const petals = 30; //min=1 max=50 step=1
const innerRadius = 20; //min=2 max=30 step=.5
const outerRadius = 2; //min=2 max=30 step=.5
const petalInnerLength = 15; //min=0 max=30 step=.5
const petalOffset = 50; //min=0 max=50 step=.5
const coreRadius = 50; //min=0 max=50 step=.5
const hatchDistance = 2; //min=.3 max=4 step=.1

const petalLength = petalInnerLength + outerRadius + innerRadius;

// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(1);

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

const petalPath = getPetalPath(innerRadius, outerRadius, petalLength);

// The walk function will be called until it returns false.
function walk(i) {
    if(i == 0) {
        const p = polygons.create();
        p.addPoints(...Array.from({length: (coreRadius * 2 * Math.PI) | 0}).map((e, i, a, f = i * 2 * Math.PI / a.length) => [coreRadius * Math.sin(f),coreRadius * Math.cos(f)]));
        p.addOutline();
        p.addHatching(1, hatchDistance/2);
        p.addHatching(-1, hatchDistance/2);
        polygons.draw(turtle, p);

        polygons.startDeferSession();
    }
    const angle = i * 2 * Math.PI / petals;
    const rot = V.rot2d(angle);

    if(i == (petals / 2 | 0)) polygons.stopDeferring();
    
    const p = polygons.create();
    p.addPoints(...petalPath.map(pt => V.trans(rot, V.add(pt, [petalOffset, 0]))));
    p.addOutline();
    p.addHatching(angle + Math.PI / 2 + .5, hatchDistance)
    polygons.draw(turtle, p);

    if(i < petals - 1) {
        return true;
    }
    
    polygons.finalizeDeferSession(turtle);
    return false;
}

function getPetalPath(cr, or, l) {
    const center = [[0,0], cr];
    const end = [[l, 0], or];
    const tps = getCirclesTangentPoints(...center, ...end);
    const startAngle = V.angle(tps[0][1]);
    const range = V.angle(tps[0][0]) - startAngle;
    
    const startAngle2 = V.angle(V.sub(tps[1][0], end[0]));
    const range2 = (V.angle(V.sub(tps[1][1], end[0])) + 2*Math.PI) - startAngle2;
    return Array.from({length: range * center[1] | 0}).map((e,i,a,f=i*range/(a.length - 1)) => { return [
        center[1] * Math.cos(startAngle + f),
        center[1] * Math.sin(startAngle + f)
    ]}).concat(
        Array.from({length: range2 * end[1] | 0}).map((e,i,a,f=i*range2/(a.length - 1)) => { return V.add(end[0], [
            end[1] * Math.cos(startAngle2 + f),
            end[1] * Math.sin(startAngle2 + f)
        ])})
    );
}

////////////////////////////////////////////////////////////////
// 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;}}}





////// Some math code that's beside the point of this turtle:
function getCirclesTangentPoints(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 [];
    
    let result = [
        [ // circle 1, point 1 and 2
            circlePointAtDirection2(c1_center, c1_radius, V.sub(internal_waypoints[0], c1_center)),
            circlePointAtDirection2(c1_center, c1_radius, V.sub(internal_waypoints[1], c1_center))
        ],
        [ // circle 2, point 1 and 2
            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;
}
function intersectCircles2(p1, r1, p2, r2) {
    let d = ((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)**.5;
    if (!(Math.abs(r1 - r2) <= d && d <= r1 + r2)) {
        return []; // no intersection, to far apart or total overlap
    }
    
    const calc = (left, right) => [[(left[0] + right[0]) / 2 + (r1**2 - r2**2) * (right[0] - left[0]) / (2 * d**2), (2 * (r1**2 + r2**2) / d**2 - ((r1**2 - r2**2)**2) / d**4 - 1)**.5 * (right[1] - left[1]) / 2]].map(t => [t[0] + t[1], t[0] - t[1]]).pop();
    
    let xs = calc(p1, p2);
    let ys = calc([...p1].reverse(), [...p2].reverse()).reverse();
    
    return [[xs[0], ys[0]], [xs[1], ys[1]]];
}
function circlePointAtDirection2(circle_center, radius, direction) { return V.add(circle_center, V.scale(direction, radius/V.len(direction))); }


////////////////////////////////////////////////////////////////
// Vector Math utility code. Created by Jurgen Westerhof 2024
// https://turtletoy.net/turtle/a424302aa8
////////////////////////////////////////////////////////////////
function init() {
    class V {
        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 = V;
}