如何判断3个或更多线段的列表是否构成封闭区域（3D）？ [英] How can I tell if a list of 3 or more line segments form a closed region (in 3D)?

问题描述

好的，这是我到目前为止：

假设：您至少有3个共面线段

1. 按开始点的x坐标或类似的方式对列表进行排序




2. 第2行的开始点位于第1行的结束点，依此类推。




3. 如果最后一个结束点位于第一个结束点，那么我知道这是一个封闭的区域

我会如何去实施C-Sharp？你认为它甚至会起作用吗？如果是这样，我应该使用哪种排序算法？

解决方案

假设线段如下所示。
$ b

  class Segment 
 {
 public Point A {get;组; } 
 public Point B {get;组; } 
} 
 
 class Point 
 {
 public double X {get;组; } 
 public double Y {get;组; } 
 public double Z {get;组; } 
} 
  

假设段是包含3个线段的 IEnumerable< Segment> 。然后你可以检查3条线段是否形成一个封闭的三角形，如下所示。

  bool closed = segments 
 .SelectMany （segment => new [] {segment.A，segment.B}）
 .GroupBy（point => new {point.X，point.Y，point.Z}）
 .All （group => group.Count（）== 2）; 
  

这并不考虑 A 和 B 是一样的。您可以轻松添加，并自行决定在这种情况下您要做什么。

OK, here's what I have so far:

Assumptions: You have at least 3 coplanar line segments

1. Sort the list by x-coordinate of start point or something

2. Step through the list and see if the start point of line2 is at the end point of line 1 and so on

3. If the end point of the last one is on the start point of the first one, then I know it is a closed region

How would I go about implementing that in C-Sharp? Do you think it will even work? If so, what sorting algorithm should I use?

解决方案

Suppose a line segment is represented as follows.

class Segment
{
    public Point A { get; set; }
    public Point B { get; set; }
}

class Point
{
    public double X { get; set; }
    public double Y { get; set; }
    public double Z { get; set; }
}

Suppose segments is an IEnumerable<Segment> containing 3 line segments. Then you can check if the 3 line segments form a closed triangle as follows.

bool closed = segments
    .SelectMany(segment => new[] { segment.A, segment.B })
    .GroupBy(point => new { point.X, point.Y, point.Z })
    .All(group => group.Count() == 2);

This doesn't consider the degenerate case of segments for which A and B are the same. You can easily add that in and decide for yourself what you want to do in that case.

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