// Forked from "Triskelion 🌀" by Jurgen
// https://turtletoy.net/turtle/e994e50d7a

const rIncPerRev = 13; //min=2 max=50 step=1
const rMin = 30; //min=5 max=50 step=1
const outline = 1; //min=0 max=1 step=1 (No, Yes)
const hatching = 2; //min=0 max=2 step=.1

const gridSize = 20; //min=1 max=50 step=1
const projectionMargin = .6; //min=0 max=10 step=.1
const segmentCapture = .16; // min=.01 max=1 step=.01
const captureWidth = 200; //min=10 max=200 step=1
// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(1);

const GRID = { TOP: 1, RIGHT: 2, BOTTOM: 4, LEFT: 8 };

// Global code will be evaluated once.
turtlelib_init();
const turtle = new ObservableTurtle();
const sls = FlyEyeFactory(
    turtle,
    gridSize,// gridSize,
    [projectionMargin-100, projectionMargin-100], //gridTopLeft,
    [100-projectionMargin, 100-projectionMargin], //gridBottomRight,
    projectionMargin, //gridMargin,
    [-captureWidth/2, -captureWidth/2], //sampleTopLeft,
    [captureWidth/2, captureWidth/2], //sampleBottomRight,
    segmentCapture//sampleTileSizeFraction
);
const polygons = new Polygons();

const add2 = (a, b) => [a[0]+b[0],a[1]+b[1]];
const sub2 = (a, b) => [a[0]-b[0],a[1]-b[1]];
const lenSq2 = (a) => a[0]**2+a[1]**2;
const len2 = (a) => lenSq2(a)**.5;
const rot2 = (a) => [Math.cos(a), -Math.sin(a), Math.sin(a), Math.cos(a)];
const trans2 = (m, a) => [m[0]*a[0]+m[2]*a[1], m[1]*a[0]+m[3]*a[1]];

const spiralPts = spiral(rIncPerRev, rMin, Math.PI, Math.PI/3);
const startR = spiralPts[0][0];
const endR = len2(spiralPts[spiralPts.length - 1]);
const width  = startR + endR;
const height = (width**2 - (width/2)**2)**.5;

const splitPts = Array.from({length: 3}).map((v, t) => spiralPts.map(p => trans2(rot2(t*4*Math.PI/3), p)).map(p => add2(trans2(rot2(t*4*Math.PI/3), [-width/2, height/3]), p)));
const rot = splitPts.map(s => s.reduce((prev, cur) => prev[1] > cur[1]? prev: cur), [0,-100])
                    .sort((a,b) => a[1] > b[1]? -1: 1)
                    .filter((v, i) => i < 2)
                    .sort((a,b) => a[0] < b[0]? -1: 1)
                    .reduce((prev, cur) => prev == null? cur: sub2(cur, prev), null)
                    .reduce((prev, cur) => prev == null? cur: rot2(Math.atan(cur/prev)), null);
const pts = splitPts.flatMap(s => s).map(pt => trans2(rot, pt));
const centerOffset = pts.reduce((p, c) => [[Math.min(p[0][0], c[0]), Math.max(p[0][1], c[0])], [Math.min(p[1][0], c[1]), Math.max(p[1][1], c[1])]], [[0,0],[0,0]]).map(i => (-i[0]-i[1])/2);
const polygonize = () => {
    const p = polygons.create();
    p.addPoints(...pts.map(pt => add2(centerOffset, pt)));
    p.addHatching(1, hatching);
    polygons.draw(turtle, p);
}
if(hatching > 0) polygonize();

const walk = (i) => outline === 0? false: turtle[i==0?'jump':'goto'](add2(centerOffset, pts.shift())) || pts.length > 0;

function spiral(rIncreasePerRev, rMin, angleOne, angleTwo) {
    const result = [];
    const res = 100; //resolution
    
    const phaseOneMax = 2 * Math.PI * Math.ceil(rMin / rIncreasePerRev) + angleOne;
    const phaseTwoMax = 2 * Math.PI * Math.ceil(rMin / rIncreasePerRev) + angleTwo;
    let phase = 0;
    let i = 0;
    while(phase < phaseOneMax || phase < phaseTwoMax) {
        phase = 2 * Math.PI * i / res;
        const r = rIncreasePerRev * i / res;
        if(phase < phaseOneMax) result.unshift([r * -Math.cos(phase), r * Math.sin(phase)]);
        if(phase < phaseTwoMax) result.push([r * Math.cos(phase), r * -Math.sin(phase)]);
        i++;
    }
    result.unshift([(phaseOneMax / (2*Math.PI)) * rIncreasePerRev * -Math.cos(phaseOneMax), (phaseOneMax / (2*Math.PI)) * rIncreasePerRev * Math.sin(phaseOneMax)]);
    result.push([(phaseTwoMax / (2*Math.PI)) * rIncreasePerRev * Math.cos(phaseTwoMax), (phaseTwoMax / (2*Math.PI)) * rIncreasePerRev * -Math.sin(phaseTwoMax)]);
    return result;
}

////////////////////////////////////////////////////////////////
// Polygon Clipping utility code - Created by Reinder Nijhoff 2019
// (Polygon binning by Lionel Lemarie 2021)
// https://turtletoy.net/turtle/a5befa1f8d
////////////////////////////////////////////////////////////////
function Polygons(){const t=[],s=25,e=Array.from({length:s**2},t=>[]),n=class{constructor(){this.cp=[],this.dp=[],this.aabb=[]}addPoints(...t){let s=1e5,e=-1e5,n=1e5,h=-1e5;(this.cp=[...this.cp,...t]).forEach(t=>{s=Math.min(s,t[0]),e=Math.max(e,t[0]),n=Math.min(n,t[1]),h=Math.max(h,t[1])}),this.aabb=[s,n,e,h]}addSegments(...t){t.forEach(t=>this.dp.push(t))}addOutline(){for(let t=0,s=this.cp.length;t<s;t++)this.dp.push(this.cp[t],this.cp[(t+1)%s])}draw(t){for(let s=0,e=this.dp.length;s<e;s+=2)t.jump(this.dp[s]),t.goto(this.dp[s+1])}addHatching(t,s){const e=new n;e.cp.push([-1e5,-1e5],[1e5,-1e5],[1e5,1e5],[-1e5,1e5]);const h=Math.sin(t)*s,o=Math.cos(t)*s,a=200*Math.sin(t),i=200*Math.cos(t);for(let t=.5;t<150/s;t++)e.dp.push([h*t+i,o*t-a],[h*t-i,o*t+a]),e.dp.push([-h*t+i,-o*t-a],[-h*t-i,-o*t+a]);e.boolean(this,!1),this.dp=[...this.dp,...e.dp]}inside(t){let s=0;for(let e=0,n=this.cp.length;e<n;e++)this.segment_intersect(t,[.1,-1e3],this.cp[e],this.cp[(e+1)%n])&&s++;return 1&s}boolean(t,s=!0){const e=[];for(let n=0,h=this.dp.length;n<h;n+=2){const h=this.dp[n],o=this.dp[n+1],a=[];for(let s=0,e=t.cp.length;s<e;s++){const n=this.segment_intersect(h,o,t.cp[s],t.cp[(s+1)%e]);!1!==n&&a.push(n)}if(0===a.length)s===!t.inside(h)&&e.push(h,o);else{a.push(h,o);const n=o[0]-h[0],i=o[1]-h[1];a.sort((t,s)=>(t[0]-h[0])*n+(t[1]-h[1])*i-(s[0]-h[0])*n-(s[1]-h[1])*i);for(let n=0;n<a.length-1;n++)(a[n][0]-a[n+1][0])**2+(a[n][1]-a[n+1][1])**2>=.001&&s===!t.inside([(a[n][0]+a[n+1][0])/2,(a[n][1]+a[n+1][1])/2])&&e.push(a[n],a[n+1])}}return(this.dp=e).length>0}segment_intersect(t,s,e,n){const h=(n[1]-e[1])*(s[0]-t[0])-(n[0]-e[0])*(s[1]-t[1]);if(0===h)return!1;const o=((n[0]-e[0])*(t[1]-e[1])-(n[1]-e[1])*(t[0]-e[0]))/h,a=((s[0]-t[0])*(t[1]-e[1])-(s[1]-t[1])*(t[0]-e[0]))/h;return o>=0&&o<=1&&a>=0&&a<=1&&[t[0]+o*(s[0]-t[0]),t[1]+o*(s[1]-t[1])]}};return{list:()=>t,create:()=>new n,draw:(n,h,o=!0)=>{reducedPolygonList=function(n){const h={},o=200/s;for(var a=0;a<s;a++){const c=a*o-100,r=[0,c,200,c+o];if(!(n[3]<r[1]||n[1]>r[3]))for(var i=0;i<s;i++){const c=i*o-100;r[0]=c,r[2]=c+o,n[0]>r[2]||n[2]<r[0]||e[i+a*s].forEach(s=>{const e=t[s];n[3]<e.aabb[1]||n[1]>e.aabb[3]||n[0]>e.aabb[2]||n[2]<e.aabb[0]||(h[s]=1)})}}return Array.from(Object.keys(h),s=>t[s])}(h.aabb);for(let t=0;t<reducedPolygonList.length&&h.boolean(reducedPolygonList[t]);t++);h.draw(n),o&&function(n){t.push(n);const h=t.length-1,o=200/s;e.forEach((t,e)=>{const a=e%s*o-100,i=(e/s|0)*o-100,c=[a,i,a+o,i+o];c[3]<n.aabb[1]||c[1]>n.aabb[3]||c[0]>n.aabb[2]||c[2]<n.aabb[0]||t.push(h)})}(h)}}}


function FlyEyeFactory(turtle, gridSize, gridTopLeft, gridBottomRight, gridMargin, sampleTopLeft, sampleBottomRight, sampleTileSizeFraction) {
    const sampleWidth = sampleBottomRight[0] - sampleTopLeft[0];
    const sampleHeight = sampleBottomRight[1] - sampleTopLeft[1];
    
    const tileWidth = sampleWidth * sampleTileSizeFraction;
    const tileHeight = sampleHeight * sampleTileSizeFraction;
    
    const sampleCenterTopLeft = V.add(sampleTopLeft, [tileWidth/2, tileHeight/2]);
    const columnIncrement = gridSize == 1? 0: (sampleWidth - tileWidth) / (gridSize - 1);
    const rowIncrement = gridSize == 1? 0: (sampleHeight - tileHeight) / (gridSize - 1);
    
    const gridWidth = gridBottomRight[0] - gridTopLeft[0];
    const gridHeight = gridBottomRight[1] - gridTopLeft[1];
    
    const gridTileWidth = (gridWidth - gridMargin * Math.max(1, gridSize - 1)) / gridSize;
    const gridTileHeight = (gridHeight - gridMargin * Math.max(1, gridSize - 1)) / gridSize;

    const flyEyeSegments = [];
    for(let c = 0; c < gridSize; c++) {
        for(let r = 0; r < gridSize; r++) {
            flyEyeSegments.push(
                new SquareLens(
                    turtle, [
                        V.add(sampleTopLeft, [columnIncrement * c, rowIncrement * r]),
                        V.add(
                            V.add(sampleTopLeft, [columnIncrement * c, rowIncrement * r]),
                            [tileWidth, tileHeight]
                        )
                    ], [
                        V.add(gridTopLeft, [c * (gridTileWidth + gridMargin), r * (gridTileHeight + gridMargin)]),
                        V.add(
                            V.add(gridTopLeft, [c * (gridTileWidth + gridMargin), r * (gridTileHeight + gridMargin)]),
                            [gridTileWidth, gridTileHeight]
                        )
                    ],
                    (c == 0? GRID.LEFT: 0) | (r == 0? GRID.TOP: 0) |
                    (c == gridSize - 1? GRID.RIGHT: 0) | (r == gridSize - 1? GRID.BOTTOM: 0)
                )
            );
        }
    }
    return flyEyeSegments;
}

function ObservableTurtle(x, y) {
    class ObservableTurtle extends Turtle {
        constructor(x, y) {
            super(x, y);
            this.observers = [];
        }
        goto(x, y) {
            const isDown = this.isdown();
            const from = this.pos();
            this.up();
            super.goto(x, y);
            if(isDown) {
                this.notifyObservers(from, this.pos());
                this.down();
            }
        }
        registerObserver(o) {
            return this.observers.push(o) - 1;
        }
        notifyObservers(...data) {
            this.observers.forEach(o => o.update(...data))
        }
    }
    return new ObservableTurtle(x, y);
}


function SquareLens(turtleToObserve, lookAt, projectTo, edge = 0, projector = null) {
    class SquareLens {
        constructor(turtleToObserve, lookAt, projectTo, bottomOrRight, projector) {
            this.turtleToObserve = turtleToObserve;
            this.turtleToObserve.registerObserver(this);
            this.edge = edge;
            this.projector = projector == null? new Turtle(): projector;

            this.lookAt = lookAt;
            this.projectTo = projectTo;

            this.midLookAt = V.add(this.lookAt[0], V.scale(V.sub(...this.lookAt.map(l => l).reverse()), .5));
            this.midProjectTo = V.add(this.projectTo[0], V.scale(V.sub(...this.projectTo.map(l => l).reverse()), .5));
            
            this.lookAtBox = [[0, 0], [1, 0], [1, 1], [0, 1]].map(e => e.map((w, i) => this.lookAt[e[i]][i]));
            this.lookAtBoxEdges = this.lookAtBox.map((e, i, a) => [e, V.sub(a[(i+1)%a.length], e)]);

            this.ratios = lookAt[0].map((e, i, a) => (projectTo[1][i] - projectTo[0][i])/(lookAt[1][i] - lookAt[0][i]));
        }
        update(...data) {
            let from = data[0];
            let to = data[1];

            const intersections = this.lookAtBoxEdges.map(edge => Intersection.info(...edge, data[0], V.sub(to, from))).filter(int => int !== false && (0 <= int[1] && int[1] < 1 && 0 <= int[2] && int[2] <= 1));
            const insiders = data.map(pt => Intersection.inside(this.lookAtBox, pt));

            const collinear = (() => {
            //check if segment from-to overlaps with border (collinear)
                if(from[0] == to[0]) { //vertical line
                    //make the line go bottom
                    let fromY = Math.min(from[1], to[1]);
                    let toY = Math.max(from[1], to[1]);
                    if(fromY < this.lookAt[0][1] && toY < this.lookAt[0][1] ||
                       fromY > this.lookAt[1][1] && toY > this.lookAt[1][1]) {
                        return false;
                    }
                    if(from[0] != this.lookAt[0][0] && from[0] != this.lookAt[1][0]) {
                        return false;
                    }
                    if(from[0] == this.lookAt[1][0] &&//right lookat
                        (this.edge & GRID.RIGHT) == 0) { //if it's not the right lens
                            return false; //skip collinear
                    }

                    if(fromY <= this.lookAt[0][1]) {
                        from = [from[0], this.lookAt[0][1]];
                    }
                    if(lookAt[1][1] <= toY) {
                        to = [from[0], this.lookAt[1][1]];
                    }
                    return true;
                } else if (from[1] == to[1]) { //horizontal line
                    //make the line go right
                    let fromX = Math.min(from[0], to[0]);
                    let toX = Math.max(from[0], to[0]);
                    if(fromX < this.lookAt[0][0] && toX < this.lookAt[0][0] ||
                       fromX > this.lookAt[1][0] && toX > this.lookAt[1][0]) {
                        return false;
                    }
                    if(from[1] != this.lookAt[0][1] && from[1] != this.lookAt[1][1]) {
                        return false;
                    }
                    if(from[1] == this.lookAt[1][1] &&//bottom lookat
                        (this.edge & GRID.BOTTOM) == 0) { //if it's not the bottom lens
                            return false; //skip collinear
                    }

                    if(fromX <= this.lookAt[0][0]) {
                        from = [this.lookAt[0][0], from[1]];
                    }
                    if(lookAt[1][0] <= toX) {
                        to = [this.lookAt[1][0], from[1]];
                    }
                    return true;
                }
                return false;
            })();
            
            if(!collinear && !insiders.every(i => i)) { //if not both inside
                if(intersections.length == 0) { //and not intersections
                    return; //bail
                }
                
                intersections.sort((a, b) => a[2] < b[2]? -1: 1);
                if(insiders.every(i => !i)) { //both outside
                    from = intersections[0][0];
                    to = intersections[intersections.length - 1][0];
                } else { //one inside
                    if(insiders[0]) {
                        to = intersections[intersections.length - 1][0];
                    } else {
                        from = intersections[0][0];
                    }
                }
            }
            
            this.projector.jump(V.add(V.mul(V.sub(from, this.midLookAt), this.ratios), this.midProjectTo));
            this.projector.goto(V.add(V.mul(V.sub(to, this.midLookAt), this.ratios), this.midProjectTo));
        }
    }
    return new SquareLens(turtleToObserve, lookAt, projectTo, edge, projector);
}

// Below is automatically maintained by Turtlelib 1.0
// Changes below this comment might interfere with its correct functioning.
function turtlelib_init() {
	turtlelib_ns_c6665b0e9b_Jurgen_Vector_Math();
	turtlelib_ns_c5f8fa95ed_Jurgen_Intersection();
}
// Turtlelib Jurgen Vector Math v 4 - start - {"id":"c6665b0e9b","package":"Jurgen","name":"Vector Math","version":"4"}
function turtlelib_ns_c6665b0e9b_Jurgen_Vector_Math() {
/////////////////////////////////////////////////////////
// Vector functions - Created by Jurgen Westerhof 2024 //
/////////////////////////////////////////////////////////
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;
}
// Turtlelib Jurgen Vector Math v 4 - end
// Turtlelib Jurgen Intersection v 4 - start - {"id":"c5f8fa95ed","package":"Jurgen","name":"Intersection","version":"4"}
function turtlelib_ns_c5f8fa95ed_Jurgen_Intersection() {
///////////////////////////////////////////////////////////////
// Intersection functions - Created by Jurgen Westerhof 2024 //
///////////////////////////////////////////////////////////////
class Intersection {
    //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 = Infinity;} else if (V.equals(result.point_1, result.point_2)) {result.intersect_count = 1;} else {result.intersect_count = 2;}}return result;}
}
this.Intersection = Intersection;
}
// Turtlelib Jurgen Intersection v 4 - end