// LL 2021

const turtle = new Slowpoke();

const density = 1;         // min=0 max=2 step=1
const spread_x = 0.5;      // min=0 max=1 step=0.01
const spread_y = 0.5;      // min=0 max=1 step=0.01
const height = 0.75;       // min=0 max=2 step=0.01
const perspective = 3;     // min=1 max=3 step=0.1
const camera_theta = 0.;   // min=-1 max=1 step=0.05
const camera_phi = 1.;     // min=-0.99 max=1 step=0.05
const camera_r = 16;       // min=0.1 max=40 step=0.1
const inside_lines = 0.2;  // min=0 max=1 step=0.01
const style = 2;           // min=0 max=3 step=1 (Preview,All outlines,Silhouette,Hatched)
const seed = 0;            // min=0 max=100 step=1

const look_at_z = 0;       /// min=-10 max=10 step=0.1
const render = 1;          /// min=0 max=1 step=1 (Voxels,Marching cubes)

var silhouette = new Silhouette();

const noise = SimplexNoise(seed ? seed : Math.floor(Math.random() * 1000));

function walk(i, t) {
	if (i==0) {
		if (t == 0 || t == 1) initOnce();
		initFrame(t);
	}

	if (silhouette.faceCount() < 1) {
		console.log(`Slowpoke: draw: ${slowpoke_draw}, skip: ${slowpoke_skip}`);
		return false;
   	}
	
	silhouette.nextFace().draw();

	return true;
}

function initFrame(t) {
	const cameraOffset = [
		 camera_r * perspective ** 3 * Math.cos((camera_theta+t*2) * Math.PI) * Math.sin((camera_phi/2+0.5) * Math.PI),
		 camera_r * perspective ** 3 * Math.sin((camera_theta+t*2) * Math.PI) * Math.sin((camera_phi/2+0.5) * Math.PI),
		-camera_r * perspective ** 3 * Math.cos((camera_phi/2+0.5) * Math.PI)
		];
	const cameraLookAt = [0, 0, look_at_z];
	viewProjectionMatrix = setupCamera(add3(cameraOffset, cameraLookAt), cameraLookAt);

	polygons = new Polygons();
	
	silhouette.processFrameModels();
	silhouette.sortFaces();

	console.log(`Models: ${silhouette.modelCount()}. Faces: ${silhouette.faceCount()}.`);
}

function initOnce(t) {
	seed_t = (t < 1 && seed == 0) ? (Math.random() * 100 | 0) : seed;
	rng = undefined;

	initScene();

	silhouette.processOnceModels();
}

function initScene() {
	const lr   = 20;  // Loop radius
	const cr   = 6;   // Circle radius
	const lseg = 1 << (9+density); // Loop segments
	const cseg = 1 << (6+density);  // Circle segments
	const twist = 0;
	const factor = 512;
	const mdl = makeTorusMountain(lr, lseg, cr, cseg, twist, factor, height * 0.2);
	//const mdl = makeTorus(lr, lseg, cr, cseg, twist);
	//const mdl = makePQTorus(3, 4, lr, lseg, cr, cseg, twist, 1);
	// Exercise to the reader: make a PQ-torus mountain
	silhouette.addModel(mdl);
}

/////////////////////////////////////////////////////////////////////
// Prototype Silhouette utility code - Created by Lionel Lemarie 2021
// https://turtletoy.net/turtle/334500a2c5

function Silhouette() {
	const models = [];
	const all_faces = [];

	class Model {
		constructor() {
			this.faces = [];
			this.edges = [];
			this.hide_overlap = true;
			this.inside_lines = inside_lines;
		}

		transform(matrix) {
			this.faces.forEach(face => {
				face.transform(matrix);
			});
		}

		processOnce() {
			//if (detail && style) this.subdivideDetail(detail_max_length);
			this.updateEdgeList();
		}

		processFrame() {
			this.faces.forEach(face => { face.projectAndAdd(); });
			this.findStaticOutlines();
			this.findProjectedOutlines();
			this.updateOutlineMasks();
		}
		
		updateOutlineMasks() {
			this.edges.forEach(edge => {
				edge.faces.forEach(face => {
					const pc = face.points.length;
					if (pc > 1) {
						for (var i=0; i<pc; i++) {
							const hash0 = getPointHash(face.points[i]);
							const hash1 = getPointHash(face.points[(i+1)%pc]);
							if (edge.hash == hash0 + hash1 || edge.hash == hash1 + hash0) {
								if (edge.state) {
									face.outline_mask |= 1 << i;
								} else {
									face.outline_mask &= ~(1 << i);
								}
							}
						}
					}	
				});
			});
		}

		addFace(points) {
			const face = new Face(points);
			this.faces.push(face);
		}

		merge(model) {
			model.faces.forEach(face => { this.faces.push(face); })
		}

		subdivideDetail(max_length) {
			var nfaces = this.faces.length;
			var loop = true;
			while (loop) {
				const old_faces = this.faces;
				this.faces = [];
				old_faces.forEach(face => {
					const new_faces = face.getSubdivided(max_length);
					new_faces.forEach(nface => { this.faces.push(nface); });
				});
				loop = this.faces.length != nfaces;
				nfaces = this.faces.length;
			}
		}

		subdivideCount(count) {
			while (count-- > 0) {
				const old_faces = this.faces;
				this.faces = [];
				old_faces.forEach(face => {
					const new_faces = face.getSubdivided(0);
					new_faces.forEach(nface => { this.faces.push(nface); });
				});
			}
		}

		updateEdgeList() {
			this.edges = [];
			const edge_lookup = {};
			this.faces.forEach(face => {
				const pc = face.points.length;
				if (pc > 1) {
					for (var i=0; i<pc; i++) {
						const hash0 = getPointHash(face.points[i]);
						const hash1 = getPointHash(face.points[(i+1)%pc]);
						if ((hash0 + hash1) in edge_lookup) {
							const edge_id = edge_lookup[hash0 + hash1];
							this.addFaceToEdge(edge_id, face);
						} else if ((hash1 + hash0) in edge_lookup) {
							const edge_id = edge_lookup[hash1 + hash0];
							this.addFaceToEdge(edge_id, face);
						} else {
							const edge_id = this.edges.length;
							edge_lookup[hash0 + hash1] = edge_id;
							this.edges.push({ faces: [face], hash: hash0 + hash1, state: 1 });
						}
					}
				}
			});
		}

		addFaceToEdge(edge_id, new_face) {
			var good = true;
			this.edges[edge_id].faces.forEach(face => {
				if (face.matches(new_face)) {
					good = false;
					if (this.hide_overlap) face.overlap = true;
					new_face.overlap = true;
				}
			});
			if (good) this.edges[edge_id].faces.push(new_face);
		}

		findStaticOutlines() {
			this.edges.forEach(edge => {
				edge.state = 1;
				for (var i=0, fl=edge.faces.length; i<fl && edge.state; i++) {
					if (edge.faces[i].overlap) continue;
					const nfi = edge.faces[i].getStaticNormal();
					for (var j=i+1; j<fl && edge.state; j++) {
						if (edge.faces[j].overlap) continue;
						const nfj = edge.faces[j].getStaticNormal();
						const d = len3(sub3(nfi, nfj));
						if (d < this.inside_lines * 2) { edge.state = 0; }
					}
				}
			});
		}

		findProjectedOutlines() {
			this.edges.forEach(edge => {
				var found_pos = false, found_neg = false;
				edge.faces.forEach(face => {
						if (!face.overlap) {
						const nf = face.getProjectedNormal();
						const EPS = 0.001;
						if (nf[2] <   EPS) found_neg = true;
						if (nf[2] >= -EPS) found_pos = true;
					}
				});
				if (found_pos && found_neg) edge.state = 1;
			});
		}
	}

	function getPointHash(point) {
		const mult = 100;
		const x0 = Math.round(point[0] * mult), y0 = Math.round(point[1] * mult), z0 = Math.round(point[2] * mult);
		return `${x0},${y0},${z0}`;
	}

	class Face {
		constructor(points) {
			this.points = [...points];
			this.z = 0;
			this.projected_points = [];
			this.outline_mask = -1;
			this.overlap = false;
		}

		draw() {
			if (this.projected_points.length < 2 || this.overlap) return;

			var good = true;
			this.projected_points.forEach(p => good &= Math.min(Math.abs(p[0]), Math.abs(p[1])) < 100 );
			if (!good) return;

			if (style == 0) {
				// turtle.jump(this.projected_points[this.projected_points.length-1]);
				// this.projected_points.forEach(p=>turtle.goto(p));
				for (var i=0; i<this.projected_points.length; i++) {
					if (this.outline_mask & (1 << i)) {
						turtle.jump(this.projected_points[i]);
						turtle.goto(this.projected_points[(i+1) % this.projected_points.length]);
					}
				}
			} else {
				const p1 = polygons.create();
				p1.addPoints(...this.projected_points);
				if (style == 1) {
					p1.addOutline();
				} else if (style > 1) {
					for (var i=0; i<this.projected_points.length; i++) {
						if (this.outline_mask & (1 << i)) {
							p1.addSegments(p1.cp[i], p1.cp[(i+1) % this.projected_points.length]);
						}
					}
					if (style > 2) {
						const hmin = 0.15, hmax = 0.9;
						const hatching = hmin + (hmax - hmin) * this.getLight();
						p1.addHatching(-Math.PI/4, hatching);
					}
				}
				polygons.draw(turtle, p1, true);
			}
		}

		getStaticNormal() {
			if (this.cached_static_normal === undefined) {
				if (this.points.length < 3) this.cached_static_normal = [0, 1, 0];
				else this.cached_static_normal = normalize3(cross3(sub3(this.points[1], this.points[0]), sub3(this.points[2], this.points[0])));
			}
			return this.cached_static_normal;
		}

		getProjectedNormal() {
			if (this.projected_points.length < 3) return [0, 1, 0];
			return normalize3(cross3(sub3(this.projected_points[1], this.projected_points[0]), sub3(this.projected_points[2], this.projected_points[0])));
		}

		getLight() {
			const n = this.getProjectedNormal();
			return n[0] * 0.5 + 0.5;
		}

		transform(matrix) {
			for (var i=0, c=this.points.length; i<c; i++) {
				this.points[i] = matrix.transform(this.points[i]);
			}
		}

		projectAndAdd() {
			if (this.overlap) return;

			this.projected_points = [];
			this.z = 0;
			this.points.forEach(point => {
				const pp = project(point);
				if (pp === undefined) return;
				this.projected_points.push(pp);
				this.z += pp[2];
			})
			if (this.projected_points.length > 0) this.z /= this.projected_points.length;

			silhouette.addFace(this);
		}

		getSubdivided(max_length) {
			var long_index = -1;
			const pc = this.points.length;

			for (var i=0; i<pc; i++) {
				const len = len3(sub3(this.points[(i+1)%pc],this.points[i]));
				if (len > max_length) {
					max_length = len;
					long_index = i;
				}
			}

			if (long_index >= 0) {
				if (pc == 4) {
					const new_faces = [];
					new_faces.push(new Face([this.points[0], this.points[1], this.points[2]]));
					new_faces.push(new Face([this.points[2], this.points[3], this.points[0]]));
					return new_faces;
				} else {
					const new_faces = [];
					const point = mulf(add3(this.points[(long_index+1)%pc],this.points[long_index]), 0.5);
					for (var i=0; i<pc; i++) {
						if (i != long_index) {
							new_faces.push(new Face([this.points[i], this.points[(i+1)%pc], point]));
						}
					}
					return new_faces;
				}
			}
			return [ this ];
		}

		matches(face) {
			const fl = face.points.length;
			if (fl != this.points.length) return false;
			if (fl < 1) return true;

			var first_id = undefined;
			{
				const hash0 = getPointHash(this.points[0]);
				for (var i=0; i<fl; i++) {
					const hash1 = getPointHash(face.points[i]);
					if (hash0 == hash1) { first_id = i; break; }
				}
			}
			if (first_id === undefined) return false;

			for (var i=1; i<fl; i++) {
				const j = (first_id - i + fl) % fl;
				const hash0 = getPointHash(this.points[i]);
				const hash1 = getPointHash(face.points[j]);
				if (hash0 != hash1) {
					for (var i2=1; i2<fl; i2++) {
						const j2 = (first_id + i2) % fl;
						const hash0 = getPointHash(this.points[i2]);
						const hash1 = getPointHash(face.points[j2]);
						if (hash0 != hash1) return false;
					}
					return true;
				}
			}
			return true;
		}
	}

	return {
		addModel: (model) => { models.push(model); },
		newModel: () => { return new Model(); },
		processFrameModels: () => { models.forEach(model => { model.processFrame(); }); },
		processOnceModels: () => { models.forEach(model => { model.processOnce(); }); },
		modelCount: () => { return models.length; },
		sortFaces: () => { all_faces.sort(function(a, b) { return a.z - b.z; }); },
		nextFace: () => { return all_faces.shift(); },
		faceCount: () => { return all_faces.length; },
		addFace: (face) => { all_faces.push(face); },
	};
}

class Matrix {
	constructor() {
		this.identity();
		this.stack = [];
	}

	identity() {
		this.matrix = [ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ];
		return this;
	}

	translate(tx, ty, tz) {
		const m2 = new Matrix();
		m2.matrix[12] = tx;
		m2.matrix[13] = ty;
		m2.matrix[14] = tz;
		return this.multiply(m2);
	}

	scale(sx, sy, sz) {
		if (sy === undefined) sy = sx;
		if (sz === undefined) sz = sy;
		const m2 = new Matrix();
		m2.matrix[0]  *= sx;
		m2.matrix[5]  *= sy;
		m2.matrix[10] *= sz;
		return this.multiply(m2);
	}

	rotateX(a) {
		const m2 = new Matrix();
		m2.matrix[5]  =  Math.cos(a);
		m2.matrix[9]  =  Math.sin(a);
		m2.matrix[6]  = -Math.sin(a);
		m2.matrix[10] =  Math.cos(a);
		return this.multiply(m2);
	}

	rotateY(a) {
		const m2 = new Matrix();
		m2.matrix[0]  =  Math.cos(a);
		m2.matrix[8]  = -Math.sin(a);
		m2.matrix[2]  =  Math.sin(a);
		m2.matrix[10] =  Math.cos(a);
		return this.multiply(m2);
	}

	rotateZ(a) {
		const m2 = new Matrix();
		m2.matrix[0]  =  Math.cos(a);
		m2.matrix[1]  = -Math.sin(a);
		m2.matrix[4]  =  Math.sin(a);
		m2.matrix[5]  =  Math.cos(a);
		return this.multiply(m2);
	}

	multiply(rhs) {
		const m1 = [...this.matrix];
		const m2 = [...rhs.matrix];
		this.matrix = [];
		for(let n=0; 16>n; n+=4) {
			for(let o=0; 4>o; o++) {
				this.matrix[n+o] = m1[n+0] * m2[0+o] + m1[n+1] * m2[4+o] + m1[n+2] * m2[8+o] + m1[n+3] * m2[12+o];
			}
		}
		return this;
	}

	transform(point) {
		const p = [...point];
		for (let i=0; i<3; i++) {
			p[i] = this.matrix[i] * point[0] + this.matrix[i+4] * point[1] + this.matrix[i+8] * point[2] + this.matrix[i+12];
		}
		return p;
	}

	push() {
		this.stack.push([...this.matrix]);
	}

	pop() {
		this.matrix = this.stack.pop();
	}
}

// Input: 2D point in -128,128 range 
function heightField2(p) {
	let x = p[0]/60, y = p[1]/60;
	let height = noise.noise2D([x,y]);
	height += .55 * noise.noise2D([x*2+3.4,y*2-56.1]);
	height += .35 * Math.abs(1-noise.noise2D([x*4+21.2,y*4+.5]));
	height += .25 * Math.abs(1-noise.noise2D([x*8+421.12,y*8+21.3]));
 	height += .05 * Math.abs(1-noise.noise2D([x*32+150.34,y*32+150.34]));
	height += 1 - 2.5 * ((p[0]/mix(1, 512, spread_x))**2 + (p[1]/mix(1, 512, spread_y))**2);
	height = Math.max(height, 0) ** 2;
	return height;
}

function mix(a, b, t) { return a * (t-1) + b * t; }

function makeTorusMountain(lr, lseg, cr, cseg, twist, factor, height) {
	const torus = silhouette.newModel();

	const lstep = Math.PI * 2 / lseg;
	const cstep = Math.PI * 2 / cseg;

	for (var i=0; i<lseg; i++) {
		const points = [];
		for (var k=0; k<2; k++) {
			points.push([]);
			const a = (i + k) * lstep;
			const cx = lr * Math.cos(a), cy = 0, cz = lr * Math.sin(a);
			const matrix = new Matrix().rotateY(a).translate(cx, cy, cz);
			for (var j=0; j<cseg; j++) {
				const b = j * cstep + Math.PI / 4 + a * twist + Math.PI;
				const x0 = ((i+k) / lseg) * factor - factor / 2;
				const z0 = (j / cseg) * factor - factor / 2;
				const h0 = heightField2([x0, z0]) * height;
				const cr2 = cr + cr * h0;
				const point = matrix.transform([cr2 * Math.cos(b), cr2 * Math.sin(b), 0]);
				points[k].push(point);
			}
		}

		for (j=0; j<cseg; j++) {
			torus.addFace([ points[0][j], points[0][(j+1)%cseg], points[1][(j+1)%cseg], points[1][j] ]);
		}
	}

	//torus.inside_lines = 0.2;
	return torus;
}

function makeTorus(lr, lseg, cr, cseg, twist) {
	const torus = silhouette.newModel();

	const lstep = Math.PI * 2 / lseg;
	const cstep = Math.PI * 2 / cseg;

	for (var i=0; i<lseg; i++) {
		const points = [];
		for (var k=0; k<2; k++) {
			points.push([]);
			const a = (i + k) * lstep;
			const cx = lr * Math.cos(a), cy = 0, cz = lr * Math.sin(a);
			const matrix = new Matrix().rotateY(a).translate(cx, cy, cz);
			for (var j=0; j<cseg; j++) {
				const b = j * cstep + Math.PI / 4 + a * twist;
				const point = matrix.transform([cr * Math.cos(b), cr * Math.sin(b), 0]);
				points[k].push(point);
			}
		}

		for (j=0; j<cseg; j++) {
			torus.addFace([ points[0][j], points[0][(j+1)%cseg], points[1][(j+1)%cseg], points[1][j] ]);
		}
	}

	return torus;
}

function makePQTorus(p, q, lr, lseg, cr, cseg, twist, star) {
	const torus = silhouette.newModel();

	const lstep = Math.PI * 2 / lseg;
	const cstep = Math.PI * 2 / cseg;

	for (var i=0; i<lseg; i++) {
		const points = [];
		for (var k=0; k<2; k++) {
			const a = (i + k) * lstep;
			const r = lr * 0.5 * (2 + Math.sin(a * q));
			const cx = r * Math.cos(a * p);
			const cy = r * 0.5 * Math.cos(a * q);
			const cz = r * Math.sin(a * p);

			const matrix = new Matrix();
			matrix.rotateY(a * p);
			matrix.translate(cx, cy, cz);

			points.push([]);
			for (var j=0; j<cseg; j++) {
				const b = j * cstep + Math.PI / 4 + a * twist;
				const factor = 1; //0.3 + (1 + Math.cos(a * p * 2)) * 0.5 * 0.7;
				const r2 = cr * ((j&1) ? 1 : star) * factor;
				const point = [
					r2 * Math.cos(b),
					r2 * Math.sin(b),
					0
				];
				const tpoint = matrix.transform(point)
				points[k].push(tpoint);
			}
		}

		for (j=0; j<cseg; j++) {
			const point00 = points[0][j];
			const point01 = points[0][(j+1)%cseg];
			const point10 = points[1][j];
			const point11 = points[1][(j+1)%cseg];

			const quad = [ point00, point01, point11, point10 ];
			torus.addFace(quad);
		}
	}

	return torus;
}

function project(op) {
	const p = transform4([op[0], op[2], op[1], 1], viewProjectionMatrix);
	const s = 5 * perspective **3;
	if (p[2] < 0) return undefined;
	return [ p[0]/p[3]*s, -p[1]/p[3]*s, p[2] ];
}

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

////////////////////////////////////////////////////////////////
// Simplex Noise utility code. Created by Reinder Nijhoff 2020
// https://turtletoy.net/turtle/6e4e06d42e
// Based on: http://webstaff.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
////////////////////////////////////////////////////////////////
function SimplexNoise(t=1){const a=[[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]],o=new Uint8Array(512),r=(Math.sqrt(3)-1)/2,h=1/3,n=(3-Math.sqrt(3))/6,s=1/6,e=(t,a)=>t[0]*a[0]+t[1]*a[1],M=(t,a)=>[t[0]-a[0],t[1]-a[1]],l=(t,a)=>t[0]*a[0]+t[1]*a[1]+t[2]*a[2],c=(t,a)=>[t[0]-a[0],t[1]-a[1],t[2]-a[2]];return new class{constructor(t=1){for(let t=0;t<512;t++)o[t]=255&t;for(let a=0;a<255;a++){const r=(t=this.hash(a+t))%(256-a)+a,h=o[a];o[a+256]=o[a]=o[r],o[r+256]=o[r]=h}}noise2D(t){const h=e(t,[r,r]),s=[Math.floor(t[0]+h),Math.floor(t[1]+h)],l=255&s[0],c=255&s[1],f=e(s,[n,n]),m=M(t,M(s,[f,f])),x=m[0]>m[1]?[1,0]:[0,1],i=M(M(m,x),[-n,-n]),u=M(m,[1-2*n,1-2*n]);let q=Math.max(0,.5-e(m,m))**4*e(a[o[l+o[c]]%12],m);return q+=Math.max(0,.5-e(i,i))**4*e(a[o[l+x[0]+o[c+x[1]]]%12],i),70*(q+=Math.max(0,.5-e(u,u))**4*e(a[o[l+1+o[c+1]]%12],u))}noise3D(t){const r=l(t,[h,h,h]),n=[Math.floor(t[0]+r),Math.floor(t[1]+r),Math.floor(t[2]+r)],e=255&n[0],M=255&n[1],f=255&n[2],m=l(n,[s,s,s]),x=c(t,c(n,[m,m,m])),[i,u]=x[0]>=x[1]?x[1]>=x[2]?[[1,0,0],[1,1,0]]:x[0]>=x[2]?[[1,0,0],[1,0,1]]:[[0,0,1],[1,0,1]]:x[1]<x[2]?[[0,0,1],[0,1,1]]:x[0]<x[2]?[[0,1,0],[0,1,1]]:[[0,1,0],[1,1,0]],q=c(c(x,i),[-s,-s,-s]),w=c(c(x,u),[-2*s,-2*s,-2*s]),D=c(x,[1-3*s,1-3*s,1-3*s]);let p=Math.max(0,.6-l(x,x))**4*l(a[o[e+o[M+o[f]]]%12],x);return p+=Math.max(0,.6-l(q,q))**4*l(a[o[e+i[0]+o[M+i[1]+o[f+i[2]]]]%12],q),p+=Math.max(0,.6-l(w,w))**4*l(a[o[e+u[0]+o[M+u[1]+o[f+u[2]]]]%12],w),32*(p+=Math.max(0,.6-l(D,D))**4*l(a[o[e+1+o[M+1+o[f+1]]]%12],D))}hash(t){const a=1103515245*((t=1103515245*(t>>1^t))^t>>3);return a^a>>16}}(t)}


// Random with seed
var rng;
function random() { if (rng === undefined) rng = new RNG(seed_t); return rng.nextFloat(); }
function RNG(t){return new class{constructor(t){this.m=2147483648,this.a=1103515245,this.c=12345,this.state=t||Math.floor(Math.random()*(this.m-1))}nextFloat(){return this.state=(this.a*this.state+this.c)%this.m,this.state/(this.m-1)}}(t)}

////////////////////////////////////////////////////////////////
// Projection from reinder's https://turtletoy.net/turtle/b3acf08303
let viewProjectionMatrix;
function setupCamera(t,e){const m=lookAt4m(t,e,[0,0,1]),n=perspective4m(.25,1);return multiply4m(n,m)}
function lookAt4m(o,n,r){const s=new Float32Array(16);n=normalize3(sub3(o,n)),r=normalize3(cross3(r,n));const t=normalize3(cross3(n,r));return s[0]=r[0],s[1]=t[0],s[2]=n[0],s[3]=0,s[4]=r[1],s[5]=t[1],s[6]=n[1],s[7]=0,s[8]=r[2],s[9]=t[2],s[10]=n[2],s[11]=0,s[12]=-(r[0]*o[0]+r[1]*o[1]+r[2]*o[2]),s[13]=-(t[0]*o[0]+t[1]*o[1]+t[2]*o[2]),s[14]=-(n[0]*o[0]+n[1]*o[1]+n[2]*o[2]),s[15]=1,s}
function perspective4m(t,n){const e=new Float32Array(16).fill(0,0);return e[5]=1/Math.tan(t/2),e[0]=e[5]/n,e[10]=e[11]=-1,e}
function multiply4m(t,r){const l=new Float32Array(16);for(let n=0;16>n;n+=4)for(let o=0;4>o;o++)l[n+o]=r[n+0]*t[0+o]+r[n+1]*t[4+o]+r[n+2]*t[8+o]+r[n+3]*t[12+o];return l}
function transform4(r,n){const t=new Float32Array(4);for(let o=0;4>o;o++)t[o]=n[o]*r[0]+n[o+4]*r[1]+n[o+8]*r[2]+n[o+12];return t}

function normalize3(a) { const len = len3(a); return scale3(a,len3<0.0001?1:1/len); }
function scale3(a,b) { return [a[0]*b,a[1]*b,a[2]*b]; }
function len3(a) { return Math.sqrt(dot3(a,a)); }
function add3(a,b) { return [a[0]+b[0],a[1]+b[1],a[2]+b[2]]; }
function sub3(a,b) { return [a[0]-b[0],a[1]-b[1],a[2]-b[2]]; }
function dot3(a,b) { return a[0]*b[0]+a[1]*b[1]+a[2]*b[2]; }
function cross3(a,b) { return [a[1]*b[2]-a[2]*b[1],a[2]*b[0]-a[0]*b[2],a[0]*b[1]-a[1]*b[0]]; }
function mulf(v, f) { return [v[0]*f,v[1]*f,v[2]*f]; }

////////////////////////////////////////////////////////////////
// Slowpoke utility code. Created by Reinder Nijhoff 2019
// https://turtletoy.net/turtle/cfe9091ad8
////////////////////////////////////////////////////////////////
function Slowpoke(o,t){const e={};return new class extends Turtle{goto(o,t){const s=Array.isArray(o)?[...o]:[o,t];if(this.isdown()){const o=[this.x(),this.y()],t=o[0].toFixed(2)+"_"+s[0].toFixed(2)+o[1].toFixed(2)+"_"+s[1].toFixed(2),i=s[0].toFixed(2)+"_"+o[0].toFixed(2)+s[1].toFixed(2)+"_"+o[1].toFixed(2);if(e[t]||e[i])return super.up(),super.goto(s),super.down(),void slowpoke_skip++;slowpoke_draw++,e[t]=e[i]=!0}super.goto(s)}}(o,t)}
var slowpoke_skip = 0, slowpoke_draw = 0;