Bezier curve learning

• explain ： Today, , Bessel curve is widely used , Especially in the field of image processing , The smooth curve generated by it is very friendly to human-computer interaction , Here are some basic concepts of Bessel curve .

introduce ： As shown in the figure , The graph contains 4 Control points , Moving at a control point , When the rest of the control points are stationary , The curve remains smooth , This is the Bessel curve .

A simple example

In the beginning , For both ends of the green line segment Q0 and Q1, Place them separately P0 and P1 The location of , Now let them move , requirement ：Q0 Go to P1 Direction ,Q1 Go to P2 Direction , Moving separately at a uniform speed , And reach the other end of the line at the same time .

Suppose there is a point on the green line B,B Also move according to the above rules , And you get the Bessel curve .

Recursively construct

1. Take the above process as an example , There are three control points at the beginning , Two line segments , Got two moving points .
   Two moving points are connected to get another line segment , Got a moving point , The trajectory of the moving point is the Bessel curve .
2. If there is a total of n Control points , At first there was n Bar segment ,(n-1) Moving point , And then recurs in turn , The locus of the last point is called Bessel curve .

Formula derivation

Click on the line ：C = (1-t)A + tB
It is recursively deduced that ：

• Reference article ： Graphics and machine learning