const dim = 30; //min=2 max=150 step=1 The number of smaller cubes in x, y and z direction that build the bigger cube.
const outlines = 1; //min=0 max=1 step=1 (No, Yes) Show outlines of all small cube. Or not.
const hatching = 1;//min=0 max=1 step=1 (No, Yes) Hatch all small cubes. Or not.
const zoom = 1; //min=.1 max=3 step=.01 Well this ehm... zooms
const chopLimits = 0; //min=0 max=1 step=1 (No, Yes) Hide small cubes on planes x=y=z=dim but cubes they would have hidden from camera are also hidden. Or not.
const inclSphere = 1; //min=0 max=1 step=1 (No, Yes) Include the small floating sphere. Or not.
const sphereR = .43; //min=.1 max=.8 step=.01 The relative radius of that floating sphere.
const inclCutoutSphere = 1; //min=0 max=1 step=1 (No, Yes) Include a cutout of a bigger sphere. Or not.
const cutoutR = 1; //min=.1 max=2 step=.01 The relative radius of that cutout sphere.
const fillCubeTo = 0; //min=0 max=1 step=.01 Like filling the cube with water.

// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(.7);

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

const sub3 = (a, b) => [a[0]-b[0],a[1]-b[1],a[2]-b[2]];
const size = 90;

const getColumnRowAndDistSq = (cubeCoord) => [cubeCoord[1]-cubeCoord[0], (cubeCoord[0]+cubeCoord[1])/2 - cubeCoord[2], cubeCoord.reduce((a,c) => a+c**2, 0)];

const bds = [[0, 0, dim-1], [0, dim-1, dim-1], [0, 0, dim-1], [dim-1, dim-1, 0], [dim-1, 0, 0], [dim-1, 0, dim-1]].map(v => getColumnRowAndDistSq(v)).reduce((a, c) => [
    [Math.min(a[0][0], c[0]), Math.max(a[0][1], c[0])],
    [Math.min(a[1][0], c[1]), Math.max(a[1][1], c[1])]
], [[Number.MAX_SAFE_INTEGER, Number.MIN_SAFE_INTEGER], [Number.MAX_SAFE_INTEGER, Number.MIN_SAFE_INTEGER]]);

const ttd = [];
const [c, r] = [bds[0][0], bds[1][0] * 2];
for(let x = 0; x < dim; x++) {
    for(let y = 0; y < dim; y++) {
        for(let z = 0; z < dim; z++) {
            const v = [x, y, z, ...getColumnRowAndDistSq([x, y, z])];
            
            if(!(
                (
                    v[2] < dim * fillCubeTo
                ) || (
                    inclSphere == 1 &&
                    sub3(Array.from({length: 3}).map(v => dim / 2), v).reduce((a, c) => a+c**2, 0) < (dim * sphereR)**2 //insert ball in center
                ) || (
                    inclCutoutSphere == 1 &&
                    sub3(Array.from({length: 3}).map(v => dim), v).reduce((a, c) => a+c**2, 0) > (dim * cutoutR)**2 //insert outer ball
                )
            )) {
                continue;
            }
            if(ttd[v[3] - c] === undefined) {
                ttd[v[3] - c] = [];
            }
            if(ttd[v[3] - c][v[4] * 2 - r] === undefined) {
                ttd[v[3] - c][v[4] * 2 - r] = v;
                continue;
            }
            if(ttd[v[3] - c][v[4] * 2 - r][5] < v[5]) {
                ttd[v[3] - c][v[4] * 2 - r] = v;
            }
        }
    }
}

const thingsToDraw = ttd.flatMap(v => v)
                        .filter(v => 
                            chopLimits == 0 || (
                                v[0] != dim - 1 &&
                                v[1] != dim - 1 &&
                                v[2] != dim - 1
                            )
                        )
                        .sort((a,b) => 
                            a[5] < b[5]? -1:
                            a[5] == b[5]? (a[2] < b[2]? -1: 1):
                            1
                        );

const SQRT3 = 3**.5;
const to = {
    up: [0, -size], //up
    righttop: [size*SQRT3/2, -size/2], //righttop
    rightbottom: [size*SQRT3/2, size/2], //rightbottom
    down: [0, size], //down
    leftbottom: [-size*SQRT3/2, size/2], //leftbottom
    lefttop: [-size*SQRT3/2, -size/2] //lefttop
}

const unitTo = [];
for(let v in to) {
    unitTo[v] = scale2(to[v], 1/dim);
}


function drawCube(turtle, cell) {
    const position = mul2([cell[3], cell[4]], [unitTo.righttop[0], unitTo.down[1]]);
    [
        [unitTo.lefttop, unitTo.righttop, [1,.7]],
        [unitTo.righttop, unitTo.down, [1,.3]],
        [unitTo.lefttop, unitTo.down, [1,.5]]
    ].forEach(v => {
        const p = polygons.create();
        p.addPoints(...[[0,0], v[0], add2(v[0], v[1]), v[1]]
            .map(v => add2(v, position))
            .map(v => scale2(v, zoom))
        );
        if(hatching == 1) p.addHatching(...v[2]);
        if(outlines == 1) p.addOutline();
        polygons.draw(turtle, p);
    });
}

// The walk function will be called until it returns false.
function walk(i) {
    if(thingsToDraw.length == 0) return false;
    drawCube(turtle, thingsToDraw.pop());
    return true;
}

/// Below is the standard lib I just copy paste under almost all my turtles

function approx1(a,b,delta=0.0001) { return -delta < a-b && a-b < delta }

////////////////////////////////////////////////////////////////
// 2D Vector Math utility code - Created by several Turtletoy users
////////////////////////////////////////////////////////////////
function norm2(a) { return scale2(a, 1/len2(a)); }
function add2(a, b) { return [a[0]+b[0], a[1]+b[1]]; }
function sub2(a, b) { return [a[0]-b[0], a[1]-b[1]]; }
function mul2(a, b) { return [a[0]*b[0], a[1]*b[1]]; }
function scale2(a, s) { return [a[0]*s,a[1]*s]; }
function lerp2(a,b,t) { return [a[0]*(1-t) + b[0]*t, a[1]*(1-t) + b[1]*t]; }
function lenSq2(a) { return a[0]**2+a[1]**2; }
function len2(a) { return Math.sqrt(lenSq2(a)); }
function rot2(a) { return [Math.cos(a), -Math.sin(a), Math.sin(a), Math.cos(a)]; }
function trans2(m, a) { return [m[0]*a[0]+m[2]*a[1], m[1]*a[0]+m[3]*a[1]]; } //Matrix(2x1) x Matrix(2x2)
function dist2(a,b) { return Math.hypot(...sub2(a,b)); }
function dot2(a,b) { return a[0]*b[0]+a[1]*b[1]; }
function cross2(a,b) { return a[0]*b[1] - a[1]*b[0]; }
function multiply2(a2x2, a) { return [(a[0]*a2x2[0])+(a[1]*a2x2[1]),(a[0]*a2x2[2])+(a[1]*a2x2[3])]; } //Matrix(2x2) x Matrix(1x2)
function intersect_info2(as, ad, bs, bd) {
    const d = [bs[0] - as[0], bs[1] - as[1]];
    const det = bd[0] * ad[1] - bd[1] * ad[0];
    if(det === 0) return false;
    const res = [(d[1] * bd[0] - d[0] * bd[1]) / det, (d[1] * ad[0] - d[0] * ad[1]) / det];
    return [...res, add2(as, scale2(ad, res[0]))];
}
function intersect_ray2(a, b, c, d) {
    const i = intersect_info2(a, b, c, d);
    return i === false? i: i[2];
}
function segment_intersect2(a,b,c,d, inclusive = true) {
    const i = intersect_info2(a, sub2(b, a), c, sub2(d, c));
    if(i === false) return false;
    const t = inclusive? 0<=i[0]&&i[0]<=1&&0<=i[1]&&i[1]<=1: 0<i[0]&&i[0]<1&&0<i[1]&&i[1]<1;
    return t?i[2]:false;
}
function approx2(a,b,delta=0.0001) { return len2(sub2(a,b)) < delta }
function eq2(a,b) { return a[0]==b[0]&&a[1]==b[1]; }
function clamp2(a, tl, br) { return [Math.max(Math.min(br[0], a[0]), tl[0]), Math.max(Math.min(br[1], a[1]), tl[1])]; }
function nearSq2(test, near, delta = .0001) {
    return near[0] - delta < test[0] && test[0] < near[0] + delta &&
           near[1] - delta < test[1] && test[1] < near[1] + delta;
}

////////////////////////////////////////////////////////////////
// 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)}}}