const bezierCurve =  {
    create(){

    },
    one(t,p1,p2){
        const [x1,y1] = p1;
        const [x2,y2] = p2;
        let x = x1 + (x2 - x1) * t;
        let y = y1 + (y2 - y1) * t;
        return [x,y];
    },
    two(t,p1,cp,p2){
        const [x1,y1] = p1;
        const [cx,cy] = cp;
        const [x2,y2] = p2;
        let x = (1 - t ) * ( 1 - t ) *  x1 + 2 * t * ( 1 - t) * cx + t * t * x2;
        let y = (1 - t ) * ( 1 - t ) *  y1 + 2 * t * ( 1 - t) * cy + t * t * y2;
        return [x,y];
    },
    three(){
        const [x1,y1] = p1;
        const [cx1,cy1] = cp1;
        const [cx2,cy2] = cp2;
        const [x2,y2] = p2;
        let x = x1 *  (1 - t ) * ( 1 - t ) * ( 1 - t ) +
                3 * cx1 * t * ( 1 - t ) * ( 1 - t ) +
                3 * cx2 * t * t * ( 1 - t ) +
                x2 * t * t * t;
        let y = y1 *  (1 - t ) * ( 1 - t ) * ( 1 - t ) +
                3 * cy1 * t * ( 1 - t ) * ( 1 - t ) +
                3 * cy2 * t * t * ( 1 - t ) +
                y2 * t * t * t;
        return [x,y];
    },
    multi:(()=>{
        var binomial = function(start,end){
            var cs = 1,bcs = 1;
            while(end > 0){
                cs *= start;
                bcs *= end;
                start --;
                end --;
            }
            return (cs/bcs);
        };
        var getPoint = (points,t)=>{
            var len = points.length;
            var x = 0,y = 0;

            for(var i = 0;i < len;i++){
                var point = points[i];
                x+= point[0]*Math.pow((1-t),(len - 1 - i)) * Math.pow(t,i) * (binomial(len - 1,i));
                y+= point[1]*Math.pow((1-t),(len - 1 - i)) * Math.pow(t,i) * (binomial(len - 1,i));
            }
            return [x,y];
        }
        return function(points,amount){
            var result = [];
            for(var i = 0 ; i < amount;i++ ){
                var point = getPoint(points,i / amount);
                result.push(point);
            }
            return result;
        }

    })()

}