cocos 贝塞尔曲线

/**
    * 二阶贝塞尔曲线运动
    * @param target 目标
    * @param duration 时间
    * @param c1 起始点
    * @param c2 控制点
    * @param to 终点
    * @param opts 自定义选项
    * @returns
    */
    public static bezierTo(target: any, duration: number, c1: Vec3, c2: Vec3, to: Vec3, opts: any) {
        opts = opts || Object.create(null);

        let twoBezier = (t: number, p1: Vec3, cp: Vec3, p2: Vec3) => {
            let x = (1 - t) * (1 - t) * p1.x + 2 * t * (1 - t) * cp.x + t * t * p2.x;
            let y = (1 - t) * (1 - t) * p1.y + 2 * t * (1 - t) * cp.y + t * t * p2.y;
            return new Vec3(x, y, 0);
        };
        opts.onUpdate = (arg: Vec3, ratio: number) => {
            target.position = twoBezier(ratio, c1, c2, to);
        };
        return tween(target).to(duration, {}, opts);
    }



    /**
     * 3阶贝塞尔曲线
     * @param target 
     * @param t 
     * @param p1 
     * @param cp1 
     * @param cp2 
     * @param p2 
     * @param opts 
     * @returns 
     */
    public static bezierTo3(target: any, t: number, p1: Vec3, cp1: Vec3, cp2: Vec3, p2: Vec3, opts: any) {
        opts = opts || Object.create(null);
        const threeBezier = (t: number, p1: Vec3, cp1: Vec3, cp2: Vec3, p2: Vec3) => {
            let x =
                (1 - t) * (1 - t) * (1 - t) * p1.x +
                3 * t * (1 - t) * (1 - t) * cp1.x +
                3 * t * t * (1 - t) * cp2.x +
                t * t * t * p2.x;
            let y =
                (1 - t) * (1 - t) * (1 - t) * p1.y +
                3 * t * (1 - t) * (1 - t) * cp1.y +
                3 * t * t * (1 - t) * cp2.y +
                t * t * t * p2.y;
            return new Vec3(x, y, 0);
        };
        opts.onUpdate = (arg: Vec3, ratio: number) => {
            target.position = threeBezier(ratio, p1, cp1, cp2, p2);
        };
        return tween(target).to(t, {}, opts);
    }










 /**
     * N阶贝塞尔曲线
     * @param target Node节点
     * @param t 时间
     * @param StartP 开始节点
     * @param cpN 经过的点
     * @param EndP 结束的节点
     * @param opts 回调
     * @returns 
     */
    public static bezierToN(target: any, t: number, StartP: Vec3, cpN: Array<Vec3>, EndP: Vec3, opts: any) {
        opts = opts || Object.create(null);
        const threeBezier = (t: number, StartP: Vec3, cpN: Array<Vec3>, EndP: Vec3) => {
            // console.log("cpN.length："+cpN.length)
            let x =
                Math.pow(1 - t, cpN.length + 1) * StartP.x +
                Math.pow(t, cpN.length + 1) * EndP.x;

            for (let index = 0; index < cpN.length; index++) {
                let val = cpN[index];

                let tNum = index + 1
                let oneTNum = cpN.length - index

                x = x + (cpN.length + 1) * Math.pow(t, tNum) * Math.pow((1 - t), oneTNum) * val.x


            }


            let y =
                Math.pow(1 - t, cpN.length + 1) * StartP.y +
                Math.pow(t, cpN.length + 1) * EndP.y;

            for (let index = 0; index < cpN.length; index++) {
                let val = cpN[index];

                let tNum = index + 1
                let oneTNum = cpN.length - index

                y = y + (cpN.length + 1) * Math.pow(t, tNum) * Math.pow((1 - t), oneTNum) * val.y


            }

            // console.log("x:" + x + "  y:" + y)

            return new Vec3(x, y, 0);
        };
        opts.onUpdate = (arg: Vec3, ratio: number) => {
            target.position = threeBezier(ratio, StartP, cpN, EndP);
        };
        return tween(target).to(t, {}, opts);
    }