dev/qt/ NaiveBezier

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.

The Code

from PySide6.QtCore import *
from PySide6.QtGui import *
from PySide6.QtWidgets import *
import sys

app = QApplication(sys.argv)

def lerp(x0,x1,t):
  res = tuple(lerpx(x0[i],x1[i],t) for i in range(len(x0)))
  return res

def lerpx(x,y,t):
  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
    curve = []
    for j in range(n+1):
      t = j*dt
      pts = self.pts
      while len(pts) > 1:
        pts = tuple(lerp(pts[i],pts[i+1],t) for i in range(len(pts)-1))
      curve.append(pts[0])
    with QPainter(self) as p:
      w = self.width()
      h = self.height()
      p.fillRect(0,0,w,h,QColor(255,255,255))
      path = QPainterPath()
      x = curve[0]
      path.moveTo(x[0],x[1])
      for x in curve[1:]:
        path.lineTo(x[0],x[1])
      p.setBrush(QColor(0,0,0,0))
      p.setPen(QPen(QColor(0,0,0),3))
      p.drawPath(path)

b = B()
b.show()
app.exec()