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        如何确定一个点是否在二维凸多边形内?

        时间:2023-05-28
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                • 本文介绍了如何确定一个点是否在二维凸多边形内?的处理方法,对大家解决问题具有一定的参考价值,需要的朋友们下面随着跟版网的小编来一起学习吧!

                  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;
                    ...
                  }
                  

                  这篇关于如何确定一个点是否在二维凸多边形内?的文章就介绍到这了,希望我们推荐的答案对大家有所帮助,也希望大家多多支持跟版网!

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