平滑贝塞尔曲线
我想平滑 iPhone 中的一些手绘线。 我在中使用了以下代码 http://webdocs.cs.ualberta.ca/~graphics /books/GraphicsGems/gems/FitCurves.c
但是，我发现有些贝塞尔曲线是错误的，第二个控制点和终点无效。 以前有人遇到过同样的问题吗？ 谢谢。
I want to smooth some hand draw lines in iphone.
I have used the following code in
http://webdocs.cs.ualberta.ca/~graphics/books/GraphicsGems/gems/FitCurves.c
However, I found that some bezier curved was wrong, the second control point and end point is invalid.
Did anybody have the same problem before?
Thanks.
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贝塞尔曲线并非设计用于穿过提供的顶点！
它们旨在塑造受控制点影响的平滑曲线。
首先，您必须决定是否要在缺失点之间进行插值，
或者如果您想过滤不平滑的数据：
过滤
您应该查看带有小平均窗口的“滑动平均值”。 （尝试 5 - 10 像素）。
其工作原理如下：（查找 wiki 以获得详细说明）
我在这里使用 10 点的平均窗口：
首先计算点 0 - 9 的平均值，并将结果输出为结果点 0
然后计算点1 - 10的平均值并输出，结果1
等等。
插值
如果要使用平滑曲线在（缺失的）点之间进行插值，可以使用分段三次样条：
通过 3 个顶点计算三次多边形的系数。
您首先通过以下方式计算立方多边形：
Point[0] - Point[2]，但您仅从 Point[0] 到 Point[1] 绘制输出。
然后你继续下一步：并计算
Point[1] - Point[3]，但仅从 p1 到 p2 绘制。
等等。
您需要在 wiki 上搜索三次插值，以获取如何计算三次多边形（有时称为三次样条）的详细说明。
Bezier Curves are not designed to go through the provided vertices!
They are designed to shape a smooth curve influenced by the control points.
First you must decide if you want to interpolate between missing points,
or if you want to filter non smooth data:
Filtering
You should look at "sliding average" with a small averaging window. (try 5 - 10 pixel).
This works as follows: (look for wiki for a detailed description)
I use here an average window of 10 points:
start by calculation of the average of points 0 - 9, and output the result as result point 0
then calculate the average of point 1 - 10 and output, result 1
And so on.
Interpolation
If you want to interpolate between (missing) points using a smooth curve, you could use piece - wise cubic splines:
You calculate the coefficients of a cubic polygon through 3 vertices.
You start with calculating the cubic polygon through:
Point[0] - Point[2], but you draw your output only from Point[0] to Point[1] .
Then you move on one step: and calculate through
Point[1] - Point[3], but you draw only from p1 to p2.
And so on.
You need to search on wiki for cubic interpolation for a detailed explanation how to caluclate a cubic polygon (sometimes called cubic spline).