Canvas.setpenopacity(0.4);

// Global code will be evaluated once.
const turtle = new Turtle();
turtle.penup();

// Cardinal Splines  ref: https://stackoverflow.com/questions/7054272/how-to-draw-smooth-curve-through-n-points-using-javascript-html5-canvas
turtle.drawSpline = (pts, tension = 0.5, isClosed = false, numOfSegments = 16) => {
    const res = []; // clone array
    const _pts = pts.slice(0);
    // The algorithm require a previous and next point to the actual point array.
    // Check if we will draw closed or open curve.
    // If closed, copy end points to beginning and first points to end
    // If open, duplicate first points to befinning, end points to end
    if (isClosed) {
        _pts.unshift(pts[pts.length - 2]);
        _pts.unshift(pts[pts.length - 4]);
        _pts.unshift(pts[pts.length - 2]);
        _pts.unshift(pts[pts.length - 4]);
        _pts.push(pts[0]);
        _pts.push(pts[1]);
    }
    else {
        _pts.unshift(pts[1]);   //copy 1. point and insert at beginning
        _pts.unshift(pts[0]);
        _pts.push(pts[pts.length - 4]); //copy last point and append
        _pts.push(pts[pts.length - 2]);
    }
    // ok, lets start..
    // 1. loop goes through point array
    // 2. loop goes through each segment between the 2 pts + 1e point before and after
    for (let i = 2; i < (_pts.length - 8); i += 4) {
        for (let t = 0; t <= numOfSegments; t++) {
            // calc tension vectors
            const t1x = (_pts[i+2] - _pts[i-2]) * tension;
            const t2x = (_pts[i+4] - _pts[i]) * tension;
            const t1y = (_pts[i+3] - _pts[i-1]) * tension;
            const t2y = (_pts[i+5] - _pts[i+1]) * tension;
            // calc step
            const st = t / numOfSegments;
            // calc cardinals
            const c1 =   2 * Math.pow(st, 3)  - 3 * Math.pow(st, 2) + 1; 
            const c2 = -(2 * Math.pow(st, 3)) + 3 * Math.pow(st, 2); 
            const c3 =       Math.pow(st, 3)  - 2 * Math.pow(st, 2) + st; 
            const c4 =       Math.pow(st, 3)  -     Math.pow(st, 2);
            // calc x and y cords with common control vectors
            const x = c1 * _pts[i]    + c2 * _pts[i+2] + c3 * t1x + c4 * t2x;
            const y = c1 * _pts[i+1]  + c2 * _pts[i+3] + c3 * t1y + c4 * t2y;
            //store points in array
            res.push(x);
            res.push(y);
        }
    }
    // draw
    turtle.goto(res[0], res[1]);
    turtle.down();
    for(let i = 2; i < res.length - 2; i += 4) turtle.goto(res[i], res[i+ 1]);
    turtle.up();
    return res;
}

//////////////////////////////////////////
const points = [];
const velocities = [];
const acceleration = [];

for (let i = 0; i < 30; i++) {
    points.push(i * (200 / 30) - 100, 0.25 * 100 * (Math.random() - Math.random()));
    velocities.push(0, 0);
    acceleration.push(0,0)
}

// The walk function will be called until it returns false.
function walk(i) {
    for (let y = 0; y < 60; y++) {
        
        t = Math.random() - Math.random()
        
        acceleration[y] = 0.05*t//(2*Math.random()-1)
        velocities[y] += 0.03 * t +(1/2)*acceleration[y]*(t**2);
        points[y] += velocities[y];
	}
	turtle.drawSpline(points);
    return i < 500;
}