Cesium 根据飞机航线计算飞机的Heading(偏航角)、Pitch(俯仰角)、Roll(翻滚角)

需求

设置飞机的一些座标位置(经纬度高度)，插值得到更多的座标位置，然后飞机按照这些座标集合形成的航线飞行，飞机的朝向、俯仰角以及飞机转弯时的翻转角根据座标集合计算得出，而不需要手动设置heading、pitch、roll。

座标插值

不知道为什么，可能是飞行速度变化太大，我用Cesium自带的插值，计算出的航线很奇怪

// 如下代码插值计算出的航线有问题
property.setInterpolationOptions({ 
    interpolationDegree : 5, 
    interpolationAlgorithm : Cesium.LagrangePolynomialApproximation 
}); 

自己写的插值计算，效果等同于Cesium自带的线性插值。
思路很简单，每次插值，就是取时间的中点，两个座标的中点。
代码如下：

/**
 * 重新采样this.DronePositions
 */
DetectsDrones.prototype.sameple = function () {
    for (let i = 0; i < 3; i++) {
        this.samepleOnce();
    }
}

/**
 * 重新采样this.DronePositions
 */
DetectsDrones.prototype.samepleOnce = function () {
    for (let i = 0; i < this.DronePositions.length - 1; i += 2) {
        let pos1 = this.DronePositions[i];
        let pos2 = this.DronePositions[i + 1];
        let time1 = dayjs(pos1.time, 'YYYY-MM-DD HH:mm:ss');
        let time2 = dayjs(pos2.time, 'YYYY-MM-DD HH:mm:ss');
        let time = time1.add(time2.diff(time1) / 2.0, 'millisecond');
        let lng = (pos1.targetPosition.lng + pos2.targetPosition.lng) / 2.0;
        let lat = (pos1.targetPosition.lat + pos2.targetPosition.lat) / 2.0;
        let height = (pos1.targetPosition.height + pos2.targetPosition.height) / 2.0;
        let heading = (pos1.targetPosition.heading + pos2.targetPosition.heading) / 2.0;
        let pitch = (pos1.targetPosition.pitch + pos2.targetPosition.pitch) / 2.0;
        let roll = (pos1.targetPosition.roll + pos2.targetPosition.roll) / 2.0;
        let pos = {
            time: time.format('YYYY-MM-DD HH:mm:ss.SSS'),
            targetPosition: {
                lng: lng,
                lat: lat,
                height: height,
                heading: heading,
                pitch: pitch,
                roll: roll,
            }
        }
        this.DronePositions.splice(i + 1, 0, pos);
    }
}

根据航线座标集合计算heading、pitch、roll

从网上抄的计算heading和pitch的方法(参考博客：https://blog.csdn.net/u010447508/article/details/105562542?_refluxos=a10)：

/**
 * 根据两个座标点,获取Heading(朝向)
 * @param { Cesium.Cartesian3 } pointA 
 * @param { Cesium.Cartesian3 } pointB 
 * @returns 
 */
function getHeading(pointA, pointB) {
    //建立以点A为原点，X轴为east,Y轴为north,Z轴朝上的座标系
    const transform = Cesium.Transforms.eastNorthUpToFixedFrame(pointA);
    //向量AB
    const positionvector = Cesium.Cartesian3.subtract(pointB, pointA, new Cesium.Cartesian3());
    //因transform是将A为原点的eastNorthUp座标系中的点转换到世界座标系的矩阵
    //AB为世界座标中的向量
    //因此将AB向量转换为A原点座标系中的向量，需乘以transform的逆矩阵。
    const vector = Cesium.Matrix4.multiplyByPointAsVector(
        Cesium.Matrix4.inverse(transform, new Cesium.Matrix4()),
        positionvector,
        new Cesium.Cartesian3()
    );
    //归一化
    const direction = Cesium.Cartesian3.normalize(vector, new Cesium.Cartesian3());
    //heading
    let heading = Math.atan2(direction.y, direction.x) - Cesium.Math.PI_OVER_TWO;
    heading = Cesium.Math.TWO_PI - Cesium.Math.zeroToTwoPi(heading);
    return Cesium.Math.toDegrees(heading);
}

/**
 * 根据两个座标点,获取Pitch(仰角)
 * @param { Cesium.Cartesian3 } pointA 
 * @param { Cesium.Cartesian3 } pointB 
 * @returns 
 */
function getPitch(pointA, pointB) {
    let transfrom = Cesium.Transforms.eastNorthUpToFixedFrame(pointA);
    const vector = Cesium.Cartesian3.subtract(pointB, pointA, new Cesium.Cartesian3());
    let direction = Cesium.Matrix4.multiplyByPointAsVector(Cesium.Matrix4.inverse(transfrom, transfrom), vector, vector);
    Cesium.Cartesian3.normalize(direction, direction);
    //因为direction已归一化，斜边长度等于1，所以余弦函数等于direction.z
    let pitch = Cesium.Math.PI_OVER_TWO - Cesium.Math.acosClamped(direction.z);
    return Cesium.Math.toDegrees(pitch);
}

根据航线座标集合计算heading、pitch、roll：
代码中this.DronePositions是无人机群的座标集合，座标放在targetPosition属性中

/**
 * 计算无人机群的heading
 */
DetectsDrones.prototype.calcHeading = function () {
    // 清空原有heading
    this.DronePositions.map(pos => {
        pos.targetPosition.heading = undefined;
    });

    for (let i = 0; i < this.DronePositions.length - 1; i++) {
        let pos1 = this.DronePositions[i];
        let pos2 = this.DronePositions[i + 1];
        let heading = -90 + getHeading(Cesium.Cartesian3.fromDegrees(pos1.targetPosition.lng, pos1.targetPosition.lat), Cesium.Cartesian3.fromDegrees(pos2.targetPosition.lng, pos2.targetPosition.lat));
        if (!pos1.targetPosition.heading) {
            pos1.targetPosition.heading = heading;
        }
        pos2.targetPosition.heading = heading;
    }
}

/**
 * 计算无人机群的pitch
 */
DetectsDrones.prototype.calcPitch = function () {
    // 清空原有pitch
    this.DronePositions.map(pos => {
        pos.targetPosition.pitch = undefined;
    });

    for (let i = 0; i < this.DronePositions.length - 1; i++) {
        let pos1 = this.DronePositions[i];
        let pos2 = this.DronePositions[i + 1];
        let pitch = getPitch(Cesium.Cartesian3.fromDegrees(pos1.targetPosition.lng, pos1.targetPosition.lat, pos1.targetPosition.height), Cesium.Cartesian3.fromDegrees(pos2.targetPosition.lng, pos2.targetPosition.lat, pos2.targetPosition.height));
        if (!pos1.targetPosition.pitch) {
            pos1.targetPosition.pitch = pitch;
        }
        pos2.targetPosition.pitch = pitch;
    }
}

/**
 * 计算无人机群的roll(不支持转弯大于90度)
 */
DetectsDrones.prototype.calcRoll = function () {
    // 清空原有roll
    this.DronePositions.map(pos => {
        pos.targetPosition.roll = undefined;
    });

    for (let i = 1; i < this.DronePositions.length - 1; i++) {
        let pos1 = this.DronePositions[i];
        let pos2 = this.DronePositions[i + 1];
        let deltaHeading = pos2.targetPosition.heading - pos1.targetPosition.heading;
        pos2.targetPosition.roll = deltaHeading / 1.5;
    }
}

效果

主要是飞机的朝向和转弯时的翻滚，俯仰角这里没体现。

遇到的问题

1. 插值计算的问题，就是设置的座标集合，是拆线，最好把它插值成平滑曲线，但是Cesium自带的插值，有时间参数，而我想仅仅通过经纬度集合来插值。
2. 我写的计算roll的方法有问题，不支持转弯大于90度的情况，花了一些时间，没搞定。转弯小于90度，凑合用，测试了几组数据没问题，但仍不确定有没有BUG。严格来讲，根据这些参数，这个roll是算不出来的，但是，该算法要求根据飞机的转弯半径及方向，给出一个相对合理的roll值。
   抛砖引玉，有没有高手给个提示，插值问题怎么解决？roll的正确的通用的计算方法？