已知两个经纬度坐标点A和B，直线AB作为矩形的中心线，垂直于AB的边长是100米，求矩形四个角点的经纬度，请使用Java写出完整逻辑

好的，以下是Java代码实现:

import java.util.*;

public class RectangleCoordinates {

    public static void main(String[] args) {
        //坐标点A和B的经纬度
        double lonA = 116.407395;
        double latA = 39.904211;
        double lonB = 116.432464;
        double latB = 39.914418;

        //计算AB中心点的经纬度
        double centerLon = (lonA + lonB) / 2;
        double centerLat = (latA + latB) / 2;

        //计算垂直于AB的边长
        double width = 100;

        //计算AB的长度
        double length = Math.sqrt(Math.pow(lonB - lonA, 2) + Math.pow(latB - latA, 2));

        //计算AB的方向角
        double direction = Math.atan2(latB - latA, lonB - lonA);

        //计算左上角
        double leftTopLon = centerLon - (width / 2) * Math.cos(direction) - (length / 2) * Math.sin(direction);
        double leftTopLat = centerLat + (width / 2) * Math.sin(direction) - (length / 2) * Math.cos(direction);

        //计算右上角
        double rightTopLon = centerLon + (width / 2) * Math.cos(direction) - (length / 2) * Math.sin(direction);
        double rightTopLat = centerLat - (width / 2) * Math.sin(direction) - (length / 2) * Math.cos(direction);

        //计算右下角
        double rightBottomLon = centerLon + (width / 2) * Math.cos(direction) + (length / 2) * Math.sin(direction);
        double rightBottomLat = centerLat - (width / 2) * Math.sin(direction) + (length / 2) * Math.cos(direction);

        //计算左下角
        double leftBottomLon = centerLon - (width / 2) * Math.cos(direction) + (length / 2) * Math.sin(direction);
        double leftBottomLat = centerLat + (width / 2) * Math.sin(direction) + (length / 2) * Math.cos(direction);

        //输出四个角点的经纬度
        System.out.printf("左上角经度：%f，左上角纬度：%f\n", leftTopLon, leftTopLat);
        System.out.printf("右上角经度：%f，右上角纬度：%f\n", rightTopLon, rightTopLat);
        System.out.printf("右下角经度：%f，右下角纬度：%f\n", rightBottomLon, rightBottomLat);
        System.out.printf("左下角经度：%f，左下角纬度：%f\n", leftBottomLon, leftBottomLat);
    }
}

这个程序输入坐标点 A 和 B 的经纬度，然后计算矩形的四个角点的经纬度，并将结果输出。注意，这个程序没有进行输入合法性检查，需要确保输入的经纬度是合法的。