Bessel curve formula derivation principle

The Bessel curve (B zier curve), also known as the Baez curve or Bezier curve, is a mathematical curve is applied to 2D graphics applications. 1962, by the French engineer Pierre Beisel (Pierre B zier) has been widely published, he used the Bessel curve to the subject for car design. Bessel curve was originally developed by Paul de Casteljau in 1959 using de Casteljau algorithm to stabilize the numerical method for the calculation of the Baez curve. The core definition of the curve: the starting point, the end point (also known as anchor), control points. Then the Bessel curve formula is how derived? What is the principle? I think the implementation of the principle of understanding Bessel curve for IOS, Android and other interface deformation cool animated very helpful Oh, such as jelly, pull down to refresh the shopping cart into a small rocket launch, animation and so on. Thinking: iOS only provides us with a method up to three order Bessel curve, then we are able to realize their own 4 order, 5 order… N order?

The Book Jane markdown grammar cannot write several formulas, I made a screenshot of the handwriting handwriting is not good, please forgive me, only knowledge sharing records, if there is a problem, please.
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Bessel curve formula derivation principle
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Bessel curve formula derivation principle
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In order to better understand the following Bessel curve point animation effect:

Bessel curve formula derivation principle
first order.Gif
Bessel curve formula derivation principle
two order.Gif
Bessel curve formula derivation principle
three order.Gif
Bessel curve formula derivation principle
four order.Gif
Bessel curve formula derivation principle
five order.Gif

After the picture carousel is not can achieve such results? Bessel curve seckill.

Bessel curve formula derivation principle
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