如何确定一个点是否在二维凸多边形内?

问题描述

我有一个凸多边形(通常只是一个旋转的正方形)，我知道所有 4 个点.如何确定给定点(黄色/绿色)是否在多边形内部?

I have a convex polygon (typically just a rotated square), and I know all of 4 points. How do I determine if a given point (yellow/green) is inside the polygon?

对于这个特定项目，我无权访问 JDK 的所有库，例如 AWT.

For this particular project, I don't have access to all of the libraries of the JDK, such as AWT.

推荐答案

本页:http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html 展示了如何做这适用于任何多边形.

This page: http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html shows how to do this for any polygon.

我有一个 Java 实现，但它太大了，无法在此处完整发布.但是，您应该能够解决:

I have a Java implementation of this, but it is too big to post here in its entirety. However, you should be able to work it out:

class Boundary {
    private final Point[] points; // Points making up the boundary
    ...


    /**
     * Return true if the given point is contained inside the boundary.
     * See: http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
     * @param test The point to check
     * @return true if the point is inside the boundary, false otherwise
     *
     */
    public boolean contains(Point test) {
      int i;
      int j;
      boolean result = false;
      for (i = 0, j = points.length - 1; i < points.length; j = i++) {
        if ((points[i].y > test.y) != (points[j].y > test.y) &&
            (test.x < (points[j].x - points[i].x) * (test.y - points[i].y) / (points[j].y-points[i].y) + points[i].x)) {
          result = !result;
         }
      }
      return result;
    }
}

这是 Point 类的草图

And here is a sketch of the Point class

/**
 * Two dimensional cartesian point.
 */
public class Point {
  public final double x;
  public final double y;
  ...
}

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