包含原始详细的多边形简体中文（或平滑）多边形 [英] Simplified (or smooth) polygons that contain the original detailed polygon

问题描述

我有一个详细的2D多边形（重presenting一个地理区域）是一个非常大的组顶点的定义。我正在寻找一种算法，将简化和平滑多边形，（减少顶点数量）与约束的面积的所得多边形必须包含详细的多边形的所有顶点。

I have a detailed 2D polygon (representing a geographic area) that is defined by a very large set of vertices. I'm looking for an algorithm that will simplify and smooth the polygon, (reducing the number of vertices) with the constraint that the area of the resulting polygon must contain all the vertices of the detailed polygon.

有关背景下，这里有一个复杂的多边形边缘的例子：

For context, here's an example of the edge of one complex polygon:

我的研究：

• 我发现道格拉斯 - 普克算法，这将减少顶点的数量 - 但由此产生的多边形不包含所有原始多边形的顶点。看到这篇文章的维基百科 Ramer - 道格拉斯 - 普克

• I found the Ramer–Douglas–Peucker algorithm which will reduce the number of vertices - but the resulting polygon will not contain all of the original polygon's vertices. See this article Ramer-Douglas-Peucker on Wikipedia

我认为扩大多边形（我相信这也被称为向外多边形抵消）。我发现这些问题：扩大多边形（凸只）和<一href="http://stackoverflow.com/questions/1109536/an-algorithm-for-inflating-deflating-offsetting-buffering-polygons"标题=充气多边形>充气多边形。但我不认为这会大大减少我的多边形的细节。

I considered expanding the polygon (I believe this is also known as outward polygon offsetting). I found these questions: Expanding a polygon (convex only) and Inflating a polygon. But I don't think this will substantially reduce the detail of my polygon.

感谢您的建议，您可以给我！

Thanks for any advice you can give me!

推荐答案

修改

截至2013年，大多数以下链接不起作用了。然而，我发现的被引论文，包括算法，仍然可在这（很慢）服务器。

As of 2013, most links below are not functional anymore. However, I've found the cited paper, algorithm included, still available at this (very slow) server.

在这里 你可以找到准确地处理你的问题的项目。虽然这主要与面积装由点，你可以将它与周边的类型定义为你的工作。

Here you can find a project dealing exactly with your issues. Although it works primarily with an area "filled" by points, you can set it to work with a "perimeter" type definition as yours.

有使用用于计算该区域的k最近邻方法。

It uses a k-nearest neighbors approach for calculating the region.

样品：

<一个href="http://repositorium.sdum.uminho.pt/request-item;jsessionid=94383BCD27BDF40B4AB3B5CF6A1788FB?handle=1822/6429&bitstream-id=25848">Here可以请求该纸的副本。

Here you can request a copy of the paper.

貌似他们 计划请求计算提供在线服务 ，但我没有测试它，也许它没有运行。

Seemingly they planned to offer an online service for requesting calculations, but I didn't test it, and probably it isn't running.

心连心！

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