{"version":3,"file":"GraphicView-GjVClkja.js","sources":["../../src/modules/aleaFigure/coordinates.js","../../src/modules/aleaFigure/grandeurs.js","../../src/modules/aleaFigure/outils.js","../../src/modules/aleaFigure/elements.js","../../src/modules/aleaFigure/getMathalea2DExport.js","../../src/modules/aleaFigure/GraphicView.js"],"sourcesContent":["import { texNombre2 } from '../../lib/outils/texNombre.js'\nimport { round } from 'mathjs'\n/**\n  * @class for coordinates\n  */\nexport class GVCoordinates {\n  r /** number */ = 0\n  x /** number */ = 0\n  y /** number */ = 0\n  theta /** number */ = 0\n  getCartesianCoordinates () /** GVCartesian */ {\n    if (this instanceof GVPolar) {\n      return new GVCartesian(\n        this.r * Math.cos(this.theta),\n        this.r * Math.sin(this.theta)\n      )\n    } else {\n      return this\n    }\n  }\n\n  getPolarCoordinates () /** GVPolar */{\n    if (this instanceof GVCartesian) {\n      return new GVPolar(\n        Math.sqrt(this.x ** 2 + this.y ** 2),\n        Math.atan(this.y / this.x))\n    } else {\n      return this\n    }\n  }\n\n  format () {\n    return `(${texNombre2(round(this.x, 3))}{;}${texNombre2(round(this.y, 3))})`.replaceAll(',', '{,}').replaceAll('{{,}}', '{,}')\n  }\n}\n/**\n      * @class for cartesian coordinates\n      */\nexport class GVCartesian extends GVCoordinates {\n  constructor (x /** number */, y /** number */) {\n    super()\n    this.x = x\n    this.y = y\n  }\n\n  format () {\n    return `(${texNombre2(round(this.x, 3))}{;}${texNombre2(round(this.y, 3))})`.replaceAll(',', '{,}').replaceAll('{{,}}', '{,}')\n  }\n}\n/**\n      * @class for polar coordinates\n      */\nexport class GVPolar extends GVCoordinates {\n  constructor (r /** number */, theta /** number */) {\n    super()\n    this.r = r\n    this.theta = theta\n  }\n\n  format () {\n    return `(${texNombre2(round(this.r, 3))}{;}${texNombre2(round(this.theta, 3))})`.replaceAll(',', '{,}').replaceAll('{{,}}', '{,}')\n  }\n}\n","import { texNombre2 } from '../../lib/outils/texNombre.js'\nimport { simplify, parse, unit, max, add, subtract, abs, log10, random, round, isConstantNode } from 'mathjs'\nimport { aleaName } from '../outilsMathjs.js'\nimport { GVGraphicObject } from './elements.js'\n\n/**\n  * Grandeur, methods for operations\n  *\n  */\nexport class GVGrandeur {\n  value /** number */\n  precision /** number */\n  unit /** string */\n  toFixed /** number */\n  nameAndValue /** string */\n  _name /** string */\n  calcul /** string */\n  constructor (name /** string | GVPoint[] */, value /** number */, precision /** number */ = 1, unit /** string */ = '') {\n    this.value = round(value, precision)\n    this.precision = precision\n    this.unit = unit\n    this.toFixed = round(this.value, this.precision)\n    this.name = name\n  }\n\n  set name (newname /** string | GVPoint[] */) {\n    if (typeof newname === 'string') {\n      this._name = newname\n    } else {\n      this._name = (aleaName(newname).map(x => x.name)).join('')\n    }\n    this.nameAndValue = `$ {${this.name}=${texNombre2(this.toFixed).replace(',', '{,}')}~${this.unit.replace('deg', '\\\\degree')}}$`.replace('~\\\\degree', '\\\\degree')\n  }\n\n  get name () { return this._name }\n  format () {\n    return `{${texNombre2(this.toFixed).replace(',', '{,}')}~${this.unit.replace('deg', '\\\\degree')}}`.replace('~\\\\degree', '\\\\degree')\n  }\n\n  aleaName (...name/** (string | GVGraphicObject)[] */) {\n    this.name = aleaName(name.map(x => {\n      if (x instanceof GVGraphicObject) {\n        return x.name\n      } else {\n        return x\n      }\n    }), name.length).join('')\n  }\n\n  multiply (a /** GVGrandeur */) {\n    const expression = simplify([this.name, a.name].filter(x => x !== '').join('*').replaceAll('{', '(').replaceAll('}', ')')).toString()\n    const calcul = parse(unit(this.toFixed + this.unit).multiply(unit(a.toFixed + a.unit)).toString())\n\n    return new GVGrandeur(\n      expression,\n\n      parseFloat(isConstantNode(calcul) ? calcul.toString() : calcul.args[0].toString()),\n      this.precision + a.precision,\n\n      isConstantNode(calcul) ? '' : calcul.args[1].toString()\n    )\n  }\n\n  divide (a /** GVGrandeur */) {\n    const expression = simplify([this.name, a.name].filter(x => x !== '').join('/').replaceAll('{', '(').replaceAll('}', ')')).toString()\n    const calcul = parse(unit(this.toFixed + this.unit).divide(unit(a.toFixed + a.unit)).toString())\n    return new GVGrandeur(\n      expression,\n\n      parseFloat(isConstantNode(calcul) ? calcul.toString() : calcul.args[0].toString()),\n      this.precision - a.precision,\n\n      isConstantNode(calcul) ? '' : calcul.args[1].toString()\n    )\n  }\n\n  add (a /** GVGrandeur */) {\n    const expression = simplify([this.name, a.name].filter(x => x !== '').join('+').replaceAll('{', '(').replaceAll('}', ')')).toString()\n    const calcul = parse(add(unit(this.toFixed + this.unit), unit(a.toFixed + a.unit)).toString())\n    return new GVGrandeur(\n      expression,\n\n      parseFloat(isConstantNode(calcul) ? calcul.toString() : calcul.args[0].toString()),\n      max(this.precision, a.precision),\n\n      isConstantNode(calcul) ? '' : calcul.args[1].toString()\n    )\n  }\n\n  subtract (a /** GVGrandeur */) {\n    const expression = simplify([this.name, a.name].filter(x => x !== '').join('-').replaceAll('{', '(').replaceAll('}', ')')).toString()\n    const calcul = parse(subtract(unit(this.toFixed + this.unit), unit(a.toFixed + a.unit)).toString())\n    return new GVGrandeur(\n      expression,\n\n      parseFloat(isConstantNode(calcul) ? calcul.toString() : calcul.args[0].toString()),\n      max(this.precision, a.precision),\n\n      isConstantNode(calcul) ? '' : calcul.args[1].toString()\n    )\n  }\n\n  hypotenuse (a /** GVGrandeur */) {\n    return a.pow(2).add(this.pow(2)).sqrt()\n  }\n\n  /**\n    * this^n\n    * @param {number} n // Integer\n    * @returns {GVGrandeur}\n    */\n  pow (n /** number */) /** GVGrandeur */ {\n    return new GVGrandeur(this.name + '^{' + n + '}', Math.pow(this.toFixed, n), n * this.precision, this.unit + '^' + n)\n  }\n\n  /**\n    * this^n\n    * @param n // Integer\n    * @returns {GVGrandeur}\n    */\n  sqrt () /** GVGrandeur */ {\n    return new GVGrandeur('\\\\sqrt{' + this.name + '}', Math.pow(this.toFixed, 0.5), Math.floor(0.5 * this.precision), 'cm')\n  }\n\n  abs () /** GVGrandeur */ {\n    return new GVGrandeur(\n      this._name,\n      abs(this.value),\n      this.precision,\n      this.unit\n    )\n  }\n\n  neg () /** GVGrandeur */ {\n    return new GVGrandeur(\n      '-' + this.name,\n      -this.value,\n      this.precision,\n      this.unit\n    )\n  }\n\n  to (newUnit /** string */) /** GVGrandeur */ {\n    const thenumber = abs(unit(this.value, this.unit))\n    const conversion = abs(thenumber.to(newUnit))\n\n    const precision = Math.max(0, this.precision - log10(parse(conversion.toString()).args[0].value / parse(thenumber.toString()).args[0].value))\n    return new GVGrandeur(\n      this.name,\n\n      parse(conversion.toString()).args[0].value,\n      precision,\n      newUnit\n    )\n  }\n}\n/**\n  * Quantity random\n  * @param {number} nmin\n  * @param {number} nmax\n  * @param {number} digit\n  * @param {string} name\n  * @param {string} unit\n  * @returns {GVGrandeur}\n  */\nexport function qrandom (nmin /** number */ = 0, nmax /** number */ = 1, digit /** number */ = max(0, -log10(abs(nmax - nmin))), name /** string */ = '', unit /** string */ = '') /** GVGrandeur */ {\n  return new GVGrandeur(\n    name,\n    round(random(nmin, nmax), max(digit, 0)),\n    digit,\n    unit\n  )\n}\n","import { GVPoint, GVPolygon, GVSegment, GVLine } from './elements.js'\nimport { GVGrandeur } from './grandeurs.js'\nexport function circularPermutation (arg /** string | any[] */, n/** number */ = Math.random() * arg.length)/** any[] */ {\n  if (typeof arg === 'string') {\n    arg = arg.split('')\n  }\n  n = parseInt((n % arg.length).toString())\n  return arg.concat(arg).splice(n, arg.length)\n}\nexport function getDimensions (...figures) {\n  const listePoints = []\n  const listeXPoints = []\n  const listeYPoints = []\n  for (const fig of figures) {\n    if (fig instanceof GVPoint) {\n      listePoints.push(fig)\n      listeXPoints.push(fig.x)\n      listeYPoints.push(fig.y)\n    } else if (fig instanceof GVPolygon) {\n      listePoints.push(...fig.vertices)\n      listeXPoints.push(fig.getDimensions()[0], fig.getDimensions()[2])\n      listeYPoints.push(fig.getDimensions()[1], fig.getDimensions()[3])\n    }\n  }\n  const xmin = Math.min(...listeXPoints)\n  const xmax = Math.max(...listeXPoints)\n  const ymin = Math.min(...listeYPoints)\n  const ymax = Math.max(...listeYPoints)\n  return [xmin, ymin, xmax, ymax]\n}\n/**\n  * Euclidean quotient\n  * @param {number} x\n  * @returns {number}\n  */\nexport function quotient (x/** number */, y/** number */)/** number */ {\n  return x - x % y\n}\nexport function name (s, ...p) {\n  p = p.map((x, k) => {\n    if (x instanceof GVGrandeur) {\n      return String.raw`${s.raw[k]}` + x.name\n    } else if (x instanceof GVSegment) {\n      return String.raw`${s.raw[k]}` + `${x.name}` // `[${x.name}]`\n    } else if (x instanceof GVLine) {\n      return String.raw`${s.raw[k]}` + `${x.name}` // `(${x.name})`\n    } else if (x instanceof GVPoint || x instanceof GVPolygon) {\n      return String.raw`${s.raw[k]}` + `${x.name}`\n    } else {\n      return String.raw`${s.raw[k]}` + `${x}`\n    }\n  })\n  return p.join('') + s.raw[s.length - 1]\n}\n","/* eslint-disable no-useless-constructor */\nimport { point, tracePoint } from '../../lib/2d/points.js'\nimport { latexParCoordonnees } from '../../lib/2d/textes.js'\n/* eslint-disable no-unused-vars */\nimport { context } from '../context.js'\nimport { GVCartesian, GVCoordinates } from './coordinates.js'\nimport { aleaName } from '../outilsMathjs.js'\nimport { dot, round, cross } from 'mathjs'\nimport { circularPermutation, getDimensions } from './outils.js'\n\n/**\n * @class\n * @classdesc Graphic object like Point, Line, Segment etc.\n */\nexport class GVGraphicObject {\n  visible\n  /** boolean */\n  _name\n  /** string */\n  color /** string */ = 'black'\n\n  constructor () {\n    this.visible = false\n    this.name = ''\n  }\n\n  aleaName (...name /** (string | GVGraphicObject)[] */) {\n    this.name = aleaName(name.map(x => {\n      if (x instanceof GVGraphicObject) {\n        return x.name\n      } else {\n        return x\n      }\n    }), name.length).join('')\n  }\n\n  set name (newname) {\n    this._name = newname\n  }\n\n  get name () {\n    return this._name\n  }\n\n  getGGB () {\n    return this.name\n  }\n\n  /**\n     * Move this right to figures\n     * @param figures\n     */\n  moveRight (...figures/** GVGraphicObject[] */) {\n    const [xmin1, ymin1, ymax1] = getDimensions(this)\n    const [, ymin2, xmax2, ymax2] = getDimensions(...figures)\n    const P1 = new GVPoint(xmin1, ymin1)\n    const P2 = new GVPoint(xmax2, ymax2)\n    const t = new GVVector(P1, P2)\n    this.move(t.add(new GVVector(4, 0)).sub(new GVVector(0, (ymax2 - ymin2 + ymax1 - ymin1) / 2)))\n  }\n\n  /**\n     * Déplace l'objet\n     * @param {GVVector} V\n     */\n  move (V /** GVVector */) {\n    if (this instanceof GVPoint) {\n      this.x = this.add(V).x\n      this.y = this.add(V).y\n    } else if (this instanceof GVPolygon) {\n      for (const P of this.vertices) {\n        P.x = P.add(V).x\n        P.y = P.add(V).y\n      }\n    }\n  }\n}\n\n/**\n * @class\n * @classdesc Caracteristics of a point in an euclidean plan\n */\nexport class GVPoint extends GVGraphicObject {\n  coordinates\n  /** GVCoordinates */\n  polarCoordinates\n  /** GVPolar */\n  cartesianCoordinates\n  /** GVCartesian */\n  type\n  /** string */\n  x\n  /** number */\n  y\n  /** number */\n  r\n  /** number */\n  theta\n  /** number */\n  ggb\n  /** string */\n  dot\n  /** any */\n  labelPoints\n  /** [GVPoint, GVPoint, GVPoint] */\n  label /** boolean */ = false\n  M2D\n\n  /** any */\n  constructor (arg1/** GVCoordinates | number */, arg2 /** number */ = 0) {\n    super()\n    if (arg1 instanceof GVCoordinates) {\n      this.coordinates = arg1\n    } else {\n      this.coordinates = new GVCartesian(arg1, arg2)\n    }\n    this.polarCoordinates = this.getPolarCoordinates()\n    this.cartesianCoordinates = this.getCartesianCoordinates()\n    this.name = ''\n    this.type = 'Point'\n    this.x = this.cartesianCoordinates.x\n    this.y = this.cartesianCoordinates.y\n    this.r = this.polarCoordinates.r\n    this.theta = this.polarCoordinates.theta\n    this.ggb = `${this.name} = (${this.x},${this.y})`\n    this.M2D = point(this.x, this.y, '', 'above right')\n  }\n\n  getPolarCoordinates ()/** GVCartesian */ {\n    return this.coordinates.getPolarCoordinates()\n  }\n\n  getCartesianCoordinates () {\n    return this.coordinates.getCartesianCoordinates()\n  }\n\n  xSVG = function (coeff) {\n    return round(this.x * coeff, 3)\n  }\n\n  ySVG = function (coeff) {\n    return -round(this.y * coeff, 3)\n  }\n\n  getRotate (O /** GVPoint */, angle /** number */) {\n    return new GVPoint(\n      new GVCartesian(\n        (this.x - O.x) * Math.cos(angle) - (this.y - O.y) * Math.sin(angle) + O.x,\n        (this.x - O.x) * Math.sin(angle) + (this.y - O.y) * Math.cos(angle) + O.y\n      ))\n  }\n\n  /**\n     *\n     * @param {GVVector|GVPoint} X\n     * @returns {GVPoint}\n     */\n  add (X) {\n    return new GVPoint(new GVCartesian(this.x + X.x, this.y + X.y))\n  }\n\n  /**\n     *\n     * @param {GVVector|GVPoint} X\n     * @returns {GVPoint}\n     */\n  sub (X) {\n    return new GVPoint(new GVCartesian(this.x - X.x, this.y - X.y))\n  }\n\n  /**\n     * homothétie de centre (0,0) de rapport k\n     * @param {number} k\n     * @returns {GVPoint}\n     */\n  multiply (k) {\n    return new GVPoint(new GVCartesian(this.x * k, this.y * k))\n  }\n\n  /**\n     * homothétie de centre (0,0) de rapport 1/k\n     * @param {number} k\n     * @returns {GVPoint}\n     */\n  divide (k) {\n    if (k !== 0) return new GVPoint(new GVCartesian(this.x / k, this.y / k))\n  }\n\n  /**\n     * retourne les coordonnées barycentrique du GVPoint dans le repère formé par les trois GVPoint en argument.\n     * @param {GVPoint} A\n     * @param {GVPoint} B\n     * @param {GVPoint} C\n     * @returns {[number,number,number]}\n     */\n  getBarycentriqueCoords (A, B, C) {\n    const a = determinant(B.sub(this), C.sub(this))\n    const b = determinant(C.sub(this), A.sub(this))\n    const c = determinant(A.sub(this), B.sub(this))\n    return [a, b, c]\n  }\n\n  /**\n     * retourne true si le GVPoint est à l'intérieur du triangle formé par les 3 GVPoints en argument\n     * @param {GVPoint} A\n     * @param {GVPoint} B\n     * @param {GVPoint} C\n     * @returns {boolean}\n     */\n  isInTriangle (A /** GVPoint */, B /** GVPoint */, C /** GVPoint */) /** boolean */ {\n    return Math.min(...this.getBarycentriqueCoords(A, B, C)) > 0 || Math.max(...this.getBarycentriqueCoords(A, B, C)) < 0\n  }\n\n  /**\n     * Get the symetric of P with this\n     * @param {GVPoint} P\n     * @returns {GVPoint}\n     */\n  getSymetric (P) {\n    return barycentre([this, P], [2, -1])\n  }\n\n  /**\n     *\n     * @param {GVPoint} O\n     * @param {number} k\n     * @returns {GVPoint}\n     */\n  getHomothetic (O, k) {\n    return new GVPoint(\n      new GVCartesian(\n        k * this.x + (1 - k) * O.x,\n        k * this.y + (1 - k) * O.y\n      ))\n  }\n\n  /**\n     * Retourne un vecteur position du GVPoint (origine (0;0) extrémité le GVPoint.\n     * @returns {GVVector}\n     */\n  getVector () {\n    return new GVVector(this.x, this.y)\n  }\n\n  /**\n     * Retourne une déclaration pour geogebra utilisé par la méthode exportGGB() qui elle est inutilisée.\n     * @returns {string}\n     */\n  getGGB () {\n    this.ggb = `${this.name} = (${this.x},${this.y})`\n    return `${this.name} = (${this.x},${this.y})`\n  }\n\n  showName (scaleppc /** number */ = 1) /** string */ {\n    let label\n    /** any */\n    const splitname = this.name.split('_')\n    const nameFormat = splitname.length === 1 ? splitname[0] : `${splitname[0]}_{${splitname[1]}}`\n    if (this.labelPoints !== undefined) {\n      const P1 = this.labelPoints[0]\n      const P3 = this.labelPoints[2]\n      const S = this.labelPoints[1]\n      const v1 = P1.sub(S).getVector().getNormed()\n      const v3 = P3.sub(S).getVector().getNormed()\n      let P /** GVPoint */\n      if (v1.colinear(v3)) { // Colinéaires\n        P = S.add(v1.getNormal().multiply(scaleppc * 0.4))\n      } else { // Non colinéaires\n        P = S.getSymetric(S.add(v1.add(v3).getNormed().multiply(scaleppc * 0.4)))\n      }\n      label = latexParCoordonnees(nameFormat, P.x, P.y, 'black', 0, 0, '', 8)\n      //\n      this.labelPoints = [P1, S, P3]\n    } else {\n      label = latexParCoordonnees(nameFormat, this.x, this.y + 0.2 * scaleppc, 'black', 0, 0, '', 8)\n    }\n    this.label = true\n    return label\n  }\n\n  showDot () {\n    const splitname = this.name.split('_')\n    let nameFormat = splitname.length === 1 ? splitname[0] : `${splitname[0]}_{${splitname[1]}}`\n    if (context.isHtml) nameFormat = `$${nameFormat}$`\n    this.dot = tracePoint(point(this.x, this.y, nameFormat, 'above'))\n    return this\n  }\n\n  set name (newname) {\n    this._name = newname\n    this.ggb = `${this.name} = (${this.x},${this.y})`\n  }\n\n  get name () {\n    return this._name\n  }\n}\n\n/**\n * @class\n * @property {number} x\n * @property {number} y\n * @property {number} norme\n */\nexport class GVVector {\n  x /** number */ = 0\n  y /** number */ = 0\n  norme\n\n  /** number */\n  constructor (arg1 /** number | GVPoint */, arg2 /** number | GVPoint */) {\n    if (typeof arg1 === 'number' && typeof arg2 === 'number') {\n      this.x = arg1\n      this.y = arg2\n    } else if (arg1 instanceof GVPoint && arg2 instanceof GVPoint) {\n      this.x = arg2.x - arg1.x\n      this.y = arg2.y - arg1.y\n    }\n    this.norme = Math.sqrt(this.x ** 2 + this.y ** 2)\n  }\n\n  /**\n     * retourne un vecteur directeur colinéaire de norme 1\n     * @returns {GVVector}\n     */\n  getNormed () {\n    const xy = Math.sqrt(this.x ** 2 + this.y ** 2)\n    return new GVVector(this.x / xy, this.y / xy)\n  }\n\n  /**\n     * retourne le vecteur normal\n     * @returns {GVVector}\n     */\n  getNormal () {\n    return new GVVector(-this.y, this.x)\n  }\n\n  /**\n     * Ajoute vectoriellement un GVPoint ou un GVVector\n     * @param {GVPoint | GVVector} X\n     * @returns {GVVector}\n     */\n  add (X) {\n    return new GVVector(this.x + X.x, this.y + X.y)\n  }\n\n  /**\n     * soustrait vectoriellement un GVPoint ou un GVVector\n     * @param {GVPoint | GVVector} X\n     * @returns {GVVector}\n     */\n  sub (X) {\n    return new GVVector(this.x - X.x, this.y - X.y)\n  }\n\n  /**\n     * multiplie le GVVector par k\n     * @param {number} k\n     * @returns {GVVector}\n     */\n  multiply (k) {\n    return new GVVector(this.x * k, this.y * k)\n  }\n\n  /**\n     * retoune l'opposé du GVVector\n     * @returns {GVVector}\n     */\n  neg () {\n    return new GVVector(-this.x, -this.y)\n  }\n\n  /**\n     * Retourne lle produit scalaire du GVVector et de X\n     * @param {GVVector|GVPoint} X\n     * @returns {number}\n     */\n  dot (X) {\n    return dot([this.x, this.y], [X.x, X.y]) // ne pas confondre ce dot qui vient de mathjs et le this.dot() de GVVector !\n  }\n\n  /**\n     * retourne le produit vectoriel du GVVector avec X\n     * @param {GVVector|GVPoint} X\n     * @returns {math.MathCollection}\n     */\n  cross (X) {\n    return cross([this.x, this.y, 0], [X.x, X.y, 0]) // ne pas confondre ce cross qui vient de mathjs et le this.cross() de GVVector !\n  }\n\n  /**\n     * retourne true si le GVVector et V sont colinéaires\n     * @param {GVVector} V\n     * @returns {boolean}\n     */\n  colinear (V) {\n    return parseFloat(cross([this.x, this.y, 0], [V.x, V.y, 0])[2].toFixed(15)) === 0\n  }\n}\n\n/**\n * @class\n * @property {GVVector} direction\n * @property {GVPoint} A\n * @property {GVPoint|GVVector} B\n * @property {string} type\n * @property {number} a\n * @property{number} b\n * @property {number} c\n * @property {string} ggb\n * @classdesc Caracteristics of a line in an euclidean plan (ax+by=c)\n */\nexport class GVLine extends GVGraphicObject {\n  direction\n  A\n  B\n  type\n  a = 0\n  b = 0\n  c = 0\n  ggb\n  // Une droite sera définie par deux points distincts ou un point et une direction\n  // Il faudrait deux constructeurs ?\n  constructor (A, B) {\n    super()\n    this.direction = B instanceof GVVector ? B : new GVVector(B.x - A.x, B.y - A.y)\n    this.A = A\n    this.B = B instanceof GVPoint ? B : new GVPoint(new GVCartesian(A.x + B.x, A.y + B.y))\n    this.getEquation()\n    this.type = 'Line'\n    this.ggb = `${this.name}: ${this.a}*x+${this.b}*y=${this.c})`\n  }\n\n  /**\n     * retourne l'ordonnée du point de la droite d'abscisse x si il existe\n     * @param {number} x\n     * @returns {undefined|number}\n     */\n  getYPoint (x) {\n    return this.b === 0 ? undefined : (this.c - this.a * x) / this.b\n  }\n\n  /**\n     * retourne l'abscisse du point de la droite d'ordonnée y si il existe\n     * @param {number} y\n     * @returns {undefined|number}\n     */\n  getXPoint (y) {\n    return this.a === 0 ? undefined : (this.c - this.b * y) / this.a\n  }\n\n  /**\n     * renseigne l'équation de la droite (ses propriétés a, b et c\n     */\n  getEquation () {\n    const directionUnit = this.direction.getNormed()\n    this.a = -directionUnit.y\n    this.b = directionUnit.x\n    this.c = this.a * this.A.x + this.b * this.A.y\n  }\n\n  /**\n     * retourne le point d'intersection de la droite avec une autre\n     * @param {GVLine} L\n     * @returns {GVPoint|undefined}\n     */\n  getIntersect (L) {\n    const delta = L.a * this.b - this.a * L.b\n    if (delta.toFixed(15) !== '0') {\n      const deltax = -(L.b * this.c - this.b * L.c)\n      const deltay = L.a * this.c - this.a * L.c\n      const point = new GVPoint(new GVCartesian(deltax / delta, deltay / delta))\n      return point\n    }\n  }\n\n  /**\n     * Retourne la perpendiculaire à cette droite passant par P\n     * @param {GVPoint} P\n     * @returns {GVLine}\n     */\n  getPerpendicularLine (P) {\n    return new GVLine(P, this.direction.getNormal())\n  }\n\n  /**\n     * Get the symétric of P with this\n     * @param {GVPoint} P\n     * @returns {GVPoint}\n     */\n  getSymetric (P) {\n    return barycentre([this.getIntersect(this.getPerpendicularLine(P)), P], [2, -1])\n  }\n\n  /**\n     * Renseigne la propriété name de l'objet ainsi que sa propriété ggb\n     * @param {string} newname\n     */\n  set name (newname) {\n    this._name = newname\n    this.ggb = `${this.name}: ${this.a}*x+${this.b}*y=${this.c})`\n  }\n\n  /**\n     * récupère la propriété name de l'objet\n     * @returns {*}\n     */\n  get name () {\n    return this._name\n  }\n}\n\n/**\n * Retourne le déterminant de deux vecteurs\n * @param {GVVector|GVPoint} X\n * @param {GVVector|GVPoint} Y\n * @returns {number}\n */\nexport function determinant (X, Y) {\n  return X.x * Y.y - X.y * Y.x\n}\n\n/**\n * Retourne le baricentre d'une liste de GVPoint affectés des coefficients d'une liste de nombres\n * @param {GVPoint[]} P\n * @param {number[]} a\n * @returns {GVPoint}\n */\nexport function barycentre (P /** GVPoint[] */, a /** number[] */) /** GVPoint */ {\n  if (Array.isArray(P) && Array.isArray(a) && P.length === a.length) {\n    const pointsPonderes = P.map((x, i) => x.multiply(a[i]))\n    return pointsPonderes.reduce((accumulator, curr) => accumulator.add(curr)).divide(a.reduce((accumulator, curr) => accumulator + curr))\n  } else {\n    window.notify('fonction barycentre() de AleaFigure mal employée', { points: P, coefficients: a })\n  }\n}\n\n/**\n * @class\n * @property {boolean} label\n * @property {string} text\n * @property {string} textColor\n * @property {boolean} direct\n * @property {'Segment'} type\n * @param {GVPoint} A\n * @param {GVPoint} B\n * @classdesc Caracteristics of a segment in an euclidean plan\n */\nexport class GVSegment extends GVLine {\n  label\n  text = ''\n  textColor = 'black'\n  direct = true\n\n  constructor (A, B) {\n    super(A, B)\n    this.type = 'Segment'\n    this.A = A\n    this.B = B\n    this.aleaName(this.A, this.B)\n    this.getEquation()\n  }\n\n  /**\n     * Retourne le label de l'objet et fixe la propriété label de l'objet à true\n     * @returns {Vide2d|LatexParCoordonnees}\n     */\n  showLabel () {\n    let label\n    const P = new GVPoint((this.A.x + this.B.x) / 2, (this.A.y + this.B.y) / 2)\n    if (context.isHtml) {\n      label = latexParCoordonnees(this.name, P.x, P.y, 'black', 0, 0, '')\n    } else {\n      label = latexParCoordonnees(this.name, P.x, P.y, 'black', 0, 0, '')\n    }\n    this.label = true\n    return label\n  }\n}\n\n/**\n * @class\n * @property {GVPoint} A // centre\n * @property {GVPoint|number} B point de passage ou rayon\n * @property {number} r rayon\n * @property {'Circle'} type\n * @classdesc Caracteristics of a circle in an euclidean plan\n */\nexport class GVCircle extends GVGraphicObject {\n  A\n  B\n  type\n  a = 0\n  b = 0\n  r = 0\n\n  constructor (A, B) {\n    super()\n    this.type = 'Circle'\n    this.A = A\n    this.B = B instanceof GVPoint ? B : A\n    this.r = B instanceof GVPoint ? Math.sqrt((A.x - B.x) ** 2 + (A.y - B.y) ** 2) : B\n  }\n\n  /**\n     * Retourne un point du cercle correspondant à l'angle donné\n     * @param {number} theta\n     * @returns {GVPoint}\n     */\n  getPoint (theta) {\n    return new GVPoint(\n      new GVCartesian(\n        this.A.x + this.r * Math.cos(theta),\n        this.A.y + this.r * Math.sin(theta)\n      )\n    )\n  }\n}\n\n/**\n * @class\n * @property {GVPoint} A\n * @property {GVPoint} B\n * @property {GVPoint} C\n * @property {number} angle\n * @property {'Angle'} type\n * @property {boolean} direct\n * @property {GVVector} vBA\n * @property {GVVector} vBC\n * @property {boolean} right = false\n * @property {strig} fillColor = 'none'\n * @property {number} fillOpacity = 0.2\n * @property {boolean} rayon = true\n * @classdesc Caracteristics of an angle\n */\nexport class GVAngle extends GVGraphicObject {\n  A\n  B\n  C\n  angle\n  type\n  direct\n  vBA\n  vBC\n  right = false\n  fillColor = 'none'\n  fillOpacity = 0.2\n  rayon = true\n\n  constructor (A, B, C) {\n    super()\n    this.type = 'Angle'\n    const vA = new GVVector(A.x, A.y)\n    const vB = new GVVector(B.x, B.y)\n    const vC = new GVVector(C.x, C.y)\n    const vBA = vA.sub(vB).getNormed()\n    const vBC = vC.sub(vB).getNormed()\n    this.vBA = vBA\n    this.vBC = vBC\n    const cos = vBA.x * vBC.x + vBA.y * vBC.y\n    this.angle = Math.acos(cos)\n    this.A = B.add(vBA)\n    this.B = B\n    this.C = B.add(vBC)\n    this.direct = cross([vBA.x, vBA.y, 0], [vBC.x, vBC.y, 0])[2] > 0\n  }\n\n  /**\n     * Pour agrandir l'angle\n     * @param {number} scale\n     */\n  scale (scale) {\n    const vBA = this.vBA.multiply(scale)\n    const vBC = this.vBC.multiply(scale)\n    this.A = this.B.add(vBA)\n    this.C = this.B.add(vBC)\n  }\n}\n\n/**\n * @class\n * @property {GVPoint[]} vertices\n * @property {string} name\n * @classdesc Caracteristics of an angle\n */\nexport class GVPolygon extends GVGraphicObject {\n  showLabels /** boolean */ = true\n\n  constructor (...args /** GVPoint[] */) {\n    super()\n    this.vertices /** GVPoint[] */ = args\n    this.name = circularPermutation(args.map(x => x.name)).join('')\n  }\n\n  /**\n     * retourne les bordures d'un GVPolygon\n     * @returns {[number,number,number,number]}\n     */\n  getDimensions () {\n    const listXPoint = this.vertices.map(M => M.x)\n    const listYPoint = this.vertices.map(M => M.y)\n    const xmin = Math.min(...listXPoint)\n    const xmax = Math.max(...listXPoint)\n    const ymin = Math.min(...listYPoint)\n    const ymax = Math.max(...listYPoint)\n    return [xmin, ymin, xmax, ymax]\n  }\n}\n\n/**\n * @class\n * @property {number} longueur\n * @property {number} largeur\n * @property {number} ratio\n * @classdesc Caracteristics of a triangle\n */\nexport class GVRectangle extends GVPolygon {\n  longueur\n  largeur\n  ratio\n  constructor (...args /** GVPoint[] */) {\n    super(...args)\n    const [A, B, C] = args\n    const dimensions = [Math.sqrt((A.x - B.x) ** 2 + (A.y - B.y) ** 2), Math.sqrt((C.x - B.x) ** 2 + (C.y - B.y) ** 2)].sort()\n    this.largeur = dimensions[0]\n    this.longueur = dimensions[1]\n    this.ratio = this.longueur / this.largeur\n  }\n}\n\n/**\n * @class\n * @classdesc Caracteristics of a triangle\n */\nexport class GVTriangle extends GVPolygon {\n  constructor (...args /** GVPoint[] */) {\n    super(...args)\n  }\n}\n","import { arcPointPointAngle, cercle } from '../../lib/2d/cercle.js'\nimport { texteSurSegment } from '../../lib/2d/codages.js'\nimport { point } from '../../lib/2d/points.js'\nimport { polygone } from '../../lib/2d/polygones.js'\nimport { segment } from '../../lib/2d/segmentsVecteurs.js'\nimport { GVPolygon, GVAngle, GVPoint, GVLine, GVSegment, GVCircle } from './elements.js'\nimport { mathalea2d } from '../2dGeneralites.js'\nexport function getMathalea2DExport (graphic /** GVGraphicView */) {\n  if (graphic.allowResize) graphic.resize()\n  const scaleppc = 20 / (graphic.ppc ?? 20)\n  const clip = { xmin: graphic.xmin - scaleppc, xmax: graphic.xmax + scaleppc, ymin: graphic.ymin - scaleppc, ymax: graphic.ymax + scaleppc }\n\n  // On ajoute tous les éléments\n  const objs = []\n\n  if (graphic.clipVisible) {\n    const drawClip = polygone(\n      point(clip.xmin, clip.ymin, '', 'above'),\n      point(clip.xmax, clip.ymin, '', 'above'),\n      point(clip.xmax, clip.ymax, '', 'above'),\n      point(clip.xmin, clip.ymax, '', 'above')\n    )\n    if (drawClip != null) objs.push(drawClip)\n  }\n\n  for (const obj of graphic.geometricExport.filter(x => x.visible)) {\n    if (obj instanceof GVPoint) {\n      if (obj.dot != null) objs.push(obj.dot)\n      if (obj.label) {\n        const label = obj.showName(scaleppc)\n        if (label != null) objs.push(label)\n      }\n    } else if (obj instanceof GVLine && !(obj instanceof GVSegment)) {\n      // objs.push(droite(obj.a, obj.b, -obj.c))\n      const points = graphic.getExtremPointGraphicLine(obj)\n      if (points != null && Array.isArray(points)) objs.push(segment(points[0], points[1], obj.color ?? 'black'))\n    } else if (obj instanceof GVSegment) {\n      if (obj.A != null && obj.B != null) {\n        objs.push(segment(obj.A, obj.B, obj.color ?? 'black'))\n      }\n      if (obj.label) {\n        const label = obj.showLabel(scaleppc)\n        if (label != null) objs.push()\n      }\n      if (obj.text !== '') {\n        if (obj.A.M2D != null && obj.B.M2D != null) {\n          const points = obj.direct ? [obj.A.M2D, obj.B.M2D] : [obj.B.M2D, obj.A.M2D]\n          objs.push(texteSurSegment(obj.text, points[0], points[1], obj.textColor ?? 'black', 0.5 * scaleppc))\n        }\n      }\n    } else if (obj instanceof GVCircle) {\n      if (obj.A.M2D != null && obj.r > 0) {\n        objs.push(cercle(obj.A.M2D, obj.r))\n      }\n    } else if (obj instanceof GVAngle) {\n      if (Math.abs(obj.angle).toFixed(13) === (Math.PI / 2).toFixed(13) && obj.right) {\n        const P1 = obj.A\n        const P3 = obj.C\n        const S = obj.B\n        if (P1 instanceof GVPoint && P3 instanceof GVPoint && S instanceof GVPoint) {\n          const v1 = P1.sub(S).getVector().getNormed().multiply(scaleppc * 0.7)\n          const v3 = P3.sub(S).getVector().getNormed().multiply(scaleppc * 0.7)\n          const P = S.add(v1.add(v3)) // .add(corr)\n          P.showDot()\n          objs.push(...graphic.addSidesPolygon(S, S.add(v1), P, S.add(v3)).map(x => segment(x.A, x.B, obj.color)))\n        }\n      } else if (obj instanceof GVPolygon) {\n        if (obj.showLabels) {\n          obj.vertices.forEach(P => {\n            if (P instanceof GVPoint) {\n              objs.push(P.showName(scaleppc))\n            }\n          })\n        } /*\n        else {\n        }\n        */\n      } else {\n        obj.scale(scaleppc)\n        if (obj.A.M2D != null && obj.C.M2D != null) {\n          const extrems = obj.direct ? [obj.A.M2D, obj.C.M2D] : [obj.C.M2D, obj.A.M2D]\n          objs.push(arcPointPointAngle(...extrems, obj.angle / Math.PI * 180, obj.fillColor !== 'none' ? obj.rayon : true, obj.fillColor ?? 'none', obj.color ?? 'black', obj.fillOpacity ?? 0))\n        }\n      }\n    } else {\n      if (obj != null) objs.push(obj)\n    }\n  }\n  for (const obj of graphic.grid) {\n    const points = graphic.getExtremPointGraphicLine(obj)\n    if (points !== undefined) objs.push(segment(...points, obj.color ?? 'black'))\n  }\n  for (const obj of graphic.axes) {\n    const points = graphic.getExtremPointGraphicLine(obj)\n    if (Array.isArray(points) && points.length >= 2) {\n      const arrow = segment(...points, obj.color ?? 'black')\n      arrow.styleExtremites = '->'\n      objs.push(arrow)\n    }\n  }\n  return mathalea2d(Object.assign({}, { mainlevee: false, pixelsParCm: graphic.ppc, scale: graphic.scale * 0.7 }, clip), objs)\n}\n","/* eslint-disable no-unused-vars */\nimport { randomInt } from 'mathjs'\nimport { GVCartesian } from './coordinates.js'\nimport { GVRectangle, GVTriangle, GVPolygon, GVVector, GVAngle, GVPoint, GVLine, GVSegment, GVCircle, barycentre } from './elements.js'\nimport { getMathalea2DExport } from './getMathalea2DExport.js'\nimport { circularPermutation, quotient } from './outils.js'\nimport { aleaName } from '../outilsMathjs.js'\n/**\n * Donne une liste d'entiers relatifs dont on connait la somme.\n * @example > listeEntiersSommeConnue(4,10,-2)\n * < [1,-2,6,5]\n * @param {int} nbElements Nombre d'éléments de la liste\n * @param {int} total Somme des éléments de la liste (peut être un nombre négatif)\n * @param {int} [valMin = 1] Valeur minimale de chaque élément (peut être un nombre négatif)\n * @return {Array} Liste d'entiers relatifs\n * @author Frédéric PIOU\n */\nexport function listeEntiersSommeConnue (nbElements, total, valMin = 1) {\n  const liste = []\n  liste.push(randomInt(valMin, total - (nbElements - 1) * valMin + 1))\n  for (let j = 1; j < nbElements - 1; j++) {\n    liste.push(randomInt(liste[j - 1] + valMin, total - (nbElements - j - 1) * valMin + 1))\n  }\n  liste.push(total)\n  for (let j = nbElements - 1; j > 0; j--) {\n    liste[j] = liste[j] - liste[j - 1]\n  }\n  return liste\n}\n/**\n  * @class\n  * @classdesc Caracteristics of a graphic view\n  * @author Frédéric PIOU\n  */\nexport class GVGraphicView {\n  names/** string[] */\n  ppc /** number */\n  scale /** number */\n  geometric /**  GVGraphicObject[] */\n  geometricExport /**  GVGraphicObject[] */\n  grid /** GVLine[] */\n  axes /** GVLine[] */\n  xmin /** number */ = 0\n  ymin /** number */ = 0\n  xmax /** number */ = 10\n  ymax /** number */ = 10\n  width /** number */\n  height /** number */\n  ratio /** number */\n  clipVisible /** boolean */ = false\n  saveRatio /** boolean */ = true\n  allowResize /** boolean */ = true\n  showLabelPoint /** boolean */ = false\n  limit /** number */ = Infinity\n  _namesAlea /** boolean */ = true\n  constructor (xmin /** number */ = 0, ymin /** number */ = 0, xmax /** number */ = 10, ymax /** number */ = 10) {\n    this.setDimensions(xmin, ymin, xmax, ymax)\n    this.names = aleaName('ABCDEFGHIJKLMNOPRSTUVZ'.split(''))\n    this.ppc = 20 // Pixels per Centimeter\n    this.scale = 1 // Scale for Tikz\n    this.geometric = []\n    this.grid = []\n    this.axes = []\n  }\n\n  set namesAlea (names /** string[] | boolean) */) {\n    if (typeof names === 'string') this.names = aleaName(names)\n    if (names === false) this.names = 'ABCDEFGHIJKLMNOPRSTUVZ'.split('')\n  }\n\n  get namesAlea () {\n    return this.names\n  }\n\n  setDimensions (xmin = -5, ymin = -5, xmax = 5, ymax = 5) {\n    this.xmin = xmin\n    this.ymin = ymin\n    this.xmax = xmax\n    this.ymax = ymax\n    this.width = this.xmax - this.xmin\n    this.height = this.ymax - this.ymin\n    this.ratio = this.height / this.width\n  }\n\n  /**\n    * Show any Objects in Mathalea2D\n    * @example\n    * show(A,B,C,ABC)\n    */\n  show (...args /**  GVGraphicObject[] */) /**  GVGraphicObject[] */ {\n    const group = []\n    args.forEach(x => {\n      if (Array.isArray(x)) {\n        group.push(...x)\n      } else if (x instanceof GVPolygon) {\n        group.push(...x.vertices)\n        group.push(...this.addSidesPolygon(...x.vertices))\n        this.addLabelsPointsPolygon(...x.vertices)\n      } else {\n        group.push(x)\n      }\n    })\n    group.forEach(x => { x.visible = true })\n    return group\n  }\n\n  addGrid (step /** number */ = 1) {\n    for (let i = this.xmin; i < quotient(this.width, step); i++) {\n      const lineX = new GVLine(new GVPoint(i, 0), new GVVector(0, 1))\n      lineX.color = 'gray'\n      this.grid.push(lineX)\n    }\n    for (let i = this.ymin; i < quotient(this.height, step); i++) {\n      const lineY = new GVLine(new GVPoint(0, i), new GVVector(1, 0))\n      lineY.color = 'gray'\n      this.grid.push(lineY)\n    }\n  }\n\n  addAxes () {\n    const lineX = new GVLine(new GVPoint(0, 0), new GVVector(0, 1))\n    this.axes.push(lineX)\n    const lineY = new GVLine(new GVPoint(0, 0), new GVVector(1, 0))\n    this.axes.push(lineY)\n  }\n\n  getDimensions (...liste /**  GVGraphicObject[] */)/** [number, number, number, number] */ {\n    const listPoint = this.getListObjectTypeSelect('Point', liste)\n    const listXPoint = listPoint.map((X/** { x } */) => { return X.x })\n    const listYPoint = listPoint.map((Y/** { y } */) => { return Y.y })\n    const xmin = Math.min(...listXPoint)\n    const xmax = Math.max(...listXPoint)\n    const ymin = Math.min(...listYPoint)\n    const ymax = Math.max(...listYPoint)\n    return [xmin, ymin, xmax, ymax]\n  }\n\n  getWidth (...liste /**  GVGraphicObject[] */) /** number */ {\n    const [xmin, , xmax] = this.getDimensions(...liste)\n    return xmax - xmin\n  }\n\n  getHeight (...liste /**  GVGraphicObject[] */) /** number */ {\n    const [, ymin, , ymax] = this.getDimensions(...liste)\n    return ymax - ymin\n  }\n\n  getUponPoint (...liste /**  GVGraphicObject[] */) /** GVPoint */ {\n    const listePoints = this.getListObjectTypeSelect('Point', liste)\n    return this.getListObjectTypeSelect('Point', liste).sort((a, b) => b.y - a.y)[listePoints.length - 1]\n  }\n\n  geBelowPoint (...liste /**  GVGraphicObject[] */) /** GVPoint */ {\n  //   const listePoints = this.getListObjectTypeSelect('Point', liste) @Fixme à quoi ça sert ?\n    return this.getListObjectTypeSelect('Point', liste).sort((a, b) => b.y - a.y)[0]\n  }\n\n  getLeftPoint (...liste /**  GVGraphicObject[] */) /** GVPoint */ {\n    const listePoints = this.getListObjectTypeSelect('Point', liste)\n    return this.getListObjectTypeSelect('Point', liste).sort((a, b) => b.x - a.x)[listePoints.length - 1]\n  }\n\n  getRightPoint (...liste /**  GVGraphicObject[] */) /** GVPoint */ {\n    const listePoints = this.getListObjectTypeSelect('Point', liste)\n    return listePoints.sort((a, b) => b.x - a.x)[0]\n  }\n\n  /**\n    * Resize window of graphic view to the created points\n    * Keep the ratio\n    */\n  resize () {\n    // On commence par déterminer les dimensions à partir des abscisses et des ordonnées extrèmes\n    const [xmin, ymin, xmax, ymax] = this.getDimensions()\n    const [width, height] = [xmax - xmin, ymax - ymin]\n    // On fait une copie des dimensions obtenues\n    let newheight = 0 + height\n    let newwidth = 0 + width\n    // On calcule le ratio obtenu\n    const ratio = height / width\n    const k = ratio / this.ratio\n    // S'il faut conserver le ratio on ne modifie qu'une seule dimension\n    if (this.saveRatio) {\n      if (k < 1) { // La largeur est plus grande\n        newheight = height / k\n      } else { // La hauteur est plus grande\n        newwidth = width * k\n      }\n    } else { // Sinon seul le ratio change\n      this.ratio = newheight / newwidth\n    }\n    // La hauteur sera utilisée dans tous les cas pour le calcul de l'échelle.\n    // Elle sera donc conservée si le ratio ne l'est pas.\n    this.ppc = this.ppc * this.height / newheight\n    this.scale = this.scale * this.height / newheight\n    const deltaX = (newwidth - width) / 2\n    const deltaY = (newheight - height) / 2\n    this.setDimensions(xmin - deltaX, ymin - deltaY, xmax + deltaX, ymax + deltaY)\n  }\n\n  /**\n    * Give the list sorted of object with a given type\n    */\n  getListObjectTypeSelect (typeSelect = 'Point', liste /**  GVGraphicObject[] */ = this.geometric)/** any */ {\n    if (liste.length === 0) liste = this.geometric\n    switch (typeSelect) {\n      case 'Point':\n        return liste.filter(obj => obj instanceof GVPoint).sort(\n          (a, b) => {\n            const nameA = a.name.split('_')\n            const nameB = b.name.split('_')\n            if (nameA[0] === nameB[0]) {\n              return parseInt(nameA[1]) - parseInt(nameB[1])\n            } else {\n              return (-1) ** (nameA[0] > nameB[0] ? 0 : 1)\n            }\n          }\n        )\n      default:\n        return this.geometric.filter(obj => !(obj instanceof GVPoint)).sort(\n          (a, b) => {\n            const nameA = a.name.split('_')\n            const nameB = b.name.split('_')\n            if (nameA[0] === nameB[0]) {\n              return parseInt(nameA[1]) - parseInt(nameB[1])\n            } else {\n              return (-1) ** (nameA[0] > nameB[0] ? 0 : 1)\n            }\n          }\n        )\n    }\n  }\n\n  /**\n    * Search the last name not used and give a new name\n    */\n  getLastNameNotUsed (typeSelect = 'Point') {\n    switch (typeSelect) {\n      case 'Point': {\n        const list = this.getListObjectTypeSelect('Point')\n        let nonUseLetter\n        let i = 0\n        do {\n          const indice = i === 0 ? '' : `_${i}`\n          nonUseLetter = this.names.find(\n            letter => list.filter(x => x.name[0] === letter).find(\n              obj => obj.name === letter + indice\n            )?.name !== letter + indice)\n          if (nonUseLetter !== undefined) nonUseLetter += indice\n          i += 1\n        } while (nonUseLetter === undefined)\n        return nonUseLetter\n      }\n      case 'Segment':\n      case 'Circle':\n      case 'Line': {\n        const list = this.getListObjectTypeSelect('Segment').concat(this.getListObjectTypeSelect('Line'))\n        let nonUseLetter\n        let i = 0\n        do {\n          const indice = i === 0 ? '' : `_${i}`\n          nonUseLetter = this.names.find(\n            letter => list.filter(x => x.name[0] === letter.toLowerCase()).find(\n              obj => obj.name === letter.toLowerCase() + indice\n            )?.name !== letter.toLowerCase() + indice)\n          if (nonUseLetter !== undefined) nonUseLetter = nonUseLetter.toLowerCase() + indice\n          i += 1\n        } while (nonUseLetter === undefined)\n        return nonUseLetter\n        // return this.names.find(letter => list.find(obj => obj.name.split('')[0] === letter.toLowerCase())?.name.split('_')[0] !== letter.toLowerCase()).toLowerCase()\n      }\n    }\n  }\n\n  /**\n    * Give a new name\n    */\n  getNewName (typeSelect = 'Point') {\n    switch (typeSelect) {\n      case 'Point':\n        return this.getLastNameNotUsed(typeSelect)\n      case 'Segment':\n      case 'Circle':\n      case 'Line':\n        return this.getLastNameNotUsed(typeSelect)\n    }\n  }\n\n  aleaNameObject (...args /**  GVGraphicObject[] */) {\n    const names = aleaName(args.length)\n    args.forEach((x, i) => { x.name = names[i] })\n  }\n\n  /**\n    * Append new objects to the euclidean plan\n    * @param {number} n Number of point to create\n    * @param {number} step For coordinates\n    * @example\n    * this.addPoint(2,0.5) --> Add two points with coordinates step 0.5 precision\n    */\n  addPoint (n /** number */ = 1, step /** number */) /** GVPoint[] */ {\n    // Il faudrait donner la possibilité d'ajouter des points définis par leurs coordonnées\n    const newPoints = []\n    for (let i = 0; i < n; i++) {\n      let obj /** GVPoint */\n      let cpt = 0\n      do {\n        cpt += 1\n        obj = new GVPoint(\n          new GVCartesian(\n            step === undefined ? Math.random() * this.width + this.xmin : quotient(Math.random() * this.width + this.xmin, step),\n            step === undefined ? Math.random() * this.height + this.ymin : quotient(Math.random() * this.height + this.ymin, step)\n          )\n        )\n      } while (cpt < this.limit && (this.isCloseToExistingPoints(obj) || this.isCloseToLineThroughtExistingPoints(obj)))\n      obj.name = this.getNewName(obj.type)\n      if (this.showLabelPoint) {\n        obj.showDot()\n        obj.showName()\n      }\n      this.geometric.push(obj)\n      newPoints.push(obj)\n    }\n    return newPoints\n  }\n\n  /**\n    * Add intersect point of two lines in the view\n    */\n  addIntersectLine (line1/** GVLine | GVCircle */, line2/** GVLine | GVCircle */) {\n    if (line1 instanceof GVLine && line2 instanceof GVLine) {\n      const delta = line1.a * line2.b - line2.a * line1.b\n      if (delta.toFixed(15) !== '0') {\n        const deltax = -(line1.b * line2.c - line2.b * line1.c)\n        const deltay = line1.a * line2.c - line2.a * line1.c\n        const point = new GVPoint(new GVCartesian(deltax / delta, deltay / delta))\n        point.name = this.getNewName(point.type)\n        this.geometric.push(point)\n        return [point]\n      }\n    } else if (line1 instanceof GVCircle && line2 instanceof GVCircle) {\n      const d = this.distance(line1.A, line2.A)\n      if (d > line1.r + line2.r || d < (Math.abs(line1.r - line2.r))) {\n        return []\n      } else {\n        const a = (line1.r ** 2 - line2.r ** 2 + d ** 2) / (2 * d)\n        const h = Math.sqrt(line1.r ** 2 - a ** 2)\n        const x2 = line1.A.x + a * (line2.A.x - line1.A.x) / d\n        const y2 = line1.A.y + a * (line2.A.y - line1.A.y) / d\n        const x3 = x2 + h * (line2.A.y - line1.A.y) / d\n        const y3 = y2 - h * (line2.A.x - line1.A.x) / d\n        const P1 = new GVPoint(new GVCartesian(x3, y3))\n        const x4 = x2 - h * (line2.A.y - line1.A.y) / d\n        const y4 = y2 + h * (line2.A.x - line1.A.x) / d\n        const P2 = new GVPoint(new GVCartesian(x4, y4))\n        P1.name = P1.name || this.getNewName(P1.type)\n        P2.name = P2.name || this.getNewName(P2.type)\n        this.geometric.push(P1, P2)\n        return [P1, P2]\n      }\n    }\n  }\n\n  /**\n    * Zoom in or out\n    */\n  zoom (k /** number */ = 1.01) {\n    const xmin = k * (this.xmin - (this.xmax + this.xmin) / 2) + (this.xmax + this.xmin) / 2\n    const xmax = k * (this.xmax - (this.xmax + this.xmin) / 2) + (this.xmax + this.xmin) / 2\n    const ymin = k * (this.ymin - (this.ymax + this.ymin) / 2) + (this.ymax + this.ymin) / 2\n    const ymax = k * (this.ymax - (this.ymax + this.ymin) / 2) + (this.ymax + this.ymin) / 2\n    this.setDimensions(xmin, ymin, xmax, ymax)\n  }\n\n  /**\n    * Give the distance between tow points, a point and a line, two lines\n    */\n  distance (P /** GVPoint */, Y /** GVPoint | GVLine */) {\n    if (Y instanceof GVPoint) {\n      return Math.sqrt((P.x - Y.x) ** 2 + (P.y - Y.y) ** 2)\n    } else {\n      return Math.abs(Y.a * P.x + Y.b * P.y - Y.c) / Math.sqrt(Y.a ** 2 + Y.b ** 2)\n    }\n  }\n\n  /**\n    * Tempt to estimate if a point is close to the existing points\n    */\n  isCloseToExistingPoints (M /** GVPoint */) {\n    const listExistingPoints = this.getListObjectTypeSelect('Point')\n    const maxDistance = Math.min(this.height, this.width) / listExistingPoints.length / 3\n    if (listExistingPoints.length > 0) { return listExistingPoints.some(X => this.distance(X, M) < maxDistance) }\n    return false\n  }\n\n  /**\n    * Tempt to estimate if a point is close to the line through the existing point\n    */\n  isCloseToLineThroughtExistingPoints (M /** GVPoint */) {\n    const listExistingPoints = this.getListObjectTypeSelect('Point')\n    const litsExistingLine = this.getListObjectTypeSelect('Line')\n    // const numberOfPoints = listExistingPoints.length\n    const numberOfObjects = listExistingPoints.length + litsExistingLine.length\n    const result = []\n    const minDimension = Math.min(this.height, this.width) / numberOfObjects / 3\n    for (let i = 0; i < listExistingPoints.length; i++) {\n      for (let j = i + 1; j < listExistingPoints.length; j++) {\n        const d = new GVLine(listExistingPoints[i], listExistingPoints[j])\n        result.push(this.distance(M, d))\n      }\n    }\n    for (let i = 0; i < litsExistingLine.length; i++) {\n      result.push(this.distance(M, litsExistingLine[i]))\n    }\n    return result.some(x => x < minDimension && parseFloat(x.toFixed(15)) !== 0)\n  }\n\n  /**\n    * Add a new line to the view with new name\n    */\n  addLine (P1 = this.addPoint()[0], P2 = this.addPoint()[0]) {\n    const line = new GVLine(P1, P2)\n    line.name = this.getNewName(line.type)\n    this.geometric.push(line)\n    return line\n  }\n\n  /**\n    * Add a new Segment to the view with new name\n    */\n  addSegment (P1 = this.addPoint()[0], P2 = this.addPoint()[0]) {\n    const segment = new GVSegment(P1, P2)\n    this.geometric.push(segment)\n    return segment\n  }\n\n  /**\n    * Add a new circle center\n    * @param {GVPoint} C\n    * @param {GVPoint} P\n    * @returns {GVCircle}\n    */\n  addCircle (C = this.addPoint()[0], X /** GVPoint | number */)/** GVCircle */ {\n    const circle = new GVCircle(C, X)\n    circle.name = this.getNewName(circle.type)\n    this.geometric.push(circle)\n    return circle\n  }\n\n  /**\n    * Get the intersect point of a line and the bordure\n    */\n  getExtremPointGraphicLine (L/** GVLine */) {\n    const x = [\n      [L.getXPoint(this.ymin), this.ymin], // [xmin,xmax]\n      [L.getXPoint(this.ymax), this.ymax] // [xmin,xmax]\n    ]\n    const y = [\n      [this.xmin, L.getYPoint(this.xmin)], // [ymin,ymax]\n      [this.xmax, L.getYPoint(this.xmax)] // [ymin,ymax]\n    ]\n    const extremites = []\n    for (const u of x) {\n      if (u.every(v => v !== undefined) && u[0] >= this.xmin && u[0] <= this.xmax) { extremites.push(u) }\n    }\n    for (const u of y) {\n      if (u.every(v => v !== undefined) && u[1] >= this.ymin && u[1] <= this.ymax) { extremites.push(u) }\n    }\n    if (extremites.length === 2) {\n      return [\n        new GVPoint(new GVCartesian(extremites[0][0], extremites[0][1])),\n        new GVPoint(new GVCartesian(extremites[1][0], extremites[1][1]))\n      ]\n    } else {\n      return undefined\n    }\n  }\n\n  /**\n    * get a point between two points\n    * @param {GVPoint} point1\n    * @param {GVPoint} point2\n    * @returns {GVPoint}\n    */\n  getNewPointBetween (A, B) {\n    const k = Math.random()\n    return new GVPoint(\n      new GVCartesian(\n        (A.x - B.x) * k + B.x,\n        (A.y - B.y) * k + B.y\n      )\n    )\n  }\n\n  /**\n    * Add point between two but not too close to extrems\n    * @param {GVPoint} A\n    * @param {GVPoint} B\n    * @returns {GVPoint}\n    */\n  addPointBetween (A /** GVPoint */, B /** GVPoint */) /** GVPoint */ {\n    const barycentricsCoords = listeEntiersSommeConnue(2, 100, 15)\n    const P = barycentre([A, B], barycentricsCoords)\n    P.name = P.name || this.getNewName(P.type)\n    this.geometric.push(P)\n    return P\n  }\n\n  addPointDistance (A /** GVPoint */, r /** number */) {\n    let P /** GVPoint */\n    const circle = new GVCircle(A, r)\n    do {\n      const theta = Math.random() * Math.PI * 2\n      P = circle.getPoint(theta)\n    } while (this.isCloseToExistingPoints(P) || this.isCloseToLineThroughtExistingPoints(P))\n    P.name = this.getNewName(P.type)\n    this.geometric.push(P)\n    return P\n  }\n\n  addPointInPolygon (...args /** GVPoint[] */) {\n    const barycentricsCoords = listeEntiersSommeConnue(args.length, 100, 20 * 3 / args.length)\n    const P = barycentre(args, barycentricsCoords)\n    P.name = P.name || this.getNewName(P.type)\n    this.geometric.push(P)\n    return P\n  }\n\n  addPointOutPolygon (...args /** GVPoint[] */) /** GVPoint */ {\n    const barycentricsCoords = listeEntiersSommeConnue(args.length, 100, 20 * 3 / args.length)\n    const aleaI = Math.round(Math.random() * (barycentricsCoords.length - 2))\n    const P = new GVLine(args[aleaI], args[aleaI + 1]).getSymetric(barycentre(args, barycentricsCoords))\n    P.name = P.name || this.getNewName(P.type)\n    this.geometric.push(P)\n    return P\n  }\n\n  addPointOnPolygon (...args /** GVPoint[] */) /** GVPoint */ {\n    const barycentricsCoords = listeEntiersSommeConnue(2, 100, 20 * 3 / 2)\n    const P = barycentre(circularPermutation(args).slice(0, 2), barycentricsCoords)\n    P.name = P.name || this.getNewName(P.type)\n    this.geometric.push(P)\n    return P\n    /*\n     const barycentricsCoords = listeEntiersSommeConnue(args.length,100,20*3/args.length)\n     barycentricsCoords[Math.round(Math.random()*(barycentricsCoords.length-2))] = 0\n     const P = barycentre(args,barycentricsCoords)\n     P.name = P.name || this.getNewName(P.type)\n     this.geometric.push(P)\n     return P\n     */\n  }\n\n  placeLabelsPolygon (...args /** GVPoint[] */) {\n    for (let i = 1; i < args.length + 1; i++) {\n      const names = [args[args.length - 1]].concat(args).concat([args[0]])\n      names[i].showName()\n      names[i].labelPoints = [names[i - 1], names[i], names[i + 1]]\n    }\n  }\n\n  addSymetric (X /** GVPoint | GVLine */, ...args /** GVPoint[] */) /** GVPoint[] */ {\n    return args.map(x => {\n      const P = X.getSymetric(x)\n      P.name = P.name || this.getNewName(P.type)\n      this.geometric.push(P)\n      return P\n    })\n  }\n\n  addTranslate (V/** GVVector */, ...args /** GVPoint[] */) /** GVPoint[] */ {\n    return args.map(X => {\n      const P = X.add(V)\n      P.name = P.name || this.getNewName(P.type)\n      this.geometric.push(P)\n      return P\n    })\n  }\n\n  move (V/** GVVetor */, ...args /** GVPoint[] */) {\n    for (const X of args) {\n      X.x = X.add(V).x\n      X.y = X.add(V).y\n    }\n  }\n\n  /**\n    * Add three point, two point or one point aligned to others\n    * @param  {Point} P1 // If no point or one point we creat new points\n    * @param  {Point} P2 // If no point or one point we creat new points\n    * @returns {GVPoint[]}\n    */\n  addPointAligned (P1 = this.addPoint()[0], P2 = this.addPoint()[0])/** GVPoint[] */ {\n    let P3\n    do {\n      const line = new GVLine(P1, P2)\n      const [X1, X2] = this.getExtremPointGraphicLine(line)\n      P3 = this.getNewPointBetween(X1, X2)\n    } while (this.isCloseToExistingPoints(P3) || this.isCloseToLineThroughtExistingPoints(P3))\n    P3.name = P3.name || this.getNewName(P3.type)\n    this.geometric.push(P3)\n    return [P1, P2, P3]\n  }\n\n  /**\n    * P1, P2, P3 with P2P1P3 rectangular in P1\n    * @param args\n    * @returns {GVPoint[]}\n    */\n  addRectPoint (...args) /** GVPoint[] */ {\n    let P3, P1, P2\n    do {\n      if (P1 !== undefined) {\n        for (let i = 0; i < 2 - args.length; i++) {\n          this.geometric.pop()\n          this.geometric.pop()\n        }\n      }\n      [P1, P2] = args.concat(this.addPoint(2 - args.length))\n      const line = (new GVLine(P1, P2)).getPerpendicularLine(P1)\n      const [X1, X2] = this.getExtremPointGraphicLine(line)\n      P3 = this.getNewPointBetween(X1, X2)\n    } while (this.isCloseToExistingPoints(P3) || this.isCloseToLineThroughtExistingPoints(P3))\n    P3.name = P3.name || this.getNewName(P3.type)\n    this.geometric.push(P3)\n    return [P1, P2, P3]\n  }\n\n  /**\n    * Distances to the sides of a triangle\n    * @param  {GVPoint} P1\n    * @param  {GVPoint} P2\n    * @param  {GVPoint} P3\n    * @returns {number}\n    */\n  distanceMinSidesVertices (P1 /** GVPoint */, P2 /** GVPoint */, P3 /** GVPoint */) /** number */ {\n    // A faire pour n'importe quel nombre de sommets ?\n    return Math.min(\n      this.distance(P1, new GVLine(P2, P3)),\n      this.distance(P2, new GVLine(P1, P3)),\n      this.distance(P3, new GVLine(P1, P2))\n    )\n  }\n\n  /**\n    * Add three points not aligned or one not aligned with the two others\n    * @param  {GVPoint} P1 If no point we create three new points\n    * @param  {GVPoint} P2 If no point we create three new points\n    * @param  {GVPoint} P3 If no point we create three new points\n    * @returns {GVPoint}\n    */\n  addNotAlignedPoint (P1 = this.addPoint()[0], P2 = this.addPoint()[0], P3 /** GVPoint */) /** GVPoint[] */ {\n    // Le troisième point est écrasé si existant\n    // Réfléchir à un ensemble plus grand de points non alignés\n    const minDimension = Math.min(this.height, this.width) / this.getListObjectTypeSelect('Point').length / 3\n    do {\n      if (P3 !== undefined) this.geometric.pop()\n      P3 = this.addPoint()[0]\n    } while (this.distanceMinSidesVertices(P1, P2, P3) < minDimension)\n    P3.name = P3.name || this.getNewName(P3.type)\n    return [P1, P2, P3]\n  }\n\n  /**\n    * Add a parallel line to another one or two parallel lines\n    * @param  {GVPoint} P If no args we create two parallels\n    * @param  {GVLine} line If no args we create two parallels\n    * @returns {GVLine}\n    */\n  addParallelLine (P = this.addPoint()[0], line = this.addLine()) {\n    const parallel = new GVLine(P, line.direction)\n    parallel.name = this.getNewName(parallel.type)\n    this.geometric.push(parallel, P, line)\n    return [line, parallel]\n  }\n\n  addPerpendicularLine (P = this.addPoint()[0], line = this.addLine()) {\n    const perpendicular = new GVLine(P, line.direction.getNormal())\n    perpendicular.name = this.getNewName(perpendicular.type)\n    this.geometric.push(perpendicular)\n    return [line, perpendicular]\n  }\n\n  /**\n    * Add the sides of a polygon\n    * @param  {...any} args\n    * @returns {}\n    */\n  addSidesPolygon (...args)/** GVSegment[] */ {\n    const sides = []\n    for (let i = 0; i < args.length - 1; i++) {\n      // sides.push(this.addSegment(args[i], args[i + 1]))\n      sides.push(this.addSegment(args[i], args[i + 1]))\n    }\n    sides.push(this.addSegment(args[args.length - 1], args[0]))\n    return sides\n  }\n\n  /**\n    * Add labels to the vertices of a polygon.\n    * @param {GVPoint[]} args\n    */\n  addLabelsPointsPolygon (...args) {\n    const last = args.length - 1\n    const vertices = [args[last]].concat(args).concat(args[0])\n    for (let i = 1; i < args.length + 1; i++) {\n      vertices[i].labelPoints = [vertices[i - 1], vertices[i], vertices[i + 1]]\n      vertices[i].showName(1.3)\n    }\n  }\n\n  addTriangle (arg1 /** number | GVPoint */, arg2 /** number | GVPoint */, arg3 /** number | GVPoint */, arg4 /** number */)/** GVTriangle */ {\n    let triangle\n    if (arg1 instanceof GVPoint && arg2 !== undefined && arg2 instanceof GVPoint && arg3 instanceof GVPoint) {\n      triangle = new GVTriangle(arg1, arg2, arg3)\n    } else if (arg1 instanceof GVPoint && arg2 instanceof GVPoint && arg3 instanceof GVPoint) {\n      triangle = new GVTriangle(...this.addNotAlignedPoint(...[arg1, arg2, arg3].filter(P => P !== undefined)))\n    } else if (arg1 instanceof GVPoint && typeof arg2 === 'number' && arg3 instanceof GVPoint && typeof arg4 === 'number') {\n      const cercle1 = this.addCircle(arg1, arg2)\n      const cercle2 = this.addCircle(arg3, arg4)\n      const [P] = this.addIntersectLine(cercle1, cercle2)\n      triangle = new GVTriangle(arg1, arg3, P)\n    } else if (typeof arg1 === 'number' && typeof arg2 === 'number' && typeof arg3 === 'number') {\n      const A = this.addPoint()[0]\n      const B = this.addPointDistance(A, arg1)\n      const cercle1 = this.addCircle(A, arg2)\n      const cercle2 = this.addCircle(B, arg3)\n      const [C] = this.addIntersectLine(cercle1, cercle2)\n      triangle = new GVTriangle(A, B, C)\n    } else if (arg1 === undefined) {\n      triangle = new GVTriangle(...this.addNotAlignedPoint())\n    }\n    return triangle\n  }\n\n  /**\n    * Add a group of 4 points making a parallelogram\n    * @param  {GVPoint} A // 0-3 point\n    * @param  {GVPoint} B // 0-3 point\n    * @param  {GVPoint} C // 0-3 point\n    * @returns {GVPolygon}\n    */\n  addParallelogram (A /** GVPoint */ = this.addPoint()[0], B /** GVPoint */ = this.addPoint()[0], C /** GVPoint */ = this.addNotAlignedPoint(A, B)[2], D = undefined)/** GVPolygon */ {\n    D = new GVPoint(\n      new GVCartesian(\n        A.x + C.x - B.x,\n        A.y + C.y - B.y\n      )\n    )\n    D.name = D.name || this.getNewName(D.type)\n    this.geometric.push(D)\n    return new GVPolygon(A, B, C, D)\n  }\n\n  addRegularPolygon (n /** number */, A /** GVPoint */ = this.addPoint()[0], B /** GVPoint */ = this.addPoint()[0])/** GVPolygon */ {\n    const points /** GVPoint[] */ = [A, B]\n    for (let i = 2; i < n; i++) {\n      const P = points[i - 2].getRotate(points[i - 1], Math.PI - 2 * Math.PI / n)\n      P.name = P.name || this.getNewName(P.type)\n      this.geometric.push(P)\n      points.push(P)\n    }\n    return new GVPolygon(...points)\n  }\n\n  /**\n   *\n   * @param {GVPoint} A\n   * @returns {GVRectangle}\n   */\n  addRectangle (A) {\n    let rectangle/** GVRectangle */\n    if (A == null) {\n      do {\n        if (rectangle !== undefined) {\n          this.geometric.pop()\n          this.geometric.pop()\n          this.geometric.pop()\n          this.geometric.pop()\n        }\n        const [A, B, D] = this.addRectPoint()\n        const C = this.addParallelogram(D, A, B).vertices[3]\n        rectangle = new GVRectangle(A, B, C, D)\n      } while (rectangle.ratio < 1.2 || rectangle.ratio > 1.7)\n    }\n    return rectangle\n  }\n\n  addRegularPolygonCenter (A /** GVPoint */ = this.addPoint()[0], B /** GVPoint */ = this.addPoint()[0], n /** number */) /** GVPoint */ {\n    const angle = Math.PI * (1 / 2 - 1 / n)\n    const coeff = 1 / (2 * Math.sin(Math.PI / n))\n    const P = new GVPoint(\n      new GVCartesian(\n        ((A.x - B.x) * Math.cos(angle) - (A.y - B.y) * Math.sin(angle)) * coeff + B.x,\n        ((A.x - B.x) * Math.sin(angle) + (A.y - B.y) * Math.cos(angle)) * coeff + B.y\n      ))\n    P.name = P.name || this.getNewName(P.type)\n    this.geometric.push(P)\n    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angles/** GVAngle[] */ = []\n    for (let i = 1; i < args.length + 1; i++) {\n      const newAngle = new GVAngle(vertices[i - 1], vertices[i], vertices[i + 1])\n      angles.push(newAngle)\n      this.geometric.push(newAngle)\n    }\n    return angles\n  }\n\n  /**\n    * Rotate points\n    * @param {Point} center\n    * @param {number} angle // Angle in radians\n    * @param {Point} args\n    * @returns {Point[]}\n    * @example\n    * this.addRotate(O, Math.PI()/2, B)\n    */\n  addRotate (center /** GVPoint */, angle /** number */, ...args /** GVPoint[] */) /** GVPoint[] */ {\n    const rotatePoints = []\n    args.map(M => {\n      const point = new GVPoint(\n        new GVCartesian(\n          (M.x - center.x) * Math.cos(angle) - (M.y - center.y) * Math.sin(angle) + center.x,\n          (M.x - center.x) * Math.sin(angle) + (M.y - center.y) * Math.cos(angle) + center.y\n        ))\n      point.name = point.name || this.getNewName(point.type)\n      this.geometric.push(point)\n      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