// Forked from "Delegated deferred polygons 🔺" by Jurgen
// https://turtletoy.net/turtle/d1095a7e5d

// Forked from "Polygon hatching" by reinder
// https://turtletoy.net/turtle/92ebe08d89

// Polygon delegated hatching and deferred drawing. Created by Jurgen Westerhof 2024
// 
// https://turtletoy.net/turtle/d1095a7e5d
//
// Original:
//
// Polygon hatching. Created by Reinder Nijhoff 2018
// @reindernijhoff
//
// https://turtletoy.net/turtle/92ebe08d89
//
// You can find the Turtle API reference here: https://turtletoy.net/syntax

const gridSize = 21; //min=1 max=50 step=1
const projectionMargin = 0; //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(.6);

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
);

// Global code will be evaluated once.
loadHatcheryNamespace();
//const turtle = new Turtle();
const polygons = new Polygons();
polygons.startDeferSession();

const hatchings = Array.from({length: 3}).map((e,i) => new LineHatching((i-1/3)*Math.PI/2, .3+i*.5, .3));

function walk(i) {
    const s = 25;
    const sp = 12.5;

    // first an invisible cube is added to the clip list.
    //if (i ==0) drawCube((3-8/2)*(s+sp),2*s-(s+sp)*(-8+9)/Math.sqrt(1.25),s,0,false);
    
    if (i < 4)  drawCube((i-1.5)*(s+sp),2*s,s);
    else if (i < 7)  drawCube((3-i/2)*(s+sp),2*s-(s+sp)*(i-3)/Math.sqrt(1.25),s);
    else if (i < 9)  drawCube((3-i/2)*(s+sp),2*s-(s+sp)*(-i+9)/Math.sqrt(1.25),s);//,9);
    
    if(i == 2) {
        polygons.stopDeferring();
    } else if(i == 9) {
        polygons.finalizeDeferSession(turtle);
    }
    return i < 9;
}

function drawCube(x,y,r) { //,skip=0,draw=true) {
    const p = [[x,y]];
    for (let i=0; i<6; i++) {
        p.push([Math.cos(i*Math.PI/3)*r+x, Math.sin(i*Math.PI/3)*r+y]);
    }
    // create 3 visible polygons for cube
    const ps = [];
    for (let i=0; i<3; i++) {
        const c = polygons.create();
        c.addPoints(p[0],p[i*2+1],p[i*2+2],p[(i*2+3)%6]);
        c.addOutline();
        c.addHatching(hatchings[i]);
        polygons.draw(turtle, c);
    }
}

///////////////////////////////////////////////////////////////////
// This is only the part of the Polygon Hatching utility code
// required in this turtle. For the full hatchery code see
// https://turtletoy.net/turtle/d068ad6040
//
///////////////////////////////////////////////////////////////////
// Polygon Hatching utility code - Created by Jurgen Westerhof 2024
// https://turtletoy.net/turtle/d068ad6040
// ////////////////////////////////////////////////////////////////
// // To be used with modified Polygon Clipping utility code
// //            Orginal: https://turtletoy.net/turtle/a5befa1f8d
// //    Polygon binning: https://turtletoy.net/turtle/95f33bd383
// // Delegated Hatching: https://turtletoy.net/turtle/d068ad6040
///////////////////////////////////////////////////////////////////
function loadHatcheryNamespace() {
    //for convenience on Turtletoy you can click the arrow to the right of the line number to collapse a class
    //////////////////////////////////////////////////// root
    class PolygonHatching {
        constructor() {
            if (this.constructor === PolygonHatching) {
                throw new Error("PolygonHatching is an abstract class and can't be instantiated.");
            }
            
            this.minX = -100;
            this.minY = -100;
            this.maxX = 100;
            this.maxY = 100;
            this.width = 200;
            this.height = 200;
            
            this.segments = [];
            
            this.init();
        }
        hatch(polygonsClass, thePolygonToHatch) {
            const e = new polygonsClass;
            e.cp.push(...thePolygonToHatch.aabb);//[-1e5,-1e5],[1e5,-1e5],[1e5,1e5],[-1e5,1e5]);
            
            this.addHatchSegments(e.dp);
            
            e.boolean(thePolygonToHatch,!1);
            thePolygonToHatch.dp=[...thePolygonToHatch.dp,...e.dp]
        }
        addHatchSegments(segments) {
            this.getSegments().forEach(e => segments.push(e));
        }
        getSegments() { return this.segments; }
        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 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)); }
            }
            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;
                }
            }
            this.Intersection = Intersection2D;
        }
    }
    this.PolygonHatching = PolygonHatching;
    class LineHatching extends PolygonHatching {
        constructor(angle, distance, inp = 0) {
            super();
            
            const h=Math.sin(angle)*distance,o=Math.cos(angle)*distance,a=200*Math.sin(angle),i=200*Math.cos(angle);
            this.segments = Array.from({length: 150/distance}).flatMap((x,y,z,t=.5+y) => [
                [h*t+i+inp*(Math.random()-.5),o*t-a+inp*(Math.random()-.5)],[h*t-i+inp*(Math.random()-.5),o*t+a+inp*(Math.random()-.5)], [-h*t+i+inp*(Math.random()-.5),-o*t-a+inp*(Math.random()-.5)],[-h*t-i+inp*(Math.random()-.5),-o*t+a+inp*(Math.random()-.5)]
            ])
        }
    }
    this.LineHatching = LineHatching;
}

////////////////////////////////////////////////////////////////
// Polygon Clipping utility code - Created by Reinder Nijhoff 2019
// (Polygon binning by Lionel Lemarie 2021) https://turtletoy.net/turtle/95f33bd383
// (Delegated Hatching by Jurgen Westerhof 2024) https://turtletoy.net/turtle/d068ad6040
// (Deferred Polygon Drawing by Jurgen Westerhof 2024) https://turtletoy.net/turtle/6f3d2bc0b5
// https://turtletoy.net/turtle/a5befa1f8d
//
// const polygons = new Polygons();
// const p = polygons.create();
// polygons.draw(turtle, p);
// polygons.list();
// polygons.startDeferSession();
// polygons.stopDeferring();
// polygons.finalizeDeferSession(turtle);
//
// p.addPoints(...[[x,y],]);
// p.addSegments(...[[x,y],]);
// p.addOutline();
// p.addHatching(angle, distance); OR p.addHatching(HatchObject); where HatchObject has a method 'hatch(PolygonClass, thisPolygonInstance)'
// p.inside([x,y]);
// p.boolean(polygon, diff = true);
// p.segment_intersect([x,y], [x,y], [x,y], [x,y]);
////////////////////////////////////////////////////////////////
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) {if(typeof t == 'object') return t.hatch(n, this);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])]}};const y=function(n,j=[]){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]||j.includes(s)||(h[s]=1)})}}return Array.from(Object.keys(h),s=>t[s])};return{list:()=>t,create:()=>new n,draw:(n,h,o=!0)=>{rpl=y(h.aabb, this.dei === undefined? []: Array.from({length: t.length - this.dei}).map((e, i) => this.dsi + i));for(let t=0;t<rpl.length&&h.boolean(rpl[t]);t++);const td=n.isdown();if(this.dsi!==undefined&&this.dei===undefined)n.pu();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);if(td)n.pd();},startDeferSession:()=>{if(this.dei!==undefined)throw new Error('Finalize deferring before starting new session');this.dsi=t.length;},stopDeferring:()=>{if(this.dsi === undefined)throw new Error('Start deferring before stopping');this.dei=t.length;},finalizeDeferSession:(n)=>{if(this.dei===undefined)throw new Error('Stop deferring before finalizing');for(let i=this.dsi;i<this.dei;i++) {rpl = y(t[i].aabb,Array.from({length:this.dei-this.dsi+1}).map((e,j)=>i+j));for(let j=0;j<rpl.length&&t[i].boolean(rpl[j]);j++);t[i].draw(n);}this.dsi=undefined;this.dei=undefined;}}}


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