查找使用C＃多边形的中轴 [英] Find medial axis of a polygon using C#
问题描述
我一直在负责找出如何找到一个多边形的中心线。我的谷歌搜索使我相信，我需要什么叫中轴。像这样的：
I've been tasked to figure out how to find the centerline of a polygon. My google searches led me to believe that what I need is called the 'Medial Axis'. Like this:
据我读过，我需要什么可以通过使用段的二维Voronoi图构建算法产生。
According to what I've read, what I need can be produced by using a 2D Voronoi diagram construction algorithm for segments.
我发现CodePlex上的Voronoi图算法（FortuneVoronoi）的C＃版本和应用我的多边形来后，我结束了这一点：
I've found a C# version of the Voronoi algorithm on codeplex (FortuneVoronoi) and after applying my polygon to it, I end up with this:
绿色是原来的多边形。橙色是的Voronoi顶点和黑线是Voronoi图的边缘。
The green is the original polygon. The orange are the Voronoi vertices and the black lines are the voronoi edges.
我可以看到什么，我需要在那些顶点气质，但我不能确定的要求下一步要过滤掉所有的东西，我不需要。
I can see the makings of what I need in those vertices, but I'm unsure of the next step required to filter out all the stuff I don't need.
我会很感激你能提供任何帮助。
I'd appreciate any help you can offer.
推荐答案
一个简单的解决方案将作为建议的意见：
One simple solution would be as suggested in the comments:
- 构建Delaunay三角的多边形顶点。
- 标识的Voronoi顶点的多边形内（见
的 http://en.wikipedia.org/wiki/Point_in_polygon ） - 输出的Voronoi边连接两个内部的Voronoi顶点。
如果你有大量的数据的交集可能是相当昂贵的。
If you have huge data the intersections might be quite costly.
然后，你可以做一个类似像问题方法，和该解决方案可以为你工作，以及。我会做它的方式：
Then you could do a similar approach like in the question, and this solution could work for you, as well. The way I would do it:
- 生成多边形顶点的Delaunay三角
- 插入。未覆盖的边缘德洛奈每个多边形边的中点。递归地做到这一点，直到所有多边形边缘被德劳内覆盖边缘。
- 标记全部德劳内边缘对应于一个多边形的边缘。
- 提取中轴按步骤3-5。在这个解决方案
- Build the Delaunay triangulation of the polygon vertices.
- Insert the midpoint of every polygon edge that is not covered by a delaunay edge. Do this recursively until all polygon edges are covered by Delaunay edges.
- Mark all Delaunay edges which correspond to a polygon edge.
- Extract the medial axis using steps 3.-5. in this solution
PS。请注意，这两个解决方案为中轴的一些的逼近的，它的计算究竟是更昂贵，但作为一个传情......你可以得到这样的结果黑色输入采样点：
PS. Note that both solutions give some approximation of the medial axis, computing it exactly is much more costly but as a teaser... you can get results like this for the black input sample points:
这篇关于查找使用C＃多边形的中轴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IT屋！
