是多边形内的点吗？(Is point inside polygon?)

我需要编写一个函数来计算一个点是否在多边形内（true / false）。

多边形总是包含4个点。我正在从SVG文件中读取多边形和点

因此对于折线，它将是前4组坐标，而对于文本X和Y，则是矩阵括号中的最后2个数字。也不知道文本的那个点是文本的中心还是左下角（假设它是这个）。

到目前为止，我得到了列表中的点和多边形的所有坐标，所以我正在那样交叉检查。

I need to write a function that will calculate if a point is inside polygon (true/false).

Polygon always contains 4 points. I'm reading polygons and points from SVG file

So for polyline it would be the first 4 sets of coordinates and for text X and Y are last 2 numbers in matrix brackets. Also don't know if that point for text is the center of text or bottom left corner (suppose it's this).

So far I got all coordinates for points and polygons in lists so I'm cross checking that way.

最满意答案

测试点是否在多边形内部的简单方法是计算多边形边缘与源自测试点的光线之间的交点数。因为您可以将光线选择为任何您想要的光线，所以通常可以方便地将光线选择为与X轴平行。代码看起来像这样：

public static bool IsInPolygon( this Point testPoint, IList<Point> vertices ) { if( vertices.Count < 3 ) return false; bool isInPolygon = false; var lastVertex = vertices[vertices.Count - 1]; foreach( var vertex in vertices ) { if( testPoint.Y.IsBetween( lastVertex.Y, vertex.Y ) ) { double t = ( testPoint.Y - lastVertex.Y ) / ( vertex.Y - lastVertex.Y ); double x = t * ( vertex.X - lastVertex.X ) + lastVertex.X; if( x >= testPoint.X ) isInPolygon = !isInPolygon; } else { if( testPoint.Y == lastVertex.Y && testPoint.X < lastVertex.X && vertex.Y > testPoint.Y ) isInPolygon = !isInPolygon; if( testPoint.Y == vertex.Y && testPoint.X < vertex.X && lastVertex.Y > testPoint.Y ) isInPolygon = !isInPolygon; } lastVertex = vertex; } return isInPolygon; } public static bool IsBetween( this double x, double a, double b ) { return ( x - a ) * ( x - b ) < 0; }

在那里填充了一些额外的代码来处理一些字面角落情况（如果测试光线直接击中顶点，则需要一些特殊处理）。

A simple way to test whether a point is inside a polygon is to count the number of intersections between the edges of the polygon and a ray originating from the test point. Because you can pick the ray to be whatever you want, it's usually convenient to pick it to be parallel to the X axis. The code for that looks something like this:

public static bool IsInPolygon( this Point testPoint, IList<Point> vertices ) { if( vertices.Count < 3 ) return false; bool isInPolygon = false; var lastVertex = vertices[vertices.Count - 1]; foreach( var vertex in vertices ) { if( testPoint.Y.IsBetween( lastVertex.Y, vertex.Y ) ) { double t = ( testPoint.Y - lastVertex.Y ) / ( vertex.Y - lastVertex.Y ); double x = t * ( vertex.X - lastVertex.X ) + lastVertex.X; if( x >= testPoint.X ) isInPolygon = !isInPolygon; } else { if( testPoint.Y == lastVertex.Y && testPoint.X < lastVertex.X && vertex.Y > testPoint.Y ) isInPolygon = !isInPolygon; if( testPoint.Y == vertex.Y && testPoint.X < vertex.X && lastVertex.Y > testPoint.Y ) isInPolygon = !isInPolygon; } lastVertex = vertex; } return isInPolygon; } public static bool IsBetween( this double x, double a, double b ) { return ( x - a ) * ( x - b ) < 0; }

There's some extra code stuffed in there to deal with some literal corner cases (if the test ray hits a vertex directly, that needs some special treatment).

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是多边形内的点吗？(Is point inside polygon?)

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