放宽钟形曲线的功能呢？ [英] easing functions for bell curves?

问题描述

罗伯特·彭纳的缓和功能可以很容易地创建各种动画行为通过移动的 X 0和1之间，作为所得的是的移动从0开始，在1 这里的例子。

Robert Penner's easing functions make it easy to create a variety of animation behaviors by moving X between 0 and 1, as the resultant Y moves starts at 0 and ends at 1. Examples here.

我想知道如果有一个钟形曲线这样一套功能？鉴于的 X 的0和1之间，这些函数将返回的是的0和1之间，从0开始和结束0

I am wondering if there is such a set of functions for bell curves? Given X between 0 and 1, these functions would return Y between 0 and 1, starting at 0 and ending at 0.

我从来没见过这样的集合，但之前，我去上拟合抛物线的所以一切都在0和1之间的配合两轴的，我想我会在这里首先检查

I've not seen such a collection, but before I get going on fitting parabolas so everything fits between 0 and 1 on both axes, I thought I'd check here first.

推荐答案

有很多常见的钟形函数的˚F的在[0,1]。我假设你希望他们满足F（0）= F（1）= F'（0）= F'（1）= 0和f（1/2）= 1。例如：

There are lots of common bell-shaped functions f on [0, 1]; I assume you want them to satisfy f(0) = f(1) = f'(0) = f'(1) = 0 and f(1/2) = 1. Examples:

• 任何对称 Beta分布密度函数，任何参数α=β> 1，是钟形并具有在端点零衍生物。也就是说， F（X）= 4 ^α* X ^（α - 1）*（1 - X）^（α - 1），其中 4 ^α是一个不断扩展它，使它上升到1：

• Any symmetric beta distribution density function, for any parameters α = β > 1, is bell-shaped and has zero derivative at the endpoints. That is, f(x) = 4^α * x^(α - 1) * (1 - x)^(α - 1), where 4^α is a constant to scale it so that it goes up to 1:

根据需要选择一个正弦函数的一段，起点和相邻波谷结束，和翻译/缩放。例如： F（X）=（SIN（2 *π*（X - 1/4））+ 1）/ 2 ：

Pick a segment of a sinusoidal function, starting and ending at adjacent troughs, and translating/scaling as desired. Example: f(x) = (sin(2 * π * (x - 1/4)) + 1) / 2:

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