变形最小的平滑折线

发布于 2024-08-05 09:56:51 字数 543 浏览 5 评论 0 原文

我有一条二维闭合折线，相当平滑。然而，定义多段线的顶点的间距并不相等。有时两个人会非常接近，有时多达四个人会非常接近。

我想平滑折线，但常规平均算法往往会缩小面积：

for (int i = 0; i < (V.Length-1); i++)
{
   PointF prev = V[i-1]; //I have code that wraps the index around.
   PointF next = V[i+1];       
   PointF pt = V[i];

   float ave_x = one_third * (prev.X + next.X + pt.X);
   float ave_y = one_third * (prev.Y + next.Y + pt.Y);

   smooth_polyline[i] = new PointF(ave_x, ave_y);
}

我的折线包含数千个点，并且两个相邻线段之间的角度通常小于 1 度。

是否有更好的方法来平滑这些曲线，使顶点间隔更均匀，而不会对面积产生太大影响？

原文

I've got a 2D closed polyline, which is reasonably smooth. The vertices that define the polyline however are not spaced equally. Sometimes two will be very close, sometimes as many as four will be very close together.

I'd like to smooth the polyline, but a regular averaging algorithm tends to shrink the area:

for (int i = 0; i < (V.Length-1); i++)
{
   PointF prev = V[i-1]; //I have code that wraps the index around.
   PointF next = V[i+1];       
   PointF pt = V[i];

   float ave_x = one_third * (prev.X + next.X + pt.X);
   float ave_y = one_third * (prev.Y + next.Y + pt.Y);

   smooth_polyline[i] = new PointF(ave_x, ave_y);
}

My polylines contain thousands of points and the angle between two adjacent segments is typically less than 1 degree.

Is there a better way to smooth these curves, something which will space the vertices more equally, without affecting the area too much?

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