New special domains (ℕ, ℤ and the likes), working with functions!
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065b88bfd0
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3 changed files with 225 additions and 47 deletions
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@ -209,5 +209,15 @@ Canvas {
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ctx.stroke();
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}
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function drawDashedLine(ctx, x1, y1, x2, y2, dashPxSize = 10) {
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var distance = Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2))
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var progPerc = dashPxSize/distance
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ctx.beginPath();
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ctx.moveTo(x1, y1);
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for(var i = progPerc/2; i < 1; i += progPerc) {
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ctx.lineTo(x1-(x1-x2)*i, y1-(y1-y2)*i)
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ctx.moveTo(x1-(x1-x2)*(i+progPerc/2), y1-(y1-y2)*(i+progPerc/2))
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}
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ctx.stroke();
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}
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}
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@ -89,8 +89,6 @@ class Domain {
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intersection(domain) { return this }
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static import(frm) { return new EmptySet() }
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static import(frm) {
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switch(frm.trim().toUpperCase()) {
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case "R":
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@ -128,8 +126,50 @@ class Domain {
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case "ℝ*⁻":
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return Domain.RME
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break;
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case "ℕ":
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case "N":
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case "ZP":
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case "ℤ⁺":
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return Domain.N
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break;
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case "NE":
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case "NP":
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case "N*":
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case "N+":
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case "ℕ*":
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case "ℕ⁺":
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case "ZPE":
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case "ZEP":
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case "Z+*":
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case "Z*+":
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case "ℤ⁺*":
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case "ℤ*⁺":
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return Domain.NE
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break;
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case "Z":
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case "ℤ":
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return Domain.Z
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break;
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case "ZM":
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case "Z-":
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case "ℤ⁻":
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return Domain.ZM
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break;
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case "ZME":
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case "ZEM":
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case "Z-*":
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case "Z*-":
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case "ℤ⁻*":
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case "ℤ*⁻":
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return Domain.ZME
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break;
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case "ZE":
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case "Z*":
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case "ℤ*":
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return Domain.ZE
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break;
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default:
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return EmptySet()
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return new EmptySet()
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break;
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}
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}
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@ -195,25 +235,76 @@ class Interval extends Domain {
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return new Interval(begin.trim(), end.trim(), openBegin, openEnd)
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}
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}
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Domain.R = new Interval(-Infinity,Infinity,true,true)
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Domain.R.displayName = "ℝ"
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Domain.RP = new Interval(0,Infinity,true,false)
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Domain.RP.displayName = "ℝ⁺"
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Domain.RM = new Interval(-Infinity,0,true,false)
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Domain.RM.displayName = "ℝ⁻"
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Domain.RPE = new Interval(0,Infinity,true,true)
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Domain.RPE.displayName = "ℝ⁺*"
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Domain.RME = new Interval(-Infinity,0,true,true)
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Domain.RME.displayName = "ℝ⁻*"
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class DomainSet extends Domain {
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constructor(values) {
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class SpecialDomain extends Domain {
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// For special domains (N, Z...)
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// isValidExpr is function returning true when number is in domain
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// false when it isn't.
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// nextValue provides the next positive value in the domain
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// after the one given.
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constructor(displayName, isValid, next = x => true, previous = x => true,
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moveSupported = true) {
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super()
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var newVals = []
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values.forEach(function(value){
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newVals.push(new Expression(value.toString()))
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})
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this.values = newVals
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this.displayName = displayName
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this.isValid = isValid
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this.nextValue = next
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this.prevValue = previous
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this.moveSupported = moveSupported
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}
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includes(x) {
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if(typeof x == 'string') x = executeExpression(x)
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return this.isValid(x)
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}
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next(x) {
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if(typeof x == 'string') x = executeExpression(x)
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return this.nextValue(x)
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}
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previous(x) {
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if(typeof x == 'string') x = executeExpression(x)
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return this.prevValue(x)
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}
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toString() {
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return this.displayName
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}
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union(domain) {
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if(domain instanceof EmptySet) return this
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if(domain instanceof DomainSet) return domain.union(this)
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if(domain instanceof UnionDomain) return new UnionDomain(this, domain)
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if(domain instanceof IntersectionDomain) return new UnionDomain(this, domain)
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if(domain instanceof MinusDomain) return new UnionDomain(this, domain)
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if(domain instanceof Interval) return new UnionDomain(this, domain)
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}
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intersection(domain) {
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if(domain instanceof EmptySet) return domain
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if(domain instanceof DomainSet) return domain.intersection(this)
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if(domain instanceof UnionDomain) return new IntersectionDomain(this, domain)
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if(domain instanceof IntersectionDomain) return new IntersectionDomain(this, domain)
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if(domain instanceof MinusDomain) return new IntersectionDomain(this, domain)
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if(domain instanceof Interval) return new IntersectionDomain(this, domain)
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}
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}
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class DomainSet extends SpecialDomain {
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constructor(values) {
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super('', x => true, x => x, true)
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console.log(values)
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var newVals = {}
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this.executedValues = []
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for(var i = 0; i < values.length; i++) {
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var expr = new Expression(values[i].toString())
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var ex = expr.execute()
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newVals[ex] = expr
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this.executedValues.push(ex)
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}
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this.executedValues.sort((a,b) => a-b)
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this.values = this.executedValues.map(val => newVals[val])
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}
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includes(x) {
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@ -223,6 +314,29 @@ class DomainSet extends Domain {
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return false
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}
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next(x) {
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if(typeof x == 'string') x = executeExpression(x)
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if(x < this.executedValues[0]) return this.executedValues[0]
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for(var i = 1; i < this.values.length; i++) {
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var prevValue = this.executedValues[i-1]
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var value = this.executedValues[i]
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if(x >= prevValue && x < value) return value
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}
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return null
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}
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previous(x) {
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if(typeof x == 'string') x = executeExpression(x)
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if(x > this.executedValues[this.executedValues.length-1])
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return this.executedValues[this.executedValues.length-1]
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for(var i = 1; i < this.values.length; i++) {
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var prevValue = this.executedValues[i-1]
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var value = this.executedValues[i]
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if(x > prevValue && x <= value) return prevValue
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}
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return null
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}
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toString() {
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return "{" + this.values.join(";") + "}"
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}
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@ -239,7 +353,7 @@ class DomainSet extends Domain {
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}
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var notIncludedValues = []
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for(var i = 0; i < this.values.length; i++) {
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var value = this.values[i].execute()
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var value = this.executedValues[i]
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if(domain instanceof Interval) {
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if(domain.begin.execute() == value && domain.openBegin) {
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domain.openBegin = false
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@ -266,7 +380,7 @@ class DomainSet extends Domain {
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}
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var includedValues = []
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for(var i = 0; i < this.values.length; i++) {
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var value = this.values[i].execute()
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var value = this.executedValues[i]
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if(domain instanceof Interval) {
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if(domain.begin.execute() == value && !domain.openBegin) {
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domain.openBegin = false
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@ -325,7 +439,6 @@ class UnionDomain extends Domain {
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if(domains.length == 1) domains = frm.trim().split("U") // Fallback
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var dom1 = parseDomain(domains.pop())
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var dom2 = parseDomain(domains.join('∪'))
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console.log('Union', dom1, dom2)
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return dom1.union(dom2)
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}
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}
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@ -365,7 +478,7 @@ class IntersectionDomain extends Domain {
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static import(frm) {
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var domains = frm.trim().split("∩")
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var dom1 = parseDomain(domains.pop())
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var dom2 = parseDomain(domains.join('∪'))
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var dom2 = parseDomain(domains.join('∩'))
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return dom1.intersection(dom2)
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}
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}
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@ -397,14 +510,41 @@ class MinusDomain extends Domain {
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Domain.RE = new MinusDomain("R", "{0}")
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Domain.RE.displayName = "ℝ*"
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Domain.R = new Interval(-Infinity,Infinity,true,true)
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Domain.R.displayName = "ℝ"
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Domain.RP = new Interval(0,Infinity,true,false)
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Domain.RP.displayName = "ℝ⁺"
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Domain.RM = new Interval(-Infinity,0,true,false)
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Domain.RM.displayName = "ℝ⁻"
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Domain.RPE = new Interval(0,Infinity,true,true)
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Domain.RPE.displayName = "ℝ⁺*"
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Domain.RME = new Interval(-Infinity,0,true,true)
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Domain.RME.displayName = "ℝ⁻*"
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Domain.N = new SpecialDomain('ℕ', x => x%1==0 && x >= 0,
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x => Math.max(Math.floor(x)+1, 0),
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x => Math.max(Math.ceil(x)-1, 0))
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Domain.NE = new SpecialDomain('ℕ*', x => x%1==0 && x > 0,
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x => Math.max(Math.floor(x)+1, 1),
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x => Math.max(Math.ceil(x)-1, 1))
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Domain.Z = new SpecialDomain('ℤ', x => x%1==0, x => Math.floor(x)+1, x => Math.ceil(x)-1)
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Domain.ZE = new SpecialDomain('ℤ*', x => x%1==0 && x != 0,
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x => Math.floor(x)+1 == 0 ? Math.floor(x)+2 : Math.floor(x)+1,
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x => Math.ceil(x)-1 == 0 ? Math.ceil(x)-2 : Math.ceil(x)-1)
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Domain.ZM = new SpecialDomain('ℤ⁻', x => x%1==0 && x <= 0,
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x => Math.min(Math.floor(x)+1, 0),
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x => Math.min(Math.ceil(x)-1, 0))
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Domain.ZME = new SpecialDomain('ℤ⁻*', x => x%1==0 && x < 0,
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x => Math.min(Math.floor(x)+1, -1),
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x => Math.min(Math.ceil(x)-1, -1))
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var refedDomains = []
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function parseDomain(domain) {
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if(!domain.includes(')') && !domain.includes('(')) return parseDomainSimple(domain)
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var domStr
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while((domStr = /\(([^)(]+)\)/.exec(domain)) !== null) {
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var dom = parseDomainSimple(domStr[1]);
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console.log(domain, domStr[0])
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var dom = parseDomainSimple(domStr[1].trim());
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domain = domain.replace(domStr[0], 'D' + refedDomains.length)
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refedDomains.push(dom)
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}
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@ -412,12 +552,14 @@ function parseDomain(domain) {
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}
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function parseDomainSimple(domain) {
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if(domain[0] == 'D') return refedDomains[parseInt(domain.substr(1))]
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if(domain.indexOf("U") >= 0 || domain.indexOf("∪") >= 0) return UnionDomain.import(domain)
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if(domain.indexOf("∩") >= 0) return IntersectionDomain.import(domain)
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if(domain.indexOf("∖") >= 0 || domain.indexOf("\\") >= 0) return MinusDomain.import(domain)
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domain = domain.trim()
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if(domain.includes("U") || domain.includes("∪")) return UnionDomain.import(domain)
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if(domain.includes("∩")) return IntersectionDomain.import(domain)
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if(domain.includes("∖") || domain.includes("\\")) return MinusDomain.import(domain)
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if(domain.charAt(0) == "{" && domain.charAt(domain.length -1) == "}") return DomainSet.import(domain)
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if(domain.indexOf("]") >= 0 || domain.indexOf("[") >= 0) return Interval.import(domain)
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if(domain.toUpperCase().indexOf("R") >= 0 || domain.indexOf("ℝ") >= 0) return Domain.import(domain)
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if(domain.includes("]") || domain.includes("[")) return Interval.import(domain)
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if(["R", "ℝ", "N", "ℕ", "Z", "ℤ"].some(str => domain.toUpperCase().includes(str)))
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return Domain.import(domain)
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if(domain[0] == 'D') return refedDomains[parseInt(domain.substr(1))]
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return new EmptySet()
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}
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@ -158,8 +158,8 @@ class Point extends DrawableObject {
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canvas.drawLine(ctx, canvasX-pointSize/2, canvasY+pointSize/2, canvasX+pointSize/2, canvasY-pointSize/2)
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break;
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case '＋':
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canvas.drawLine(ctx, canvasX, canvasY-pointSize/2, canvasX, canvasY+pointSize/2)
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canvas.drawLine(ctx, canvasX-pointSize/2, canvasY, canvasX+pointSize/2, canvasY)
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ctx.fillRect(canvasX-pointSize/2, canvasY-1, pointSize, 2)
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ctx.fillRect(canvasX-1, canvasY-pointSize/2, 2, pointSize)
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break;
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}
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var text = this.getLabel()
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@ -265,10 +265,10 @@ class Function extends ExecutableObject {
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var posY = canvas.y2px(this.expression.execute(this.labelX))
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switch(this.labelPosition) {
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case 'above':
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canvas.drawVisibleText(ctx, text, posX-textSize.width/2, posY-textSize.height)
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canvas.drawVisibleText(ctx, text, posX-textSize.width, posY-textSize.height)
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break;
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case 'below':
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canvas.drawVisibleText(ctx, text, posX-textSize.width/2, posY+textSize.height)
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canvas.drawVisibleText(ctx, text, posX-textSize.width, posY+textSize.height)
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break;
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}
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@ -279,13 +279,38 @@ class Function extends ExecutableObject {
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// Drawing small traits every 2px
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var pxprecision = 2
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var previousX = canvas.px2x(0)
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var previousY = expr.execute(previousX)
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var previousY;
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var draw = function(currentX) {
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}
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console.log('Drawing', inDomain, inDomain instanceof MathLib.SpecialDomain)
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if(inDomain instanceof MathLib.SpecialDomain && inDomain.moveSupported) {
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previousX = inDomain.previous(previousX)
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if(previousX === null) previousX = inDomain.next(canvas.px2x(0))
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previousY = expr.execute(previousX)
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while(previousX !== null && canvas.x2px(previousX) < canvas.canvasSize.width) {
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var currentX = inDomain.next(previousX)
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var currentY = expr.execute(currentX)
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if(currentX === null) break;
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if((inDomain.includes(currentX) || inDomain.includes(previousX)) &&
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(outDomain.includes(currentY) || outDomain.includes(previousY))) {
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canvas.drawDashedLine(ctx, canvas.x2px(previousX), canvas.y2px(previousY), canvas.x2px(currentX), canvas.y2px(currentY))
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ctx.fillRect(canvas.x2px(previousX)-5, canvas.y2px(previousY)-1, 10, 2)
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ctx.fillRect(canvas.x2px(previousX)-1, canvas.y2px(previousY)-5, 2, 10)
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}
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previousX = currentX
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previousY = currentY
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}
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// Drawing the last cross
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ctx.fillRect(canvas.x2px(previousX)-5, canvas.y2px(previousY)-1, 10, 2)
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ctx.fillRect(canvas.x2px(previousX)-1, canvas.y2px(previousY)-5, 2, 10)
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} else {
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previousY = expr.execute(previousX)
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for(var px = pxprecision; px < canvas.canvasSize.width; px += pxprecision) {
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var currentX = canvas.px2x(px)
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var currentY = expr.execute(currentX)
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if((inDomain.includes(currentX) || inDomain.includes(previousX)) &&
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(outDomain.includes(currentY) || outDomain.includes(previousY)) &&
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Math.abs(previousY-currentY)<100) { // 100 per 2px is a lot (probably inf to inf issue)
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Math.abs(previousY-currentY)<100) {
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canvas.drawLine(ctx, canvas.x2px(previousX), canvas.y2px(previousY), canvas.x2px(currentX), canvas.y2px(currentY))
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}
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previousX = currentX
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@ -293,6 +318,7 @@ class Function extends ExecutableObject {
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}
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}
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}
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}
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class GainBode extends ExecutableObject {
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