创建“分数”贝塞尔样条？
我有一条 4 控制点贝塞尔曲线，代表一些计时内容。第一个控制固定为 (0, 0)，最后一个控制固定为 (1, 1)。中间的两个点定义了一条贝塞尔曲线，指定如何从 0 到 1。
现在我需要根据第一条曲线创建第二条曲线。第二条曲线也需要从 (0, 0) 到 (1, 1)。但我想要第一条曲线的某个分数的形状，例如它应该看起来像第一条曲线的前 0.75。
换句话说，如果我将这些曲线用于计时目的，并且我跟踪曲线#1 10 秒，同时跟踪曲线#2 7.5 秒，则它们在被跟踪期间遵循相同的路径。 （有意义吗？）
考虑到小数（本例中为 0.75）参数，有没有办法获取第一条曲线的控制点并将它们“缩放”到第二条曲线中？
谢谢。
I have a 4-control-point bezier curve that represents some timing stuff. The first control is fixed at (0, 0) and the last control is fixed at (1, 1). The two points in between define a bezier curve that specifies how I get from 0 to 1.
Now I need to create a second curve, based off the first one. This second curve also needs to go from (0, 0) to (1, 1). But I'd like to to have the shape of some fraction of the first curve, for example it should look like the first 0.75 of the first curve.
In other words, if I'm using these curves for timing purposes, and I trace curve #1 for 10 seconds, and simultaneously trace curve #2 for 7.5 seconds, they follow the same path during the time they're both being traced. (Make sense?)
Is there a way to take the control points of the first curve and "scale" them into the second curve, given that fractional (0.75 in this example) parameter?
Thanks.
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也许这会有所帮助： 细分贝塞尔曲线。您不会“缩放”控制点，而是计算新的控制点。
此页面有一些很好的小程序演示该算法。
Perhaps this will help: Subdividing a Bezier curve. You don't "scale" the control points, you calculate new ones.
This page has some nice applets demonstrating the algorithm.