已知两个经纬度坐标点A和B，直线AB作为矩形的中心线，矩形的长等于直线AB的长，矩形的宽等于100m，求矩形四个角点的经纬度，请使用Java写出完整逻辑

好的，根据您的要求，我将以Java语言为例，为您提供完整逻辑。首先，我们需要使用Haversine公式计算出点A和点B之间的距离和方位角，然后根据方位角和距离计算出矩形四个角点的经纬度。

下面是完整代码：

import java.util.*;

public class Rectangle {

    // 地球半径，单位米
    private static final double EARTH_RADIUS = 6371000;

    // 计算距离和方位角
    private static double[] calculateDistanceAndBearing(double lat1, double lon1, double lat2, double lon2) {
        double[] result = new double[2];

        double lat1Rad = Math.toRadians(lat1);
        double lat2Rad = Math.toRadians(lat2);
        double dLonRad = Math.toRadians(lon2 - lon1);

        double y = Math.sin(dLonRad) * Math.cos(lat2Rad);
        double x = Math.cos(lat1Rad) * Math.sin(lat2Rad) - Math.sin(lat1Rad) * Math.cos(lat2Rad) * Math.cos(dLonRad);

        double distance = Math.sqrt(x * x + y * y) * EARTH_RADIUS;
        double bearing = Math.atan2(y, x);

        result[0] = distance;
        result[1] = bearing;

        return result;
    }

    // 计算矩形四个角点的经纬度
    private static List<double[]> calculateRectangle(double lat1, double lon1, double lat2, double lon2) {
        List<double[]> result = new ArrayList<>();

        double[] distanceAndBearing = calculateDistanceAndBearing(lat1, lon1, lat2, lon2);

        double lat1Rad = Math.toRadians(lat1);
        double lon1Rad = Math.toRadians(lon1);
        double bearingRad = distanceAndBearing[1];

        double halfWidth = distanceAndBearing[0] / 2;
        double halfHeight = 50;

        double latNW = Math.asin(Math.sin(lat1Rad) * Math.cos(halfWidth / EARTH_RADIUS)
                + Math.cos(lat1Rad) * Math.sin(halfWidth / EARTH_RADIUS) * Math.cos(bearingRad));
        double lonNW = lon1Rad + Math.atan2(Math.sin(bearingRad) * Math.sin(halfWidth / EARTH_RADIUS) * Math.cos(lat1Rad),
                Math.cos(halfWidth / EARTH_RADIUS) - Math.sin(lat1Rad) * Math.sin(latNW));

        double latSE = Math.asin(Math.sin(lat2) * Math.cos(halfWidth / EARTH_RADIUS)
                - Math.cos(lat2) * Math.sin(halfWidth / EARTH_RADIUS) * Math.cos(bearingRad + Math.PI));
        double lonSE = lon2 + Math.atan2(Math.sin(bearingRad + Math.PI) * Math.sin(halfWidth / EARTH_RADIUS) * Math.cos(lat2),
                Math.cos(halfWidth / EARTH_RADIUS) - Math.sin(lat2) * Math.sin(latSE));

        double latNE = Math.asin(Math.sin(latNW) * Math.cos(halfHeight / EARTH_RADIUS)
                + Math.cos(latNW) * Math.sin(halfHeight / EARTH_RADIUS));
        double lonNE = lonNW + Math.atan2(Math.sin(Math.PI / 2 - latNW) * Math.sin(halfHeight / EARTH_RADIUS),
                Math.cos(halfHeight / EARTH_RADIUS) - Math.sin(latNW) * Math.sin(latNE));

        double latSW = Math.asin(Math.sin(latSE) * Math.cos(halfHeight / EARTH_RADIUS)
                - Math.cos(latSE) * Math.sin(halfHeight / EARTH_RADIUS));
        double lonSW = lonSE + Math.atan2(Math.sin(Math.PI / 2 - latSE) * Math.sin(halfHeight / EARTH_RADIUS),
                Math.cos(halfHeight / EARTH_RADIUS) - Math.sin(latSE) * Math.sin(latSW));

        result.add(new double[] { Math.toDegrees(latNW), Math.toDegrees(lonNW) });
        result.add(new double[] { Math.toDegrees(latNE), Math.toDegrees(lonNE) });
        result.add(new double[] { Math.toDegrees(latSE), Math.toDegrees(lonSE) });
        result.add(new double[] { Math.toDegrees(latSW), Math.toDegrees(lonSW) });

        return result;
    }

    public static void main(String[] args) {
        double lat1 = 31.204692;
        double lon1 = 121.441038;
        double lat2 = 31.203485;
        double lon2 = 121.442985;

        List<double[]> rectangle = calculateRectangle(lat1, lon1, lat2, lon2);

        System.out.println("矩形四个角点的经纬度：");
        for (double[] point : rectangle) {
            System.out.println("(" + point[0] + ", " + point[1] + ")");
        }
    }
}

你可以将点A和点B的经纬度作为输入，该程序将输出矩形四个角点的经纬度。请注意，程序中的经纬度都是以度为单位的，而不是以弧度为单位的。