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const draw = 0; //min=0 max=5 step=1 (All for screen, All for plotter, Grid for plotter, Axis for plotter, Function for plotter, Text for plotter) const title = 'Function plot'; //type=string const type = 0; //min=0 max=1 step=1 (Graph of a function: Use y = formulatext with variable x, Parametric equation: Use x = parametricFormulaX and y = parametricFormulaY both with variable t) const formulaText = '1.5*x**.5 + 1.5*Math.sin(x*Math.PI) * .0625*x'; //type=string const parametricFormulaX = 'Math.sin(t) * t/5'; //type=string const parametricFormulaY = 'Math.cos(t) * t/5'; //type=string const tMin = 0; //min=-100 max=0 step=1; const tMax = 10; //min=1 max=100 step=1 const xMin = -1; //min=-50 max=-1 step=1 const xMax = 19; //min=1 max=50 step=1 const xTick = 1; //min=.01 max=10 step=.01 const xSpace = 200; //min=20 max=200 step=1 const yMin = -1; //min=-50 max=-1 step=1 const yMax = 9; //min=1 max=50 step=1 const yTick = 1; //min=.01 max=10 step=.01 const ySpace = 100; //min=20 max=200 step=1 const whenLabelsDontFit = 0; //min=0 max=1 step=1 (Diagonal, Skip) If diagonal doesn't fit it's diagonal AND skip const tickLabels = 0; //min=0 max=1 step=1 (Inside, Outside) const axisLabels = 1; //min=0 max=1 step=1 (Same as tickLabels, Outside) const resolutionPwr = 8; //min=0 max=10 step=1 const asymptoteDelta = 100; //min=0 max=10000 step=100 When delta between f(x[n]) and f(x[n+1]) is greater than this value it's interpreted as an asymptote // DISCLAIMER! // A lot of unstructured garbage code here... but it works, I think. // And I don't bother to clean it up anymore. const DISPLAY_ATTEMPT = { DIAGONAL: 0, SKIP: 1 }; const DISPLAY_LABELS = { HORIZONTAL: 0, DIAGONAL: 1 }; const resolution = 1/2**resolutionPwr; const opacity = draw == 0?.2:1; // You can find the Turtle API reference here: https://turtletoy.net/syntax Canvas.setpenopacity(opacity); // Global code will be evaluated once. init(); const turtle = new MeasuringTurtle(); const translate = (transpose = [0,0], scale = [1,1]) => (x, y) => (y === undefined? x: [x,y]).map((e,i) => e * scale[i] + transpose[i]); const t = translate([0,0], [.8,.8]); const fn = new Formula(formulaText); const fnx = new Formula(parametricFormulaX); const fny = new Formula(parametricFormulaY); if(draw == 4) { turtle.up(); turtle.resetBbox(); } setup(turtle, t); turtle.down(); if([0, 1, 4].includes(draw)) plot(turtle, t, fn, xMin, xMax, yMin, yMax, xSpace, ySpace, resolution); if([0, 1, 5].includes(draw)) drawTitle(turtle, t, xSpace, ySpace, turtle.getBbox()); function drawTitle(turtle, t, xSpace, ySpace, bbox) { //this 'bbox' is a little cheat using measuringTurtle to get the text right const topLeft = t(-xSpace / 2, -ySpace / 2); const topRight = t(xSpace / 2, -ySpace / 2); const maxWidth = 160;//topRight[0] - topLeft[0]; //title (() => { const text = new Text(getFont('HersheySerifBold')); const maxHeight = 100 + Math.min(topLeft[1], bbox[0][1]) - 13; const textSize = [text.size(turtle, title, 1)].map(size => Math.min(maxHeight / size.height, maxWidth / size.width)).pop(); let size = text.size(turtle, title, textSize); const dims = text.dimensions(textSize); for(let i = 0; i < 1/opacity; i++) { turtle.jump( - size.width / 2, Math.min(topLeft[1], bbox[0][1]) - dims.descenders - 3); text.print(turtle, title, textSize); } })(); //formulaText (() => { const text = new Text(getFont('HersheySerifMed')); const fnText = `${formulaText.replace(/Math\.E/g, 'e').replace(/Math\./g, '').replace(/([^\d])(\.\d+)/g, '$10$2')}`; const fnXText = `${parametricFormulaX.replace(/Math\.E/g, 'e').replace(/Math\./g, '').replace(/([^\d])(\.\d+)/g, '$10$2')}`; const fnYText = `${parametricFormulaY.replace(/Math\.E/g, 'e').replace(/Math\./g, '').replace(/([^\d])(\.\d+)/g, '$10$2')}`; const textSize = .4; const dims = text.dimensions(textSize); const descriptions = [ `${tMin} <= t <= ${tMax}`, `${type == 0? `y = ${fnText}`: `x = ${fnXText}`}`, `y = ${fnYText}` ]; const size = text.size(turtle, descriptions[1], textSize); const size2 = type == 0? size: text.size(turtle, descriptions[2], textSize); size.width = type == 0? size.width: Math.max(size.width, size2.width); const bottomLeft = t(-xSpace / 2, ySpace / 2); bottomLeft[1] = Math.max(bottomLeft[1], bbox[1][1]); for(let i = 0; i < 1/opacity; i++) { for(let j = 1; j < (type==0?2:4); j++) { turtle.jump( - size.width / 2, bottomLeft[1] + size.height *j* 1.5); text.print(turtle, descriptions[j%3], textSize); } if(type == 1) { turtle.jump( - size.width / 2 - 5, bottomLeft[1] + size.height * 3 - .6); text.print(turtle, '{', textSize*3); } } })(); } function plot(turtle, t, fn, xMin, xMax, yMin, yMax, xSpace, ySpace, resolution) { const rawSets = []; let rawPts = []; for(let t = (type == 0?xMin:tMin); t <= (type == 0?xMax:tMax); t+=resolution) { let yVal = type==0? fn.solve({x:t}): fnx.solve({t: t}); let xVal = type == 0? t: fny.solve({t: t}); if(isNaN(yVal) || isNaN(xVal)) { if(rawPts.length > 0) { rawPtsSets.push(rawPts); rawPts = []; } continue; } if(rawPts.length > 0) { if(asymptoteDelta < Math.abs(yVal - rawPts[rawPts.length - 1][1]) || asymptoteDelta < Math.abs(xVal - rawPts[rawPts.length - 1][0])) { rawSets.push(rawPts); rawPts = []; } } rawPts.push( [xVal, yVal] ); } if(rawPts.length > 0) { rawSets.push(rawPts); } const inRange = (pt) => xMin <= pt[0] && pt[0] <= xMax && yMin <= pt[1] && pt[1] <= yMax; const rangeRays = [ [[xMin, yMin], [xMax - xMin, 0]], [[xMax, yMin], [0, yMax - yMin]], [[xMax, yMax], [xMin - xMax, 0]], [[xMin, yMax], [0, yMin - yMax]], ]; const edgeIntersections = (c, n) => rangeRays.map(ray => Intersection.info(c, V.sub(n, c), ...ray)).filter(info => 0 < info[1] && info[1] < 1 && 0 <= info[2] && info[2] < 1).sort((a,b) => a[1] < b[1]? -1: 1); const refinedPts = []; for(let i = 0; i < rawSets.length; i++) { const rawSet = rawSets[i]; let refSet = []; for(let j = 0; j < rawSet.length; j++) { if(j == rawSet.length - 1) { if(inRange(rawSet[j])) refSet.push(rawSet[j]); if(refSet.length > 1) refinedPts.push(refSet); break; } const c = rawSet[j]; const n = rawSet[j+1]; const currentInRange = inRange(c); const nextInRange = inRange(n); if(currentInRange) { refSet.push(c); if(nextInRange) continue; const infos = edgeIntersections(c, n); if(infos.length > 0) refSet.push(infos[0][0]); refinedPts.push(refSet); refSet = []; continue; } if(nextInRange) { const infos = edgeIntersections(c, n); if(infos.length > 0) refSet.push(infos[0][0]); continue; } const infos = edgeIntersections(c, n); if(infos.length > 0) { // line from c to n intersects with two graph edges refinedPts.push([ infos[0][0], infos[1][0] ]); } // line from c to n does not intersect } } const tt = translate([xSpace * (.5 - xMax / (xMax - xMin)), -(ySpace * (.5 - yMax / (yMax - yMin)))], [xSpace / (xMax - xMin),-ySpace / (yMax - yMin)]); for(let k = 0; k < refinedPts.length; k++) { for(let i = 0; i < 1/opacity; i++) { for(let j = 0; j < refinedPts[k].length; j++) { turtle[j==0?'jump':'goto'](t(tt(refinedPts[k][j]))); } } } } function setup(turtle, t) { const yAxis = getAxis(t, true, xMin, xMax, xTick, xSpace, ySpace); const xAxis = getAxis(t, false, yMin, yMax, yTick, xSpace, ySpace); if(draw < 4) { [...yAxis, ...xAxis].forEach(e => { for(let i = 0; i < (e[2]?1/opacity:1); i++) { turtle.jump(e[0]); turtle.goto(e[1]); } }); } if(![0, 1, 5].includes(draw)) { return; } const text = new Text(getFont('HersheySerifMed')); const displayInside = tickLabels == 0; const axisInside = axisLabels == 0? displayInside: false; const xtickLabelsY = displayInside? xAxis.filter(e => e[2])[0][0][1]: yAxis[0][0][1]; const ytickLabelsX = displayInside? yAxis.filter(e => e[2])[0][0][0]: xAxis[0][0][0]; let displayedOrigin = false; let labelAngle = 0; let xTickSize = yAxis.length <= 1? 200: yAxis[1][0][0] - yAxis[0][0][0]; let skipLabel = 1; let displayLabelsX = DISPLAY_LABELS.HORIZONTAL; const xNegTicks = xMin / xTick | 0; const tickTexts = []; for(let i = displayInside?1:0, tick = xNegTicks + (displayInside? 1: 0); i < yAxis.length - (displayInside? 1: 0); i++, tick++) { tickText = {text: `${Math.round(tick * xTick * 1000) / 1000}`}; tickText.size = text.size(turtle, tickText.text, .3); if(whenLabelsDontFit == DISPLAY_ATTEMPT.DIAGONAL) { labelAngle = labelAngle == 0? (tickText.size.width > xTickSize? 60: labelAngle): labelAngle; } tickTexts[i] = tickText; } displayLabelsX = labelAngle == 0? DISPLAY_LABELS.HORIZONTAL: DISPLAY_LABELS.DIAGONAL; const maxSize = tickTexts.reduce((a,c) => Math.max(a, displayLabelsX == DISPLAY_LABELS.HORIZONTAL? c.size.width: c.size.height * 1.5), 0) if(maxSize > xTickSize) { skipLabel = Math.ceil(maxSize / xTickSize); } for(let i = displayInside?1:0, tick = xNegTicks + (displayInside? 1: 0); i < yAxis.length - (displayInside? 1: 0); i++, tick++) { if(tick%skipLabel == 0) { turtle.seth(tick == 0? 0: labelAngle); for(let j = 0; j < 1/opacity; j++) { turtle.jump(displayInside && tick == 0? ytickLabelsX - tickTexts[i].size.width - tickTexts[i].size.height/2: yAxis[i][0][0] - (displayLabelsX == DISPLAY_LABELS.HORIZONTAL? tickTexts[i].size.width / 2: (tick < 0?tickTexts[i].size.height:tickTexts[i].size.height /1.5)), xtickLabelsY + (displayLabelsX == DISPLAY_LABELS.HORIZONTAL|| tick == 0? tickTexts[i].size.height * 1.5: tickTexts[i].size.height * .7)); text.print(turtle, tickTexts[i].text, .3); } } turtle.seth(0); size = text.size(turtle, `y`, .4); if(tick === 0) { for(let j = 0; j < 1/opacity; j++) { turtle.jump(yAxis[i][0][0] + (size.height / 2)*(axisInside?1:-1), yAxis[i][1][1] + size.height*(axisInside?1:-1)); text.print(turtle, `y`, .4); } } } const yNegTicks = yMin / yTick | 0; for(let i = displayInside?1:0, tick = yNegTicks + (displayInside? 1: 0); i < xAxis.length - (displayInside? 1: 0); i++, tick++) { tickText = `${Math.round(tick * yTick * 1000) / 1000}`; let size = text.size(turtle, `${tickText}`, .3); for(let j = 0; j < 1/opacity; j++) { if(!displayInside || tick != 0) { turtle.jump(ytickLabelsX - size.width - size.height /2, xAxis[i][0][1] + size.height / 2); text.print(turtle, `${tickText}`, .3); } } size = text.size(turtle, `x`, .4); if(tick === 0) { for(let j = 0; j < 1/opacity; j++) { turtle.jump(xAxis[i][1][0] + (size.width / 2)*(axisInside?-2:1), xAxis[i][0][1] + (size.height / 2)*(axisInside?-1:1)); text.print(turtle, `x`, .4); } } } } function getAxis(t, vertical, min, max, tick, xSpace, ySpace) { const space = vertical? xSpace: ySpace; const negTicks = min / tick; const posTicks = max / tick; const offset = space * (.5 - max / (max - min)); const spacePerTick = (space / (posTicks - negTicks)); const lines = []; for(let ti = negTicks | 0; ti <= posTicks | 0; ti++) { if(draw == 2 && ti == 0) continue; if(draw == 3 && ti != 0) continue; if(vertical) { lines.push([t(ti * spacePerTick + offset, ySpace/2), t(ti * spacePerTick + offset, -ySpace/2), ti == 0]); } else { lines.push([t(-xSpace/2, -(ti * spacePerTick + offset)), t(xSpace/2, -(ti * spacePerTick + offset)), ti == 0]); } } return lines; } function getFont(name) { return { HersheySerifBold: {"name":"HersheySerifBold","unitsPerEm":1000,"ascent":800,"descent":-200,"capHeight":500,"xHeight":300,"glyphs":"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HersheySerifBoldItalic: 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HersheySerifMed: 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"}, HersheySerifMedItalic: 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"}, }[name]; } function MeasuringTurtle(x, y) { class MeasuringTurtle extends Turtle { bbox = [[0,0], [0,0]]; constructor(x, y) { super(x, y); } goto(x, y) { super.goto(x, y); if(this.bbox === undefined) this.resetBbox(); this.bbox = [this.pos()].map(p => [ [Math.min(this.bbox[0][0], p[0]), Math.min(this.bbox[0][1], p[1])], [Math.max(this.bbox[1][0], p[0]), Math.max(this.bbox[1][1], p[1])], ]).pop(); } resetBbox() { this.bbox = [this.pos(),this.pos()]; } getBbox() { return this.bbox; } } return new MeasuringTurtle(x, y); } ///////////////////////////////////////////////////////////////// // 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 = [ //ordered by operator precedence (PEMDAS) ['**', (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; #ready; 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++) { //Skip whitespace if(/\s/.test(str[i])) continue; //Parse Math namespace 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.${m.groups.payload} is undefined`); } if(m.groups.const) { tokens.push([types.Literal, Math[m.groups.payload]]); } else { tokens.push([types.Function, m.groups.payload]); } i+=m.groups.payload.length-1; continue nextToken; } //Parse variable // taking a shortcut here: unicode in variable names not accepted: https://stackoverflow.com/questions/1661197/what-characters-are-valid-for-javascript-variable-names m = new RegExp('^' + '\.'.repeat(i) + '(?<payload>[a-zA-Z_$][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; } //Parse unary 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; } //Parse (group) (including function parameters) 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: ${str.substr(i)}`); } //Parse literal m = new RegExp(`^.{${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; } //Parse operator 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; } //Something I didn't think of occured 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, //Map required variables to values assuming 0 if not set 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)); //Resolve functions 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)]; } } //Resolve (group)s 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]]]; } } //Resolve unary 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--; } } //Resolve operators 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; } } }); //Get solution if(tokens.length == 1 && tokens[0][0] == types.Literal) { return tokens[0][1]; } //Something I didn't think of occured console.error('Something went wrong solving token ' + i, tokens); throw new Error('Something went wrong solving token ' + i); } } return new Formula(string); } //////////////////////////////////////////////////////////////// // Text utility code. Created by Reinder Nijhoff 2024 // https://turtletoy.net/turtle/0f84fd3ae4 // Modifications by Jurgen Westerhof 2024: https://turtletoy.net/turtle/9aef87b45e // - Does not force turtle to operate in radians // - Now respects turtle.isdown() and doesn't print if true // - Text.size(turtle, str, scale = 1) returns properties of text str to be printed // - Text.bbox(turtle, str, scale = 1) returns bounding box of text str to be printed // - Text.dimensions(scale = 1) returns properties of fontData for scale // - Text.bboxPrint(turtle, str, scale = 1) prints the text and returns the absolute bounding box //////////////////////////////////////////////////////////////// function Text(fontData) { const decode = (data) => { const b = atob(data), a = new Int16Array(b.length / 2), g = {}; for (let i = 0; i < b.length; i+=2) { a[i / 2 | 0] = b.charCodeAt(i) | (b.charCodeAt(i + 1) << 8); } for (let i = 0;i < a.length; i++) { let u = String.fromCharCode(a[i++]), x = a[i++], d = [], p = []; for (;a[i] !== -16384; i++) a[i] === 16384 ? (d.push(p), p = []) : p.push(a[i]); g[u] = { x, d }; } return g; } const rotAdd = (a, b, h) => [Math.cos(h)*a[0] - Math.sin(h)*a[1] + b[0], Math.cos(h)*a[1] + Math.sin(h)*a[0] + b[1]]; const data = Object.fromEntries(Object.entries(fontData).map(([key, value]) => [key, key === 'glyphs' ? decode(value) : value])); class RangeFinderTurtle extends Turtle { constructor(x, y) {super(x, y);this.reset();} goto(x, y) {super.goto(x, y);const [a, b] = this.pos();this.rangeX = [Math.min(a, this.rangeX? this.rangeX[0]: a), Math.max(a, this.rangeX? this.rangeX[1]: a)];this.rangeY = [Math.min(b, this.rangeY? this.rangeY[0]: b), Math.max(b, this.rangeY? this.rangeY[1]: b)];} reset() {const [a, b] = this.pos();this.rangeX = [a, a];this.rangeY = [b, b];} bbox() { return [[this.rangeX[0], this.rangeY[0]], [this.rangeX[1], this.rangeY[1]]]; } } class Text { print (t, str, scale = 1) { const isDown = t && t.isdown(); let pos = t ? [t.x(), t.y()] : [0,0], h = t ? t.h() * 2*Math.PI/t.fullCircle() : 0, o = pos, s = scale / data.unitsPerEm; str.split('').map(c => { if (c == '\n') { pos = o = rotAdd([0, 10 * scale], o, h); return; } const glyph = (data.glyphs[c] || data.glyphs[' ']), d = glyph.d; d.forEach( (p, k) => { t && t.up(); for (let i=0; i<p.length; i+=2) { t && t.goto(rotAdd([p[i]*s, p[i+1]*s], pos, h)); t && (!isDown || t.down()); } }); pos = rotAdd([glyph.x*s, 0], pos, h); }); if(isDown) t.down(); return rotAdd([0, 10*scale], pos, h); } bboxPrint(t, str, scale = 1) { const rft = new RangeFinderTurtle(t.pos()); rft.degrees(t.fullCircle()); rft.seth(t.h()); rft.up(); this.print(rft, str, scale); this.print(t, str, scale); return rft.bbox(); } size(t, str, scale = 1) { const rft = new RangeFinderTurtle(); rft.up(); this.print(rft, str, scale); return { width: rft.rangeX[1] - rft.rangeX[0], height: rft.rangeY[1] - rft.rangeY[0], bbox: t.h() === 0? rft.bbox(): this.bbox(t, str, scale) } } bbox(t, str, scale = 1) { const rft = new RangeFinderTurtle(); rft.degrees(t.fullCircle()); rft.seth(t.h()); rft.up(); this.print(rft, str, scale); return rft.bbox(); } dimensions(scale = 1, standardCharacter = 'x') { const t = new Turtle(); const x = this.size(t, standardCharacter, scale); const allLower = this.size(t, 'abcdefghijklmnopqrstuvwxyz', scale); const allUpper = this.size(t, 'ABCDEFGHIJKLMNOPQRSTUVWXYZ', scale); // property names from: https://www.onlineprinters.co.uk/magazine/font-sizes/ return { height: x.height, width: x.width, ascenders: Math.abs(allLower.bbox[0][1]) - x.height, descenders: Math.abs(allLower.bbox[1][1]), capitalHeight: Math.abs(allUpper.bbox[0][1]), capitalDescenders: Math.abs(allUpper.bbox[1][1]) }; } } return new Text(); } 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 path(vectors) {return vectors.reduce((a,c) => a.length==0?[c]:[...a, V.add(c, a[a.length-1])], []);} 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; }