package bianjie;
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import java.text.DecimalFormat;
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public class ThreePointCircle {
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/**
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* 根据圆上三个点计算圆心和半径
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*
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* @param point1 第一个点坐标，格式 "x,y"
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* @param point2 第二个点坐标，格式 "x,y"
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* @param point3 第三个点坐标，格式 "x,y"
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* @return 包含圆心和半径的字符串，例如 "圆心: 10.00,10.00; 半径: 5.00"
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*/
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public static String getCircleFromPoints(String point1, String point2, String point3) {
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try {
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// 1. 解析坐标点
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double[] p1 = parsePoint(point1);
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double[] p2 = parsePoint(point2);
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double[] p3 = parsePoint(point3);
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double x1 = p1[0], y1 = p1[1];
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double x2 = p2[0], y2 = p2[1];
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double x3 = p3[0], y3 = p3[1];
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// 2. 计算分母 D
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// 如果 D 为 0，说明三点共线，无法构成圆
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double D = 2 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2));
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if (Math.abs(D) < 1e-9) {
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return "错误: 输入的三个点共线，无法确定一个圆。";
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}
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// 3. 计算圆心坐标 (centerX, centerY)
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// 公式：
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// Ux = x^2 + y^2
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// centerX = (Ux1*(y2-y3) + Ux2*(y3-y1) + Ux3*(y1-y2)) / D
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// centerY = (Ux1*(x3-x2) + Ux2*(x1-x3) + Ux3*(x2-x1)) / D
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double sumSq1 = x1 * x1 + y1 * y1;
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double sumSq2 = x2 * x2 + y2 * y2;
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double sumSq3 = x3 * x3 + y3 * y3;
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double centerX = (sumSq1 * (y2 - y3) + sumSq2 * (y3 - y1) + sumSq3 * (y1 - y2)) / D;
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double centerY = (sumSq1 * (x3 - x2) + sumSq2 * (x1 - x3) + sumSq3 * (x2 - x1)) / D;
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// 4. 计算半径 (圆心到任意一点的距离)
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double radius = Math.sqrt(Math.pow(centerX - x1, 2) + Math.pow(centerY - y1, 2));
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// 5. 格式化输出 (保留两位小数，可根据需求调整)
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DecimalFormat df = new DecimalFormat("#.##");
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return String.format("圆心: %s,%s; 半径: %s",
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df.format(centerX),
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df.format(centerY),
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df.format(radius));
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} catch (NumberFormatException e) {
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return "错误: 坐标格式不正确，请使用 'x,y' 格式 (例如: '1.5,2.5')";
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} catch (Exception e) {
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return "错误: " + e.getMessage();
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}
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}
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/**
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* 辅助方法：将字符串 "x,y" 解析为 double 数组 [x, y]
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*/
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private static double[] parsePoint(String pointStr) {
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String[] parts = pointStr.split(",");
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if (parts.length != 2) {
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throw new IllegalArgumentException("坐标格式无效: " + pointStr);
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}
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double x = Double.parseDouble(parts[0].trim());
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double y = Double.parseDouble(parts[1].trim());
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return new double[]{x, y};
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}
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}
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