问题描述
我正在使用CoreGraphics绘制二次贝塞尔曲线，但想计算曲线的最小/最大值.我不是来自数学背景，所以这有点麻烦.有人对解决此问题有任何文章或想法吗?
I am using CoreGraphics to draw a quadratic bezier but want to computer the min/max value of the curve. I am not from a mathematical background so this has become a bit troublesome. Does anyone have any articles or ideas about how to solve this?
推荐答案
对于二次贝塞尔曲线，这实际上很简单.
For a quadratic Bezier, this is actually quite simple.
将三个控制点定义为P0 = (x0,y0)，P1 = (x1,y1)和P2 = (x2,y2).要在x中找到极值，请求解以下方程:
Define your three control points as P0 = (x0,y0), P1 = (x1,y1) and P2 = (x2,y2). To find the extrema in x, solve this equation:
t = (x0 - x1) / (x0 - 2*x1 + x2)
如果为0 <= t <= 1，则在t处评估曲线并将位置存储为Px.对y做同样的事情:
If 0 <= t <= 1, then evaluate your curve at t and store the location as Px. Do the same thing for y:
t = (y0 - y1) / (y0 - 2*y1 + y2)
同样，如果为0 <= t <= 1，则在t处评估曲线并将位置存储为Py.最后，找到包含P0，P2，Px(如果找到)和Py(如果找到)的与轴对齐的边界框.此边界框还将紧密约束2D二次Bezier曲线.
Again, if 0 <= t <= 1, evaluate your curve at t and store the location as Py. Finally, find the axis-aligned bounding box containing P0, P2, Px (if found) and Py (if found). This bounding box will also tightly bound your 2D quadratic Bezier curve.
这篇关于使用CoreGraphics查找二次贝塞尔曲线的最小值/最大值的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持！