Android 地图bezier曲线点的计算

我正在计算一条bezier曲线到地理位置点之间的必要点数，以便在Google Maps V2上绘制这条线。我的问题是，如果必须在“太平洋上空”划一条线，例如，起点在东京，终点在温哥华，那么这条线就不能正常工作。这些点的计算方向是错误的（绕地球向东），而不是向西。跨大西洋或亚洲的位置点计算和绘制正确

我的代码或思维中的错误在哪里

以下是用于计算的代码：

public static ArrayList<LatLng> bezier(LatLng p1, LatLng p2, double arcHeight, double skew, boolean up){
    ArrayList<LatLng> list = new ArrayList<LatLng>();
    try {
        if(p1.longitude > p2.longitude){
            LatLng tmp = p1;
            p1 = p2;
            p2 = tmp;
        }

        LatLng c = midPoint(p1, p2, 0);
        Log.v(TAG, "P1: " + p1.toString());
        Log.v(TAG, "P2: " + p2.toString());
        Log.v(TAG, "C: " + c.toString());

        double cLat = c.latitude;
        double cLon = c.longitude;


         //add skew and arcHeight to move the midPoint
        if(Math.abs(p1.longitude - p2.longitude) < 0.0001){
            if(up){
                cLon -= arcHeight;
            }else{
                cLon += arcHeight;
                cLat += skew;
            }
        }else{
            if(up){
                cLat += arcHeight;
            }else{
                cLat -= arcHeight;
                cLon += skew;
            }
        }

        list.add(p1);
         //calculating points for bezier
        double tDelta = 1.0/10;
        for (double t = 0;  t <= 1.0; t+=tDelta) {
            double oneMinusT = (1.0-t);
            double t2 = Math.pow(t, 2);
            double lon = oneMinusT * oneMinusT * p1.longitude
                        + 2 * oneMinusT * t * cLon
                        + t2 * p2.longitude;
            double lat = oneMinusT * oneMinusT * p1.latitude
                        + 2 * oneMinusT * t * cLat
                         + t2 * p2.latitude;
            Log.v(TAG, "t: " + t + "[" + lat +"|" + lon + "]");
            list.add(new LatLng(lat, lon));
        }

        list.add(p2);
    } catch (Exception e) {
        Log.e(TAG, "bezier", e);
    }
    return list;
}

这是地图的截图：

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我决定将地理位置转换为a，然后进行计算。这起作用了

以下是变化：

//inside bezier(...)

CartesianCoordinates cart1 = new CartesianCoordinates(p1);
CartesianCoordinates cart2 = new CartesianCoordinates(p2);
CartesianCoordinates cart3 = new CartesianCoordinates(cLat, cLon);

for (double t = 0; t <= 1.0; t += tDelta) {
    double oneMinusT = (1.0 - t);
    double t2 = Math.pow(t, 2);

    double y = oneMinusT * oneMinusT * cart1.y + 2 * t * oneMinusT * cart3.y + t2 * cart2.y;
    double x = oneMinusT * oneMinusT * cart1.x + 2 * t * oneMinusT * cart3.x + t2 * cart2.x;
    double z = oneMinusT * oneMinusT * cart1.z + 2 * t * oneMinusT * cart3.z + t2 * cart2.z;
    LatLng control = CartesianCoordinates.toLatLng(x, y, z);
    if (Config.DEBUG) 
        Log.v(TAG, "t: " + t + control.toString());
    list.add(control);
}

计算两个坐标中点的方法（可能不是100%完全数学正确）：

---

我决定将地理位置转换为a，然后进行计算。这起作用了

以下是变化：

//inside bezier(...)

CartesianCoordinates cart1 = new CartesianCoordinates(p1);
CartesianCoordinates cart2 = new CartesianCoordinates(p2);
CartesianCoordinates cart3 = new CartesianCoordinates(cLat, cLon);

for (double t = 0; t <= 1.0; t += tDelta) {
    double oneMinusT = (1.0 - t);
    double t2 = Math.pow(t, 2);

    double y = oneMinusT * oneMinusT * cart1.y + 2 * t * oneMinusT * cart3.y + t2 * cart2.y;
    double x = oneMinusT * oneMinusT * cart1.x + 2 * t * oneMinusT * cart3.x + t2 * cart2.x;
    double z = oneMinusT * oneMinusT * cart1.z + 2 * t * oneMinusT * cart3.z + t2 * cart2.z;
    LatLng control = CartesianCoordinates.toLatLng(x, y, z);
    if (Config.DEBUG) 
        Log.v(TAG, "t: " + t + control.toString());
    list.add(control);
}

计算两个坐标中点的方法（可能不是100%完全数学正确）：

---

您可能希望将此设置为正确答案，以便其他人不会在尝试回答时查看它。您介意给出您的中点方法吗？我正在尝试实现一个非常接近于此的目标：）您可能希望将此设置为正确答案，这样其他人就不会通过查看来尝试回答。您介意给出您的中点方法吗？我正在努力实现与此非常接近的目标：）

private static class CartesianCoordinates {
private static final int R = 6371; // approximate radius of earth
double x;
double y;
double z;

public CartesianCoordinates(LatLng p) {
    this(p.latitude, p.longitude);
}

public CartesianCoordinates(double lat, double lon) {
    double _lat = Math.toRadians(lat);
    double _lon = Math.toRadians(lon);

    x = R * Math.cos(_lat) * Math.cos(_lon);
    y = R * Math.cos(_lat) * Math.sin(_lon);
    z = R * Math.sin(_lat);
}

public static LatLng toLatLng(double x, double y, double z){
        return new LatLng(Math.toDegrees(Math.asin(z / R)), Math.toDegrees(Math.atan2(y, x)));
    }
}

private static LatLng midPoint(LatLng p1, LatLng p2) throws IllegalArgumentException{

    if(p1 == null || p2 == null)
        throw new IllegalArgumentException("two points are needed for calculation");

    double lat1;
    double lon1;
    double lat2;
    double lon2;

    //convert to radians
    lat1 = Math.toRadians(p1.latitude);
    lon1 = Math.toRadians(p1.longitude);
    lat2 = Math.toRadians(p2.latitude);
    lon2 = Math.toRadians(p2.longitude);

    double x1 = Math.cos(lat1) * Math.cos(lon1);
    double y1 = Math.cos(lat1) * Math.sin(lon1);
    double z1 = Math.sin(lat1);

    double x2 = Math.cos(lat2) * Math.cos(lon2);
    double y2 = Math.cos(lat2) * Math.sin(lon2);
    double z2 = Math.sin(lat2);

    double x = (x1 + x2)/2;
    double y = (y1 + y2)/2;
    double z = (z1 + z2)/2;

    double lon = Math.atan2(y, x);
    double hyp = Math.sqrt(x*x + y*y);

    // HACK: 0.9 and 1.1 was found by trial and error; this is probably *not* the right place to apply mid point shifting
    double lat = Math.atan2(.9*z, hyp); 
    if(lat>0) lat = Math.atan2(1.1*z, hyp);

    if(Config.DEBUG)
        Log.v(TAG, Math.toDegrees(lat) + " " + Math.toDegrees(lon));

    return new LatLng(Math.toDegrees(lat),  Math.toDegrees(lon));
}