AJB AJB - 5 months ago 41
jQuery Question

Fibonacci Drawing in html5 canvas

Currently I'm looking at this code but can't figure out what's wrong.

function fibNumbers() {
return [0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
}

function continiusFib(a) {
var b = fibNumbers(),
c = Math.floor(a),
d = Math.ceil(a);
if (d >= b.length)
return null;
a = Math.pow(a - c, 1.15);
return b[c] + (b[d] - b[c]) * a
}

function drawSpiral(pointA, pointB) {
var b = pointA;
var c = pointB;
ctx.translate(b.x, b.y);
b = Math.sqrt(((c.x - b.x) * (c.x - b.x)) + ((c.y - b.y) * (c.y - b.y)));
d = 1 / Math.sqrt(((c.x - b.x) * (c.x - b.x)) + ((c.y - b.y) * (c.y - b.y)));
c = Math.acos(c.x - b.x);
0 > Math.asin(c.y - b.y) && (c = 2 * Math.PI - c);
ctx.rotate(c);
ctx.scale(b / 5, b / 5);
var d = Math.PI / 100;
ctx.moveTo(0, 0);
for (var e = 0; e < 50 * (fibNumbers().length - 1) ; e++) {
var f = e * d, g = continiusFib(e / 50),
h = Math.cos(f) * g,
f = Math.sin(f) * g;
ctx.lineTo(h, f);
}
ctx.scale(5 / b, 5 / b);
ctx.rotate(-c);
//ctx.stroke();
}


What I want is to draw Fibonacci Spiral which is different from Golden Spiral

I also have this question for other reference.
enter image description here

enter image description here

Answer

In your function drawSpiral, in the fourth line you do:

b = Math.sqrt(((c.x - b.x) * (c.x - b.x)) + ((c.y - b.y) * (c.y - b.y)));

So, b should be a scalar now, but then you try to access b.x and b.y in the next line, which don't exist anymore:

d = 1 / Math.sqrt(((c.x - b.x) * (c.x - b.x)) + ((c.y - b.y) * (c.y - b.y)));

This happens again with c in the 6-7th lines. This might be why your code isn't working.


I tried to make it work with my own code. I'm not sure at all about the math, but I based my algorithm on the snippet you posted on the question, using some of the mouse-tracking code from @Blindman67's answer.

The spiral

This is the important part. It returns an array with the spiral's points (I use another function to actually render them). The idea is to draw a spiral using the continuous-fibonacci function you provided. It starts at point A and forces the scaling so that the radius at one turn is the distance between point A and point B. It also adds an angle offset so the angle at one turn is the angle between point A and B.

Edited to address comment: I changed the for loop to a while loop that continues drawing until the spiral reaches a maximum radius. I also changed some names and added comments to try to make the algorithm clearer.

var getSpiral = function(pA, pB, maxRadius){
    // 1 step = 1/4 turn or 90ยบ    
    var precision = 50; // Lines to draw in each 1/4 turn
    var stepB = 4; // Steps to get to point B

    var angleToPointB = getAngle(pA,pB); // Angle between pA and pB
    var distToPointB = getDistance(pA,pB); // Distance between pA and pB

    var fibonacci = new FibonacciGenerator();

    // Find scale so that the last point of the curve is at distance to pB
    var radiusB = fibonacci.getNumber(stepB);
    var scale = distToPointB / radiusB;

    // Find angle offset so that last point of the curve is at angle to pB
    var angleOffset = angleToPointB - stepB * Math.PI / 2;

    var path = [];    
    var i, step , radius, angle;

    // Start at the center
    i = step = radius = angle = 0;

    // Continue drawing until reaching maximum radius
    while (radius * scale <= maxRadius){

        path.push({
            x: scale * radius * Math.cos(angle + angleOffset) + pA.x,
            y: scale * radius * Math.sin(angle + angleOffset) + pA.y
        });

        i++; // Next point
        step = i / precision; // 1/4 turns at point    
        radius = fibonacci.getNumber(step); // Radius of Fibonacci spiral
        angle = step * Math.PI / 2; // Radians at point
    }    
    return path;
};

Fibonacci sequence

The code to generate the continuous fibonacci numbers is basically yours, but I changed some names to help me understand it. I also added a generator function so it could work up to any number:

var FibonacciGenerator = function(){
    var thisFibonacci = this;

    // Start with 0 1 2... instead of the real sequence 0 1 1 2...
    thisFibonacci.array = [0, 1, 2];

    thisFibonacci.getDiscrete = function(n){

        // If the Fibonacci number is not in the array, calculate it
        while (n >= thisFibonacci.array.length){
            var length = thisFibonacci.array.length;
            var nextFibonacci = thisFibonacci.array[length - 1] + thisFibonacci.array[length - 2];
            thisFibonacci.array.push(nextFibonacci);
        }

        return thisFibonacci.array[n];
    };

    thisFibonacci.getNumber = function(n){
        var floor = Math.floor(n);
        var ceil = Math.ceil(n);

        if (Math.floor(n) == n){
            return thisFibonacci.getDiscrete(n);
        }

        var a = Math.pow(n - floor, 1.15);

        var fibFloor = thisFibonacci.getDiscrete(floor);
        var fibCeil = thisFibonacci.getDiscrete(ceil);

        return fibFloor + a * (fibCeil - fibFloor);
    };

    return thisFibonacci;
};

Distance and angle between points

To make code clearer, I used a couple helper functions to work with 2D points:

var getDistance = function(p1, p2){
    return Math.sqrt(Math.pow(p1.x-p2.x, 2) + Math.pow(p1.y-p2.y, 2));
};

var getAngle = function(p1, p2){
    return Math.atan2(p2.y-p1.y, p2.x-p1.x);
};

The whole thing: JSFiddle and Updated-to-address-comment JSFiddle

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