算法找到封闭贝塞尔曲线边框？ [英] An algorithm to find bounding box of closed bezier curves?

问题描述

我在寻找一种算法来寻找边界直角轴封闭的二次贝塞尔曲线框（最大/最小分）：

I'm looking for an algorithm to find bounding box (max/min points) of a closed quadratic bezier curve in Cartesian axis:

input: C (a closed bezier curve)
output: A B C D points

注意：上图显示的平滑曲线。它可能是不顺利。 （有角）

Note: above image shows a smooth curve. it could be not smooth. (have corners)

推荐答案

嗯，我会说，你加入的所有端点的边界框开始。然后，你经历所有的贝塞尔元素。我认为在公式中的问题是这个：

Well, I would say you start by adding all endpoints to your bounding box. Then, you go through all the bezier elements. I assume the formula in question is this one:

从该提取物分别两个公式为X，和Y。通过采取衍生物（过零点）测试既为极值。那么相应的点添加到您的边框为好。

From this extract two formulas for X, and Y respectively. Test both for extrema by taking the derivative (zero crossings). Then add the corresponding points to your bounding box as well.

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