return swap? [[result[1][1],result[1][0]],[result[0][1],result[0][0]]]: result;}
    }
    
    this.PT = PathTools;
    
    class Complex {
        static add(a,b)     { return V.add(a,b); }
        static sub(a,b)     { return V.sub(a,b); }
        static scale(a,s)   { return V.scale(a,s); }
        static mult(a,b)    { return [a[0]*b[0]-a[1]*b[1],a[0]*b[1]+a[1]*b[0]]; }
        static sqrt(a)      { return [[Math.hypot(...a)**.5, Math.atan2(...a.reverse()) / 2]].map(ra => [ra[0]*Math.cos(ra[1]), ra[0]*Math.sin(ra[1])]).pop(); }
    }
    this.C = Complex;
    
    class Numbers {
        static approx(a,b,p)        { return Math.abs(a-b) < (p === undefined? .001: p); }
        static clamp(a, min, max)   { return Math.min(Math.max(a, min), max); }
        static rotateClamp(a, min, max) {
            if(min == max) return min;
            while (a < min) { a+=(max-min); }
            while (a > max) { a-=(max-min); }
            return a;
        }
    }
    this.N = Numbers;

    class Matrix {
        static bayer(order) { return [...Array(1<<order)].map((_,y,a) => { const g = (k=order,x)=>k--&&4*g(k,x)|2*(x>>k)+3*(y>>k&1)&3; return a.map(g); }); }
        static rotate(m) { return m[0].map((e, i) => m.map(r => r[i]).reverse()); }
        static rotateCCW(m) { return m[0].map((e, i) => m.map(r => r[r.length-1-i])); }
        static add(a,b) { return a.map((e, c) => e.map((e, r) => a[c][r] + b[c][r])); }
        static sub(a,b) { return a.map((e, c) => e.map((e, r) => a[c][r] - b[c][r])); }
        static multiply(a,b) { return Array.from({length: b.length}, (e,resCol) => Array.from({length: a[0].length}, (e,resRow) => b[resCol].reduce((acc, c, bRow) => acc + a[bRow][resRow] * b[resCol][bRow], 0)));}
        static scale(a,s) { return a.map((e, c) => e.map((e, r) => a[c][r] * s)); }
        static random(c,r,fillFn = Math.random) { return Array.from({length: c}, (e,i) => Array.from({length: r}, e => fillFn(c, r))); }
        static identity(d) { return Array.from({length: d}, (e,c) => Array.from({length: d}, (e, r) => c==r?1:0 )); }
        static log(m, name, logFn = console.log) { if(name != undefined) logFn(name); if(m === undefined || (typeof m == 'object' && (m[0] === undefined || m[0][0] === undefined))) { return logFn(`Failed to log matrix:`, m); } logFn(m[0].map((e,r) => m.map((e,c) => m[c][r]).join(', ')).join('\n')); }
        static invert(m) { let _A = m.map(col => col.map(cell => cell));/*clone matrix*/let temp;const N = _A.length;const E = Array.from({length: N}, (e,i) => Array.from({length: _A[0].length}, (e,j) => i==j?1:0));for (let k = 0; k < N; k++) {temp = _A[k][k];for (let j = 0; j < N; j++) {_A[k][j] /= temp;E[k][j] /= temp;}for (let i = k + 1; i < N; i++) {temp = _A[i][k];for (let j = 0; j < N; j++) {_A[i][j] -= _A[k][j] * temp;E[i][j] -= E[k][j] * temp;}}}for (let k = N - 1; k > 0; k--) {for (let i = k - 1; i >= 0; i--) {temp = _A[i][k];for (let j = 0; j < N; j++) {_A[i][j] -= _A[k][j] * temp;E[i][j] -= E[k][j] * temp;}}}return E; }
        static determinant(m) { return m.length == 1 ?m[0][0] :m.length == 2 ? m[0][0]*m[1][1]-m[0][1]*m[1][0] :m[0].reduce((r,e,i) => r+(-1)**(i+2)*e*this.determinant(m.slice(1).map(c => c.filter((_,j) => i != j))), 0)}
        static flip(m) { return Array.from({length: m[0].length}, (_, r) => Array.from({length: m.length}, (e, c) => m[c][r])); }
        static sum(m) { return m.reduce((a, c) => a + c.reduce((aa, cc) => aa + cc, 0), 0); }
    }
    this.M = Matrix;
    
    class Algorithms {
        static nthTriangular(n) { return ((n * n) + n) / 2; }
    }
    this.A = Algorithms;
}