如何确定点是否在2D凸多边形内？ [英] How to determine if a point is inside a 2D convex polygon?

问题描述

我有一个凸多边形（通常只是一个旋转的方形），我知道所有4个点。如何确定给定点（黄色/绿色）是否在内多边形？

解决方案

http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html 显示如何做这对于任何多边形。

我有这个Java的实现，但是它太大而不能完整地发布在这里。然而，你应该能够解决它：

  class Boundary {
 private final Point [] points; //构成边界的点
 ... 
 
 
 / ** 
 *如果给定点包含在边界内，则返回true。 
 *参见：http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html 
 * @param test检查
 * @return true如果点在边界内，则否则返回false 
 * 
 * / 
 public boolean contains（Point test）{
 int i; 
 int j; 
布尔结果= false; （（points [i] .y> test.y）！
 for（i = 0，j = points.length-1; i （test.x<（points [j] .x  -  points [i] .x）*（test.y  -  points [i] .y）/（points [j] .y-points [i] .y）+ points [i] .x））{
 result =！result; 
} 
} 
返回结果; 
 
 
 $ / code $ / pre 
 
 
这里是Point类的草图 p> 
 
 
  / ** 
 *二维笛卡尔点。 
 * / 
 public class Point {
 public final double x; 
 public final double y; 
 ... 
} 
  
 
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?



EDIT:  For this particular project, I don't have access to all of the libraries of the JDK, such as AWT.
解决方案
This page: http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html shows how to do this for any polygon.

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;
    }
}
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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