New special domains (ℕ, ℤ and the likes), working with functions!

2020-12-25 19:30:19 +01:00 · 2020-12-25 19:30:19 +01:00 · ef87b8362c
parent 065b88bfd0
commit ef87b8362c
3 changed files with 225 additions and 47 deletions
--- a/qml/LogGraphCanvas.qml
+++ b/qml/LogGraphCanvas.qml
@ -209,5 +209,15 @@ Canvas {
        ctx.stroke();
    }
    
-    
+    function drawDashedLine(ctx, x1, y1, x2, y2, dashPxSize = 10) {
+        var distance = Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2))
+        var progPerc = dashPxSize/distance
+        ctx.beginPath();
+        ctx.moveTo(x1, y1);
+        for(var i = progPerc/2; i < 1; i += progPerc) {
+            ctx.lineTo(x1-(x1-x2)*i, y1-(y1-y2)*i)
+            ctx.moveTo(x1-(x1-x2)*(i+progPerc/2), y1-(y1-y2)*(i+progPerc/2))
+        }
+        ctx.stroke();
+    }
 }
--- a/qml/js/mathlib.js
+++ b/qml/js/mathlib.js
@ -89,8 +89,6 @@ class Domain {
    
    intersection(domain) { return this }
    
-    static import(frm) { return new EmptySet() }
-    
    static import(frm) {
        switch(frm.trim().toUpperCase()) {
            case "R":
@ -128,8 +126,50 @@ class Domain {
            case "ℝ*⁻":
                return Domain.RME
                break;
+            case "ℕ":
+            case "N":
+            case "ZP":
+            case "ℤ⁺":
+                return Domain.N
+                break;
+            case "NE":
+            case "NP":
+            case "N*":
+            case "N+":
+            case "ℕ*":
+            case "ℕ⁺":
+            case "ZPE":
+            case "ZEP":
+            case "Z+*":
+            case "Z*+":
+            case "ℤ⁺*":
+            case "ℤ*⁺":
+                return Domain.NE
+                break;
+            case "Z":
+            case "ℤ":
+                return Domain.Z
+                break;
+            case "ZM":
+            case "Z-":
+            case "ℤ⁻":
+                return Domain.ZM
+                break;
+            case "ZME":
+            case "ZEM":
+            case "Z-*":
+            case "Z*-":
+            case "ℤ⁻*":
+            case "ℤ*⁻":
+                return Domain.ZME
+                break;
+            case "ZE":
+            case "Z*":
+            case "ℤ*":
+                return Domain.ZE
+                break;
            default:
-                return EmptySet()
+                return new EmptySet()
                break;
        }
    }
@ -195,25 +235,76 @@ class Interval extends Domain {
        return new Interval(begin.trim(), end.trim(), openBegin, openEnd)
    }
 }
-Domain.R = new Interval(-Infinity,Infinity,true,true)
-Domain.R.displayName = "ℝ"
-Domain.RP = new Interval(0,Infinity,true,false)
-Domain.RP.displayName = "ℝ⁺"
-Domain.RM = new Interval(-Infinity,0,true,false)
-Domain.RM.displayName = "ℝ⁻"
-Domain.RPE = new Interval(0,Infinity,true,true)
-Domain.RPE.displayName = "ℝ⁺*"
-Domain.RME = new Interval(-Infinity,0,true,true)
-Domain.RME.displayName = "ℝ⁻*"

-class DomainSet extends Domain {
-    constructor(values) {
+class SpecialDomain extends Domain {
+    // For special domains (N, Z...)
+    // isValidExpr is function returning true when number is in domain
+    // false when it isn't.
+    // nextValue provides the next positive value in the domain
+    // after the one given.
+    constructor(displayName, isValid, next = x => true, previous = x => true, 
+                moveSupported = true) {
        super()
-        var newVals = []
-        values.forEach(function(value){
-            newVals.push(new Expression(value.toString()))
-        })
-        this.values = newVals
+        this.displayName = displayName
+        this.isValid = isValid
+        this.nextValue = next
+        this.prevValue = previous
+        this.moveSupported = moveSupported
+    }
+    
+    includes(x) {
+        if(typeof x == 'string') x = executeExpression(x)
+        return this.isValid(x)
+    }
+    
+    next(x) {
+        if(typeof x == 'string') x = executeExpression(x)
+        return this.nextValue(x)
+    }
+    
+    previous(x) {
+        if(typeof x == 'string') x = executeExpression(x)
+        return this.prevValue(x)
+    }
+    
+    toString() {
+        return this.displayName
+    }
+    
+    union(domain) {
+        if(domain instanceof EmptySet) return this
+        if(domain instanceof DomainSet) return domain.union(this)
+        if(domain instanceof UnionDomain) return new UnionDomain(this, domain)
+        if(domain instanceof IntersectionDomain) return new UnionDomain(this, domain)
+        if(domain instanceof MinusDomain) return new UnionDomain(this, domain)
+        if(domain instanceof Interval) return new UnionDomain(this, domain)
+    }
+    
+    intersection(domain) {
+        if(domain instanceof EmptySet) return domain
+        if(domain instanceof DomainSet) return domain.intersection(this)
+        if(domain instanceof UnionDomain) return new IntersectionDomain(this, domain)
+        if(domain instanceof IntersectionDomain) return new IntersectionDomain(this, domain)
+        if(domain instanceof MinusDomain) return new IntersectionDomain(this, domain)
+        if(domain instanceof Interval) return new IntersectionDomain(this, domain)
+    }
+}
+
+
+class DomainSet extends SpecialDomain {
+    constructor(values) {
+        super('', x => true, x => x, true)
+        console.log(values)
+        var newVals = {}
+        this.executedValues = []
+        for(var i = 0; i < values.length; i++) {
+            var expr = new Expression(values[i].toString())
+            var ex = expr.execute()
+            newVals[ex] = expr
+            this.executedValues.push(ex)
+        }
+        this.executedValues.sort((a,b) => a-b)
+        this.values = this.executedValues.map(val => newVals[val])
    }
    
    includes(x) {
@ -223,6 +314,29 @@ class DomainSet extends Domain {
        return false
    }
    
+    next(x) {
+        if(typeof x == 'string') x = executeExpression(x)
+        if(x < this.executedValues[0]) return this.executedValues[0]
+        for(var i = 1; i < this.values.length; i++) {
+            var prevValue = this.executedValues[i-1]
+            var value = this.executedValues[i]
+            if(x >= prevValue && x < value) return value
+        }
+        return null
+    }
+    
+    previous(x) {
+        if(typeof x == 'string') x = executeExpression(x)
+        if(x > this.executedValues[this.executedValues.length-1]) 
+            return this.executedValues[this.executedValues.length-1]
+        for(var i = 1; i < this.values.length; i++) {
+            var prevValue = this.executedValues[i-1]
+            var value = this.executedValues[i]
+            if(x > prevValue && x <= value) return prevValue
+        }
+        return null
+    }
+    
    toString() {
        return "{" + this.values.join(";") + "}"
    }
@ -239,7 +353,7 @@ class DomainSet extends Domain {
        }
        var notIncludedValues = []
        for(var i = 0; i < this.values.length; i++) {
-            var value = this.values[i].execute()
+            var value = this.executedValues[i]
            if(domain instanceof Interval) {
                if(domain.begin.execute() == value && domain.openBegin) {
                    domain.openBegin = false
@ -266,7 +380,7 @@ class DomainSet extends Domain {
        }
        var includedValues = []
        for(var i = 0; i < this.values.length; i++) {
-            var value = this.values[i].execute()
+            var value = this.executedValues[i]
            if(domain instanceof Interval) {
                if(domain.begin.execute() == value && !domain.openBegin) {
                    domain.openBegin = false
@ -325,7 +439,6 @@ class UnionDomain extends Domain {
        if(domains.length == 1) domains = frm.trim().split("U") // Fallback
        var dom1 = parseDomain(domains.pop())
        var dom2 = parseDomain(domains.join('∪'))
-        console.log('Union', dom1, dom2)
        return dom1.union(dom2)
    }
 }
@ -365,7 +478,7 @@ class IntersectionDomain extends Domain {
    static import(frm) {
        var domains = frm.trim().split("∩")
        var dom1 = parseDomain(domains.pop())
-        var dom2 = parseDomain(domains.join('∪'))
+        var dom2 = parseDomain(domains.join('∩'))
        return dom1.intersection(dom2)
    }
 }
@ -397,14 +510,41 @@ class MinusDomain extends Domain {
 Domain.RE = new MinusDomain("R", "{0}")
 Domain.RE.displayName = "ℝ*"

+Domain.R = new Interval(-Infinity,Infinity,true,true)
+Domain.R.displayName = "ℝ"
+Domain.RP = new Interval(0,Infinity,true,false)
+Domain.RP.displayName = "ℝ⁺"
+Domain.RM = new Interval(-Infinity,0,true,false)
+Domain.RM.displayName = "ℝ⁻"
+Domain.RPE = new Interval(0,Infinity,true,true)
+Domain.RPE.displayName = "ℝ⁺*"
+Domain.RME = new Interval(-Infinity,0,true,true)
+Domain.RME.displayName = "ℝ⁻*"
+Domain.N = new SpecialDomain('ℕ', x => x%1==0 && x >= 0, 
+                             x => Math.max(Math.floor(x)+1, 0), 
+                             x => Math.max(Math.ceil(x)-1, 0))
+Domain.NE = new SpecialDomain('ℕ*', x => x%1==0 && x > 0, 
+                              x => Math.max(Math.floor(x)+1, 1), 
+                              x => Math.max(Math.ceil(x)-1, 1))
+Domain.Z = new SpecialDomain('ℤ', x => x%1==0, x => Math.floor(x)+1, x => Math.ceil(x)-1)
+Domain.ZE = new SpecialDomain('ℤ*', x => x%1==0 && x != 0, 
+                              x => Math.floor(x)+1 == 0 ? Math.floor(x)+2 : Math.floor(x)+1, 
+                              x => Math.ceil(x)-1 == 0 ? Math.ceil(x)-2 : Math.ceil(x)-1)
+Domain.ZM = new SpecialDomain('ℤ⁻', x => x%1==0 && x <= 0,
+                              x => Math.min(Math.floor(x)+1, 0),
+                              x => Math.min(Math.ceil(x)-1, 0))
+Domain.ZME = new SpecialDomain('ℤ⁻*', x => x%1==0 && x < 0, 
+                               x => Math.min(Math.floor(x)+1, -1), 
+                               x => Math.min(Math.ceil(x)-1, -1))
+
+
 var refedDomains = []

 function parseDomain(domain) {
    if(!domain.includes(')') && !domain.includes('(')) return parseDomainSimple(domain)
    var domStr
    while((domStr = /\(([^)(]+)\)/.exec(domain)) !== null) {
-        var dom = parseDomainSimple(domStr[1]);
-        console.log(domain, domStr[0])
+        var dom = parseDomainSimple(domStr[1].trim());
        domain = domain.replace(domStr[0], 'D' + refedDomains.length)
        refedDomains.push(dom)
    }
@ -412,12 +552,14 @@ function parseDomain(domain) {
 }

 function parseDomainSimple(domain) {
-    if(domain[0] == 'D') return refedDomains[parseInt(domain.substr(1))]
-    if(domain.indexOf("U") >= 0 || domain.indexOf("∪") >= 0) return UnionDomain.import(domain)
-    if(domain.indexOf("∩") >= 0) return IntersectionDomain.import(domain)
-    if(domain.indexOf("∖") >= 0 || domain.indexOf("\\") >= 0) return MinusDomain.import(domain)
+    domain = domain.trim()
+    if(domain.includes("U") || domain.includes("∪")) return UnionDomain.import(domain)
+    if(domain.includes("∩")) return IntersectionDomain.import(domain)
+    if(domain.includes("∖") || domain.includes("\\")) return MinusDomain.import(domain)
    if(domain.charAt(0) == "{" && domain.charAt(domain.length -1) == "}") return DomainSet.import(domain)
-    if(domain.indexOf("]") >= 0 || domain.indexOf("[") >= 0) return Interval.import(domain)
-    if(domain.toUpperCase().indexOf("R") >= 0 || domain.indexOf("ℝ") >= 0) return Domain.import(domain)
+    if(domain.includes("]") || domain.includes("[")) return Interval.import(domain)
+    if(["R", "ℝ", "N", "ℕ", "Z", "ℤ"].some(str => domain.toUpperCase().includes(str)))
+        return Domain.import(domain)
+    if(domain[0] == 'D') return refedDomains[parseInt(domain.substr(1))]
    return new EmptySet()
 }
--- a/qml/js/objects.js
+++ b/qml/js/objects.js
@ -158,8 +158,8 @@ class Point extends DrawableObject  {
                canvas.drawLine(ctx, canvasX-pointSize/2, canvasY+pointSize/2, canvasX+pointSize/2, canvasY-pointSize/2)
                break;
            case '＋':
-                canvas.drawLine(ctx, canvasX, canvasY-pointSize/2, canvasX, canvasY+pointSize/2)
-                canvas.drawLine(ctx, canvasX-pointSize/2, canvasY, canvasX+pointSize/2, canvasY)
+                ctx.fillRect(canvasX-pointSize/2, canvasY-1, pointSize, 2)
+                ctx.fillRect(canvasX-1, canvasY-pointSize/2, 2, pointSize)
                break;
        }
        var text = this.getLabel()
@ -265,10 +265,10 @@ class Function extends ExecutableObject {
        var posY = canvas.y2px(this.expression.execute(this.labelX))
        switch(this.labelPosition) {
            case 'above':
-                canvas.drawVisibleText(ctx, text, posX-textSize.width/2, posY-textSize.height)
+                canvas.drawVisibleText(ctx, text, posX-textSize.width, posY-textSize.height)
                break;
            case 'below':
-                canvas.drawVisibleText(ctx, text, posX-textSize.width/2, posY+textSize.height)
+                canvas.drawVisibleText(ctx, text, posX-textSize.width, posY+textSize.height)
                break;
                
        }
@ -279,17 +279,43 @@ class Function extends ExecutableObject {
        // Drawing small traits every 2px
        var pxprecision = 2
        var previousX = canvas.px2x(0)
-        var previousY = expr.execute(previousX)
-        for(var px = pxprecision; px < canvas.canvasSize.width; px += pxprecision) {
-            var currentX = canvas.px2x(px)
-            var currentY = expr.execute(currentX)
-            if((inDomain.includes(currentX) || inDomain.includes(previousX)) &&
-                (outDomain.includes(currentY) || outDomain.includes(previousY)) &&
-                Math.abs(previousY-currentY)<100) { // 100 per 2px is a lot (probably inf to inf issue)
-                    canvas.drawLine(ctx, canvas.x2px(previousX), canvas.y2px(previousY), canvas.x2px(currentX), canvas.y2px(currentY))
+        var previousY;
+        var draw = function(currentX) {
+        }
+        console.log('Drawing', inDomain, inDomain instanceof MathLib.SpecialDomain)
+        if(inDomain instanceof MathLib.SpecialDomain && inDomain.moveSupported) {
+            previousX = inDomain.previous(previousX)
+            if(previousX === null) previousX = inDomain.next(canvas.px2x(0))
+            previousY = expr.execute(previousX)
+            while(previousX !== null && canvas.x2px(previousX) < canvas.canvasSize.width) {
+                var currentX = inDomain.next(previousX)
+                var currentY = expr.execute(currentX)
+                if(currentX === null) break;
+                if((inDomain.includes(currentX) || inDomain.includes(previousX)) &&
+                    (outDomain.includes(currentY) || outDomain.includes(previousY))) {
+                    canvas.drawDashedLine(ctx, canvas.x2px(previousX), canvas.y2px(previousY), canvas.x2px(currentX), canvas.y2px(currentY))
+                    ctx.fillRect(canvas.x2px(previousX)-5, canvas.y2px(previousY)-1, 10, 2)
+                    ctx.fillRect(canvas.x2px(previousX)-1, canvas.y2px(previousY)-5, 2, 10)
                }
-            previousX = currentX
-            previousY = currentY
+                previousX = currentX
+                previousY = currentY
+            }
+            // Drawing the last cross
+            ctx.fillRect(canvas.x2px(previousX)-5, canvas.y2px(previousY)-1, 10, 2)
+            ctx.fillRect(canvas.x2px(previousX)-1, canvas.y2px(previousY)-5, 2, 10)
+        } else {
+            previousY = expr.execute(previousX)
+            for(var px = pxprecision; px < canvas.canvasSize.width; px += pxprecision) {
+                var currentX = canvas.px2x(px)
+                var currentY = expr.execute(currentX)
+                if((inDomain.includes(currentX) || inDomain.includes(previousX)) &&
+                    (outDomain.includes(currentY) || outDomain.includes(previousY)) &&
+                    Math.abs(previousY-currentY)<100) {
+                        canvas.drawLine(ctx, canvas.x2px(previousX), canvas.y2px(previousY), canvas.x2px(currentX), canvas.y2px(currentY))
+                    }
+                previousX = currentX
+                previousY = currentY
+            }
        }
    }
 }