b23_zuma/assets/script/zuma/Bezier.ts

/** @format */

export class Bezier {
    //  对外变量
    private static p0: cc.Vec2 // 起点
    private static p1: cc.Vec2 // 贝塞尔点
    private static p2: cc.Vec2 // 终点
    private static step: number = 0 // 分割份数

    //  辅助变量
    private static ax: number = 0
    private static ay: number = 0
    private static bx: number = 0
    private static by: number = 0

    private static A: number = 0
    private static B: number = 0
    private static C: number = 0

    private static total_length: number = 0 // 长度

    public constructor() {}

    //  速度函数
    private static Speed(t: number): number {
        return Math.sqrt(this.A * t * t + this.B * t + this.C)
    }

    //  长度函数
    private static Length(t: number): number {
        let temp1: number = Math.sqrt(this.C + t * (this.B + this.A * t))
        let temp2: number = 2 * this.A * t * temp1 + this.B * (temp1 - Math.sqrt(this.C))
        let temp3: number = Math.log(this.B + 2 * Math.sqrt(this.A) * Math.sqrt(this.C))
        let temp4: number = Math.log(this.B + 2 * this.A * t + 2 * Math.sqrt(this.A) * temp1)
        let temp5: number = 2 * Math.sqrt(this.A) * temp2
        let temp6: number = (this.B * this.B - 4 * this.A * this.C) * (temp3 - temp4)

        return (temp5 + temp6) / (8 * Math.pow(this.A, 1.5))
    }

    //  长度函数反函数，使用牛顿切线法求解
    private static InvertL(t: number, l: number): number {
        let t1: number = t
        let t2: number = 0
        do {
            t2 = t1 - (this.Length(t1) - l) / this.Speed(t1)
            if (Math.abs(t1 - t2) < 0.000001) break
            t1 = t2
        } while (true)
        return t2
    }

    //  返回所需总步数
    public static init($p0: cc.Vec2, $p1: cc.Vec2, $p2: cc.Vec2, $speed: number): number {
        this.p0 = $p0
        this.p1 = $p1
        this.p2 = $p2
        //step = 30;

        this.ax = this.p0.x - 2 * this.p1.x + this.p2.x
        this.ay = this.p0.y - 2 * this.p1.y + this.p2.y
        this.bx = 2 * this.p1.x - 2 * this.p0.x
        this.by = 2 * this.p1.y - 2 * this.p0.y

        this.A = 4 * (this.ax * this.ax + this.ay * this.ay)
        this.B = 4 * (this.ax * this.bx + this.ay * this.by)
        this.C = this.bx * this.bx + this.by * this.by

        //  计算长度
        this.total_length = this.Length(1)

        //  计算步数
        this.step = Math.floor(this.total_length / $speed)
        if (this.total_length % $speed > $speed / 2) this.step++

        return this.step
    }

    // 根据指定nIndex位置获取锚点：返回坐标和角度
    public static getAnchorPoint(nIndex: number): any[] {
        if (nIndex >= 0 && nIndex <= this.step) {
            let t: number = nIndex / this.step
            //  如果按照线性增长，此时对应的曲线长度
            let l: number = t * this.total_length
            //  根据L函数的反函数，求得l对应的t值
            t = this.InvertL(t, l)

            //  根据贝塞尔曲线函数，求得取得此时的x,y坐标
            let xx: number = (1 - t) * (1 - t) * this.p0.x + 2 * (1 - t) * t * this.p1.x + t * t * this.p2.x
            let yy: number = (1 - t) * (1 - t) * this.p0.y + 2 * (1 - t) * t * this.p1.y + t * t * this.p2.y

            //  获取切线
            let Q0: cc.Vec2 = new cc.Vec2((1 - t) * this.p0.x + t * this.p1.x, (1 - t) * this.p0.y + t * this.p1.y)
            let Q1: cc.Vec2 = new cc.Vec2((1 - t) * this.p1.x + t * this.p2.x, (1 - t) * this.p1.y + t * this.p2.y)

            //  计算角度
            let dx: number = Q1.x - Q0.x
            let dy: number = Q1.y - Q0.y
            let radians: number = Math.atan2(dy, dx)
            let degrees: number = (radians * 180) / Math.PI

            return [xx, yy, degrees]
        } else {
            return []
        }
    }
}