This is an example of drawing a Bezier curve the 'naive' way, that is, we use lerping (linear interpolation) recursively.
For an excellent youtube video on how Bezier's work, see [Freya Holmér's video here](https://www.youtube.com/watch?v=aVwxzDHniEw).

## The Code
```python
from PySide6.QtCore import *
from PySide6.QtGui import *
from PySide6.QtWidgets import *
import sys

app = QApplication(sys.argv)

def lerp(x0,x1,t):
  'lerp between two vectors'
  res = tuple(lerpx(x0[i],x1[i],t) for i in range(len(x0)))
  return res

def lerpx(x,y,t):
  'lerp between two real numbers'
  return x + t*(y-x)

class B(QWidget):
  def __init__(self):
    super().__init__()
    self.resize(640,480)
    self.pts = ((10,10),(20,300),(300,45),(500,350))
  def paintEvent(self,e):
    # draw the bezier the naive way by recursively lerping
    n = 100
    dt = 1.0/n

    # compute the points of the curve
    curve = []
    for j in range(n+1): # n+1 so we include the endpoint
      t = j*dt
      pts = self.pts
      while len(pts) > 1:
        # use lerping to get from n points to n-1, and stop when only one point remains
        pts = tuple(lerp(pts[i],pts[i+1],t) for i in range(len(pts)-1))
      curve.append(pts[0])

    # clear the window and draw our curve
    with QPainter(self) as p:
      w = self.width()
      h = self.height()
      p.fillRect(0,0,w,h,QColor(255,255,255)) # clear the window
      path = QPainterPath()
      x = curve[0]
      path.moveTo(x[0],x[1])
      for x in curve[1:]:
        path.lineTo(x[0],x[1]) # connect our points with lines
      p.setBrush(QColor(0,0,0,0))
      p.setPen(QPen(QColor(0,0,0),3))
      p.drawPath(path)
      
b = B()
b.show()
app.exec()
```