The letter C ©️
Using my code from Formulae 🧮 you can specify formulas for variables. i and n are placeholders for the iteration and total number of c's respectively. Check examples below:
The letter C ©️ (variation)
The letter C ©️ (variation)
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const seed = 'random seed'; //type=string
const numberOfCs = 16; //min=1 max=50 step=1
const startRadius = 3; //min=1 max=50 step=.1
const endRadius = 95; //min=51 max=150 step=.1
const lengthFn = '.25 + .75 * Math.random()'; //type=string
const strokeFn = '.5'; //type=string
const marginFn = '.15'; //type=string
const angleFn = 'Math.random()'; //type=string
const hatchAngleFn = 'Math.random() * 2 * Math.PI'; //type=string
const hatchDistanceFn = '1'; //type=string
// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(1);
// Global code will be evaluated once.
init();
R.seed(seed);
const turtle = new Turtle();
const polygons = new Polygons();
const items = generateCs();
const hatchAngleFormula = new Formula(hatchAngleFn);
const hatchDistanceFormula = new Formula(hatchDistanceFn);
// The walk function will be called until it returns false.
function walk(i) {
const path = getPath(items[i].r, items[i].stroke, items[i].angle, items[i].range, items[i].margin);
const p = polygons.create();
p.addPoints(...path);
p.addOutline();
p.addHatching(hatchAngleFormula.solve({i: i, n: numberOfCs - 1}), hatchDistanceFormula.solve({i: i, n: numberOfCs - 1}));
polygons.draw(turtle, p);
return i < items.length - 1;
}
function getPath(r, stroke, angle, range, margin) {
const fromAngle = angle - range/2;
const toAngle = angle+range/2;
const path = [];
for(let i = 1, max = Math.ceil(r * range); i < max; i++) {
path.push([
r * Math.cos(fromAngle + i*range/max),
r * Math.sin(fromAngle + i*range/max)
]);
}
const endCenter = [
(r + stroke/2) * Math.cos(toAngle),
(r + stroke/2) * Math.sin(toAngle)
];
for(let i = 0, max = Math.ceil(Math.PI * stroke/2); i <= max; i++) {
path.push(V.add(endCenter, [
stroke * .5 * Math.cos(toAngle + Math.PI - i*Math.PI/max),
stroke * .5 * Math.sin(toAngle + Math.PI - i*Math.PI/max)
]));
}
r+=stroke;
for(let i = 1, max = Math.ceil(r * range); i < max; i++) {
path.push([
r * Math.cos(toAngle - i*range/max),
r * Math.sin(toAngle - i*range/max)
]);
}
const startCenter = [
(r - stroke/2) * Math.cos(fromAngle),
(r - stroke/2) * Math.sin(fromAngle)
];
for(let i = 0, max = Math.ceil(Math.PI * stroke/2); i <= max; i++) {
path.push(V.add(startCenter, [
stroke * .5 * Math.cos(fromAngle - i*Math.PI/max),
stroke * .5 * Math.sin(fromAngle - i*Math.PI/max)
]));
}
return path;
}
function generateCs() {
const lengthFormula = new Formula(lengthFn);
const strokeFormula = new Formula(strokeFn);
const marginFormula = new Formula(marginFn);
const angleFormula = new Formula(angleFn);
const items = [];
for(let i = 0; i < numberOfCs; i++) {
items.push({
stroke: strokeFormula.solve({i: i, n: numberOfCs - 1}),
margin: marginFormula.solve({i: i, n: numberOfCs - 1})
});
}
const sum = items.reduce((a,c) => a + c.stroke + c.margin, 0);
for(let i = 0, r = startRadius; i < numberOfCs; i++) {
items[i].r = r;
items[i].stroke = items[i].stroke * (endRadius - startRadius) / sum;
items[i].margin = items[i].margin * (endRadius - startRadius) / sum;
r += items[i].stroke + items[i].margin;
}
for(let i = 0, r = startRadius; i < numberOfCs; i++) {
items[i].endings = 2 * Math.asin((items[i].stroke/2) / (items[i].r+(items[i].stroke/2)));
items[i].angle = angleFormula.solve({i: i, n: numberOfCs - 1}) * 2 * Math.PI,
items[i].range = lengthFormula.solve({i: i, n: numberOfCs - 1}) * (2 * Math.PI - items[i].endings);
}
return items;
}
/////////////////////////////////////////////////////////////////
// Formula parser and solver - Created by Jurgen Westerhof 2024
// https://turtletoy.net/turtle/187a81ec7d
/////////////////////////////////////////////////////////////////
function Formula(string) {
const types = {'Function': 'Function','Literal': 'Literal','Variable': 'Variable','Arithmetic': 'Arithmetic','Unary': 'Unary'};
const operators = [['**', (a, b) => a**b],['*', (a, b) => a*b],['/', (a, b) => a/b],['%', (a, b) => a%b],['+', (a, b) => a+b],['-', (a, b) => a-b],['<<', (a, b) => a<<b],['>>', (a, b) => a>>b],['|', (a, b) => a|b],['^', (a, b) => a^b],['&', (a, b) => a&b]];
class Formula {
#variables;#parsed;#raw;
constructor(string) {this.#raw = string;this.#variables = [];this.#parsed = this.tokenize(string);}
getVariables() {return this.#variables.map(e => e);}
getParsed() {const clone = (v) => (typeof v == 'object')? v.map(vv => clone(vv)): v;return this.#parsed.map(v => clone(v));}
tokenize(str) {const tokens = [];let m;nextToken: for(let i = 0; i < str.length; i++) {if(/\s/.test(str[i])) continue;if(str.substr(i, 5) == 'Math.') {i += 5;m = new RegExp(`^.{${i}}(?<payload>(?<const>[A-Z][A-Z0-9]*)|(?<fn>[a-z][a-z0-9]*)).*?`).exec(str);if(Math[m.groups.payload] === undefined) {console.error(`Math.${m.groups.payload} is undefined`);}if(m.groups.const) {tokens.push([types.Literal, Math[m.groups.payload]]);} else {tokens.push([types.Function, m.groups.payload]);}i+=m.groups.payload.length-1;continue nextToken;}m = new RegExp('^' + '\.'.repeat(i) + '(?<payload>[a-zA-Z_$][0-9a-zA-Z_$]*).*').exec(str);if(m !== null) {tokens.push([types.Variable, m.groups.payload]);if(!this.#variables.includes(m.groups.payload)) {this.#variables.push(m.groups.payload);}i+= m.groups.payload.length - 1;continue nextToken;}if((tokens.length == 0 || tokens[tokens.length - 1][0] == types.Arithmetic) && (str[i] == '-' || str[i] == '+' || str[i] == '~')) {tokens.push([types.Unary, str[i]]);continue nextToken;}if(str[i] == '(') {const isFunction = (tokens.length > 0 && tokens[tokens.length - 1][0] == types.Function);let cnt = 1;let k = i + 1;let j = 0;let fnArgs = [];for(; 0 < cnt && k+j < str.length; j++) {if(str[k+j] == '(') cnt++;if(str[k+j] == ')') cnt--;if(str[k+j] == ',' && cnt == 1) {fnArgs.push(this.tokenize(str.substr(i+1, j)));i += j+1;k += j+1;j=0;}}if(cnt == 0) {if(isFunction) {fnArgs.push(this.tokenize(str.substr(i+1, j-1)));tokens[tokens.length - 1].push(fnArgs)} else {tokens.push(this.tokenize(str.substr(i+1, j-1)));}i += j;continue nextToken;}console.error(`Opened bracket at character ${i} not closed: ${str.substr(i)}`);throw new Error(`Opened bracket at character ${i} not closed: ${str.substr(i)}`);}m = new RegExp(`^.{${i}}(?<payload>\\d+(\\.\\d+)?|\\.\\d+).*?`).exec(str);if(m !== null) {tokens.push([types.Literal, +m.groups.payload]);i+=m.groups.payload.length-1;continue nextToken;}m = new RegExp(`^.{${i}}(?<payload>\\${operators.map(o => o[0].split('').join('\\')).join('|\\')})`).exec(str);if(m !== null) {tokens.push([types.Arithmetic, m.groups.payload]);i+=m.groups.payload.length-1;continue nextToken;}console.error(`Unable to parse '${str}' because a character at ${i}: ${str[i]}`);throw new Error(`Unable to parse '${str}' because a character at ${i}: ${str[i]}`);}return tokens;}
solve(variableMap = {}) {return this.solveInt(this.#parsed,this.#variables.reduce((a, c) => {let val = 0;if(variableMap[c] === undefined) {console.warn(`Variable ${c} not set in argument to solve() of ${this.#raw}.`);throw new Error(`Variable ${c} not set in argument to solve() of ${this.#raw}.`);} else {val = variableMap[c];}return {...a, [c]: val};}, {}));}
solveInt(tokenss, variableMap) {if(tokenss.length == 0) return 0;const clone = (v) => (typeof v == 'object')? v.map(vv => clone(vv)): v;const tokens = tokenss.map(v => clone(v));for(let i = 0; i < tokens.length; i++) {if(tokens[i][0] == types.Function) {const literals = tokens[i][2].map(v => this.solveInt(v, variableMap));tokens[i] = [types.Literal, Math[tokens[i][1]].apply(null, literals)];}}for(let i = 0; i < tokens.length; i++) {if(typeof tokens[i][0] == 'object') {tokens[i] = [types.Literal, this.solveInt(tokens[i], variableMap)];}if(tokens[i][0] == types.Variable) {tokens[i] = [types.Literal, typeof variableMap[tokens[i][1]] == 'function'? variableMap[tokens[i][1]](variableMap): variableMap[tokens[i][1]]];}}for(let i = 0; i < tokens.length; i++) {if(tokens[i][0] == types.Unary) {switch(tokens[i][1]) {case '-':case '+':tokens[i+1][1] = tokens[i+1][1]*(tokens[i][1]=='-'?-1:1);break;case '~':tokens[i+1][1] = ~tokens[i+1][1];}tokens.splice(i, 1);i--;}}operators.forEach(op => {for(let i = 0; i < tokens.length; i++) {if(tokens[i][0] == types.Arithmetic && tokens[i][1] == op[0]) {tokens[i-1][1] = op[1](tokens[i-1][1], tokens[i+1][1]);tokens.splice(i, 2);i-=2;}}});if(tokens.length == 1 && tokens[0][0] == types.Literal) {return tokens[0][1];}console.error('Something went wrong solving token ' + i, tokens);throw new Error('Something went wrong solving token ' + i);}
}
return new Formula(string);
}
function 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 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;
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;}
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 = Intersection2D;
class PathTools {
static bezier(p1, cp1, cp2, p2, steps = null) {steps = (steps === null? Math.max(3, (V.len(V.sub(cp1, p1)) + V.len(V.sub(cp2, cp1)) + V.len(V.sub(p2, cp2))) | 0): steps) - 1; return Array.from({length: steps + 1}).map((v, i, a, f = i/steps) => [[V.lerp(p1, cp1, f),V.lerp(cp1, cp2, f),V.lerp(cp2, p2, f)]].map(v => V.lerp(V.lerp(v[0], v[1], f), V.lerp(v[1], v[2], f), f))[0]);}
// https://stackoverflow.com/questions/18655135/divide-bezier-curve-into-two-equal-halves#18681336
static splitBezier(p1, cp1, cp2, p2, t=.5) {const e = V.lerp(p1, cp1, t);const f = V.lerp(cp1, cp2, t);const g = V.lerp(cp2, p2, t);const h = V.lerp(e, f, t);const j = V.lerp(f, g, t);const k = V.lerp(h, j, t);return [[p1, e, h, k], [k, j, g, p2]];}
static circular(radius,verticeCount,rotation=0) {return Array.from({length: verticeCount}).map((e,i,a,f=i*2*Math.PI/verticeCount+rotation) => [radius*Math.cos(f),radius*Math.sin(f)])}
static circle(r){return this.circular(r,Math.max(12, r*2*Math.PI|0));}
static arc(radius, extend = 2 * Math.PI, clockWiseStart = 0, steps = null, includeLast = false) { return [steps == null? (radius*extend+1)|0: steps].map(steps => Array.from({length: steps}).map((v, i, a) => [radius * Math.cos(clockWiseStart + extend*i/(a.length-(includeLast?1:0))), radius * Math.sin(clockWiseStart + extend*i/(a.length-(includeLast?1:0)))])).pop(); }
static draw(turtle, path) {path.forEach((pt, i) => turtle[i==0?'jump':'goto'](pt));}
static drawTour(turtle, path) {this.draw(turtle, path.concat([path[0]]));}
static drawPoint(turtle, pt, r = .1) {this.drawTour(turtle, this.circle(r).map(e => V.add(e, pt)));}
static drawArrow(turtle, s, d, width = 6, length = 3) {turtle.jump(s);const arrowHeadBase = V.add(s,d);turtle.goto(arrowHeadBase);turtle.goto(V.add(arrowHeadBase, V.trans(V.rot2d(-V.angle(d)), [-length, width/2])));turtle.jump(V.add(arrowHeadBase, V.trans(V.rot2d(-V.angle(d)), [-length, -width/2])));turtle.goto(arrowHeadBase);}
static circlesTangents(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 = Intersection.circles(c1_center, c1_radius + (internal?c2_radius:-c2_radius), ...middle_circle);
if(!internal_waypoints.intersect_occurs) return [];
const circlePointAtDirection2 = (circle_center, radius, direction) => V.add(circle_center, V.scale(direction, radius/V.len(direction)));
const result = [
[
circlePointAtDirection2(c1_center, c1_radius, V.sub(internal_waypoints.point_1, c1_center)),
circlePointAtDirection2(c1_center, c1_radius, V.sub(internal_waypoints.point_2, c1_center))
],
[
circlePointAtDirection2(c2_center, c2_radius, internal?
V.sub(c1_center, internal_waypoints.point_1):
V.sub(internal_waypoints.point_1, c1_center)),
circlePointAtDirection2(c2_center, c2_radius, internal?
V.sub(c1_center, internal_waypoints.point_2):
V.sub(internal_waypoints.point_2, c1_center))
]
];
return swap? [[result[1][1],result[1][0]],[result[0][1],result[0][0]]]: result;
}
static vectors(path) {return Array.from({length: path.length - 1}).map((e, i) => V.sub(path[i+1], path[i]));}
static redistributeLinear(path, length = .5) {
const p = path.map(pt => [...pt]);
const result = [[...p[0]]];
let pointer = 1;
doneAll: while(pointer < p.length) {
let l = length;
while(pointer < p.length) {
const distance = V.len(V.sub(p[pointer], p[pointer - 1]));
if(distance < l) {
l-=distance;
pointer++;
continue;
}
if(distance == l) {
if(pointer < p.length - 1) result.push([...p[pointer]]);
pointer++;
break doneAll;
}
if(l < distance) {
const newPoint = V.lerp(p[pointer-1], p[pointer], l/distance);
if(pointer < p.length - 1) result.push([...newPoint]);
p[pointer - 1] = newPoint;
break;
}
}
}
result.push(p.pop());
return result;
}
static length(path) { return this.lengths(path).reduce((c, a) => a + c, 0); }
static lengths(path) { return path.map((e, i, a) => V.len(V.sub(e, a[(i+1)%a.length]))).filter((e, i, a) => i < a.length - 1); }
static intersectInfoRay(path, origin, direction) {
const vectors = this.vectors(path);
const ri = vectors.map((e, i) => [i, Intersection.info(origin, direction, path[i], e)])
.filter(e => 0 <= e[1][2] && e[1][2] <= 1 && 0 < e[1][1])
.sort(e => e[1][1]);
if(ri.length == 0) return false;
const hit = ri[0];
const lengths = this.lengths(path);
const length = lengths.reduce((a, c) => a + c, 0);
let l = 0;
for(let i = 0; i < hit[0]; i++) {
l += lengths[i];
}
return [hit[1][0], (l + (lengths[hit[0]] * hit[1][2])) / length, hit[1][1]];
}
static lerp(path, part) {
if(part < 0 || 1 < part) throw new Error('Range of part is 0 to 1, got ' + path);
const lengths = this.lengths(path);
const length = lengths.reduce((a, c) => a + c, 0);
let l = length * part;
for(let i = 0; i < lengths.length; i++) {
if(lengths[i] < l) {
l-=lengths[i];
continue;
}
return V.lerp(path[i], path[i+1], l / V.len(V.sub(path[i+1], path[i])));
}
return [...path[path.length - 1]];
}
}
this.PT = PathTools;
class Complex {
static add(a,b) { return V.add(a,b); }
static sub(a,b) { return V.sub(a,b); }
static scale(a,s) { return V.scale(a,s); }
static mult(a,b) { return [a[0]*b[0]-a[1]*b[1],a[0]*b[1]+a[1]*b[0]]; }
static sqrt(a) { return [[Math.hypot(...a)**.5, Math.atan2(...a.reverse()) / 2]].map(ra => [ra[0]*Math.cos(ra[1]), ra[0]*Math.sin(ra[1])]).pop(); }
}
this.C = Complex;
class Numbers {
static approx(a,b,p) { return Math.abs(a-b) < (p === undefined? .001: p); }
static clamp(a, min, max) { return Math.min(Math.max(a, min), max); }
static rotateClamp(a, min, max) {
if(min == max) return min;
while (a < min) { a+=(max-min); }
while (a > max) { a-=(max-min); }
return a;
}
static lerp(a, b, t) { return V.lerp([a], [b], t); };
}
this.N = Numbers;
class Matrix {
static bayer(order) { return [...Array(1<<order)].map((_,y,a) => { const g = (k=order,x)=>k--&&4*g(k,x)|2*(x>>k)+3*(y>>k&1)&3; return a.map(g); }); }
static rotate(m) { return m[0].map((e, i) => m.map(r => r[i]).reverse()); }
static rotateCCW(m) { return m[0].map((e, i) => m.map(r => r[r.length-1-i])); }
static add(a,b) { return a.map((e, c) => e.map((e, r) => a[c][r] + b[c][r])); }
static sub(a,b) { return a.map((e, c) => e.map((e, r) => a[c][r] - b[c][r])); }
static multiply(a,b) { return Array.from({length: b.length}, (e,resCol) => Array.from({length: a[0].length}, (e,resRow) => b[resCol].reduce((acc, c, bRow) => acc + a[bRow][resRow] * b[resCol][bRow], 0)));}
static scale(a,s) { return a.map((e, c) => e.map((e, r) => a[c][r] * s)); }
static random(c,r,fillFn = Math.random) { return Array.from({length: c}, (e,i) => Array.from({length: r}, e => fillFn(c, r))); }
static identity(d) { return Array.from({length: d}, (e,c) => Array.from({length: d}, (e, r) => c==r?1:0 )); }
static log(m, name, logFn = console.log) { if(name != undefined) logFn(name); if(m === undefined || (typeof m == 'object' && (m[0] === undefined || m[0][0] === undefined))) { return logFn(`Failed to log matrix:`, m); } logFn(m[0].map((e,r) => m.map((e,c) => m[c][r]).join(', ')).join('\n')); }
static invert(m) { let _A = m.map(col => col.map(cell => cell));/*clone matrix*/let temp;const N = _A.length;const E = Array.from({length: N}, (e,i) => Array.from({length: _A[0].length}, (e,j) => i==j?1:0));for (let k = 0; k < N; k++) {temp = _A[k][k];for (let j = 0; j < N; j++) {_A[k][j] /= temp;E[k][j] /= temp;}for (let i = k + 1; i < N; i++) {temp = _A[i][k];for (let j = 0; j < N; j++) {_A[i][j] -= _A[k][j] * temp;E[i][j] -= E[k][j] * temp;}}}for (let k = N - 1; k > 0; k--) {for (let i = k - 1; i >= 0; i--) {temp = _A[i][k];for (let j = 0; j < N; j++) {_A[i][j] -= _A[k][j] * temp;E[i][j] -= E[k][j] * temp;}}}return E; }
static determinant(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.determinant(m.slice(1).map(c => c.filter((_,j) => i != j))), 0)}
static flip(m) { return Array.from({length: m[0].length}, (_, r) => Array.from({length: m.length}, (e, c) => m[c][r])); }
static sum(m) { return m.reduce((a, c) => a + c.reduce((aa, cc) => aa + cc, 0), 0); }
}
this.M = Matrix;
class Algorithms {
static nthTriangular(n) { return ((n * n) + n) / 2; }
}
this.A = Algorithms;
class Random {
static #apply(seed) {
// Seedable random number generator by David Bau: http://davidbau.com/archives/2010/01/30/random_seeds_coded_hints_and_quintillions.html
!function(a,b,c,d,e,f,g,h,i){function j(a){var b,c=a.length,e=this,f=0,g=e.i=e.j=0,h=e.S=[];for(c||(a=[c++]);d>f;)h[f]=f++;for(f=0;d>f;f++)h[f]=h[g=s&g+a[f%c]+(b=h[f])],h[g]=b;(e.g=function(a){for(var b,c=0,f=e.i,g=e.j,h=e.S;a--;)b=h[f=s&f+1],c=c*d+h[s&(h[f]=h[g=s&g+b])+(h[g]=b)];return e.i=f,e.j=g,c})(d)}function k(a,b){var c,d=[],e=typeof a;if(b&&"object"==e)for(c in a)try{d.push(k(a[c],b-1))}catch(f){}return d.length?d:"string"==e?a:a+"\0"}function l(a,b){for(var c,d=a+"",e=0;e<d.length;)b[s&e]=s&(c^=19*b[s&e])+d.charCodeAt(e++);return n(b)}function m(c){try{return o?n(o.randomBytes(d)):(a.crypto.getRandomValues(c=new Uint8Array(d)),n(c))}catch(e){return[+new Date,a,(c=a.navigator)&&c.plugins,a.screen,n(b)]}}function n(a){return String.fromCharCode.apply(0,a)}var o,p=c.pow(d,e),q=c.pow(2,f),r=2*q,s=d-1,t=c["seed"+i]=function(a,f,g){var h=[];f=1==f?{entropy:!0}:f||{};var o=l(k(f.entropy?[a,n(b)]:null==a?m():a,3),h),s=new j(h);return l(n(s.S),b),(f.pass||g||function(a,b,d){return d?(c[i]=a,b):a})(function(){for(var a=s.g(e),b=p,c=0;q>a;)a=(a+c)*d,b*=d,c=s.g(1);for(;a>=r;)a/=2,b/=2,c>>>=1;return(a+c)/b},o,"global"in f?f.global:this==c)};if(l(c[i](),b),g&&g.exports){g.exports=t;try{o=require("crypto")}catch(u){}}else h&&h.amd&&h(function(){return t})}(this,[],Math,256,6,52,"object"==typeof module&&module,"function"==typeof define&&define,"random");
Math.seedrandom(seed);
}
static seedRandom() { this.#apply(new Date().getMilliseconds()); }
static seedDaily() { this.#apply(new Date().toDateString()); }
static seed(seed) { this.#apply(seed); }
static getInt(min, max) {
if(max == undefined) {
max = min + 1;
min = 0;
}
const [mi, ma] = [Math.min(min, max), Math.max(min, max)];
return (mi + Math.random() * (ma - mi)) | 0;
}
static get(min, max) {
if(min == undefined) {
return Math.random();
}
if(max == undefined) {
max = min;
min = 0;
}
const [mi, ma] = [Math.min(min, max), Math.max(min, max)];
return mi + Math.random() * (ma - mi);
}
static getAngle(l = 1) { return l * this.get(0, 2*Math.PI); }
}
this.R = Random;
}
////////////////////////////////////////////////////////////////
// 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;}}}