第四章第三题（几何：估算面积）(Geography: estimate areas)

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第四章第三题（几何：估算面积）(Geography: estimate areas)

• *4.3（几何：估算面积）应用4.1节图中以下地点的GPS位置：Georgia州的Atlanta、Florida州的Orlando、Georgia州的Savannah、North Carolina州的Charlotte。计算被这四个城市所围起来的区域的面积。（提示：使用编程练习题4.2中的公式来计算两个城市之间的距离。将多边形分为两个三角形，使用编程练习题2.19中的公式计算三角形面积。）
  *4.3(Geography: estimate areas) Use the GPS locations for Atlanta, Georgia; Orlando, Florida; Savannah, Georgia; and Charlotte, North Carolina in the figure in Section 4.1 to compute the estimated area enclosed by these four cities. (Hint: Use the formula in Programming Exercise 4.2 to compute the distance between two cities. Divide the polygon into two triangles and use the formula in Programming Exercise 2.19 to compute the area of a triangle.)
• 参考代码：

package chapter04;

public class Code_03 {
    public static void main(String[] args) {
        final double d1, d2, d3, d4, d5, A1, A2;
        final double HalfSumLengthSide1, HalfSumLengthSide2;
        final double x1, y1, x2, y2, x3, y3, x4, y4;
        final double x1Radian,y1Radian,x2Radian,y2Radian;
        final double x3Radian,y3Radian,x4Radian,y4Radian;
        final double EARTH_AVERAGE_RADIUS = 6371.01;

        x1 = 35.2270869;
        y1 = -80.8431267;
        x1Radian = Math.toRadians(x1);
        y1Radian = Math.toRadians(y1);

        x2 = 33.7489954;
        y2 = -84.3879824;
        x2Radian = Math.toRadians(x2);
        y2Radian = Math.toRadians(y2);

        x3 = 32.0835407;
        y3 = -81.0998342;
        x3Radian = Math.toRadians(x3);
        y3Radian = Math.toRadians(y3);

        x4 = 28.5383355;
        y4 = -81.3792365;
        x4Radian = Math.toRadians(x4);
        y4Radian = Math.toRadians(y4);

        d1 = EARTH_AVERAGE_RADIUS * Math.acos(Math.sin(x1Radian) * Math.sin(x2Radian)
                + Math.cos(x1Radian) * Math.cos(x2Radian) * Math.cos(y1Radian - y2Radian));

        d2 = EARTH_AVERAGE_RADIUS * Math.acos(Math.sin(x1Radian) * Math.sin(x3Radian)
                + Math.cos(x1Radian) * Math.cos(x3Radian) * Math.cos(y1Radian - y3Radian));

        d3 = EARTH_AVERAGE_RADIUS * Math.acos(Math.sin(x4Radian) * Math.sin(x2Radian)
                + Math.cos(x4Radian) * Math.cos(x2Radian) * Math.cos(y4Radian - y2Radian));

        d4 = EARTH_AVERAGE_RADIUS * Math.acos(Math.sin(x3Radian) * Math.sin(x4Radian)
                + Math.cos(x3Radian) * Math.cos(x4Radian) * Math.cos(y3Radian - y4Radian));

        d5 = EARTH_AVERAGE_RADIUS * Math.acos(Math.sin(x3Radian) * Math.sin(x2Radian)
                + Math.cos(x3Radian) * Math.cos(x2Radian) * Math.cos(y3Radian - y2Radian));

        HalfSumLengthSide1 = (d1 + d2 + d5) / 2;
        HalfSumLengthSide2 = (d3 + d4 + d5) / 2;

        A1 = Math.pow(HalfSumLengthSide1 * (HalfSumLengthSide1 - d1)
                * (HalfSumLengthSide1 - d2) * (HalfSumLengthSide1 - d5), 0.5);

        A2 = Math.pow(HalfSumLengthSide2 * (HalfSumLengthSide2 - d3)
                * (HalfSumLengthSide2 - d4) * (HalfSumLengthSide2 - d5), 0.5);

        System.out.println("The estimated area enclosed by these four cities is " + (A1 + A2));
    }
}

• 结果显示：

The estimated area enclosed by these four cities is 117863.34165942381

Process finished with exit code 0

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