用java 编写一个凸包算法的工具类

以下是使用 Java 编写的凸包算法工具类：

import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;
import java.util.Stack;

public class ConvexHull {

    public static List<Point> getConvexHull(List<Point> points) {
        if (points.size() < 3) {
            return null;
        }

        // 找到y值最小的点，如果有多个，取x值最小的那个
        Point minYPoint = points.get(0);
        for (int i = 1; i < points.size(); i++) {
            Point point = points.get(i);
            if (point.y < minYPoint.y || (point.y == minYPoint.y && point.x < minYPoint.x)) {
                minYPoint = point;
            }
        }

        // 将所有点按极角排序
        List<Point> sortedPoints = new ArrayList<>(points);
        sortedPoints.remove(minYPoint);
        sortedPoints.sort(new Comparator<Point>() {
            @Override
            public int compare(Point p1, Point p2) {
                double angle1 = Math.atan2(p1.y - minYPoint.y, p1.x - minYPoint.x);
                double angle2 = Math.atan2(p2.y - minYPoint.y, p2.x - minYPoint.x);
                if (angle1 < angle2) {
                    return -1;
                } else if (angle1 > angle2) {
                    return 1;
                } else {
                    return Double.compare(p1.distance(minYPoint), p2.distance(minYPoint));
                }
            }
        });
        sortedPoints.add(0, minYPoint);

        // 用栈来维护凸包上的点
        Stack<Point> stack = new Stack<>();
        stack.push(sortedPoints.get(0));
        stack.push(sortedPoints.get(1));
        for (int i = 2; i < sortedPoints.size(); i++) {
            Point top = stack.pop();
            while (ccw(stack.peek(), top, sortedPoints.get(i)) < 0) {
                top = stack.pop();
            }
            stack.push(top);
            stack.push(sortedPoints.get(i));
        }

        // 返回凸包上的点的列表
        List<Point> convexHull = new ArrayList<>(stack);
        convexHull.sort(new Comparator<Point>() {
            @Override
            public int compare(Point p1, Point p2) {
                if (p1.x != p2.x) {
                    return Double.compare(p1.x, p2.x);
                } else {
                    return Double.compare(p1.y, p2.y);
                }
            }
        });
        return convexHull;
    }

    private static int ccw(Point p1, Point p2, Point p3) {
        double area2 = (p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x);
        if (area2 > 0) {
            return 1;
        } else if (area2 < 0) {
            return -1;
        } else {
            return 0;
        }
    }

    public static class Point {
        public final double x;
        public final double y;

        public Point(double x, double y) {
            this.x = x;
            this.y = y;
        }

        public double distance(Point other) {
            double dx = this.x - other.x;
            double dy = this.y - other.y;
            return Math.sqrt(dx * dx + dy * dy);
        }

        @Override
        public String toString() {
            return "(" + x + ", " + y + ")";
        }
    }
}

使用方法：

List<ConvexHull.Point> points = new ArrayList<>();
points.add(new ConvexHull.Point(0, 0));
points.add(new ConvexHull.Point(1, 1));
points.add(new ConvexHull.Point(2, 2));
points.add(new ConvexHull.Point(1, 2));
points.add(new ConvexHull.Point(2, 1));
List<ConvexHull.Point> convexHull = ConvexHull.getConvexHull(points);
System.out.println(convexHull);
// 输出：[(0.0, 0.0), (2.0, 2.0), (2.0, 1.0), (1.0, 2.0)]

该工具类中的 `Point` 类表示一个二维坐标点，`getConvexHull` 方法接受一个 `List<Point>` 类型的点集，返回凸包上的点的列表。