Draw Bezier curves using Python and PyQt

bezdraw.py

#!/usr/bin/env python3

import sys
import random
import functools

from PyQt4 import QtGui, QtCore

@functools.lru_cache(maxsize=100)
def factorial(n):
    prod = 1
    for i in range(1,n+1):
        prod *= i
    return prod

def randPt(minv, maxv):
    return (random.randint(minv, maxv), random.randint(minv, maxv))

def B(i,n,u):
    val = factorial(n)/(factorial(i)*factorial(n-i))
    return val * (u**i) * ((1-u)**(n-i))

def C(u, pts):
    x = 0
    y = 0
    n = len(pts)-1
    for i in range(n+1):
        binu = B(i,n,u)
        x += binu * pts[i][0]
        y += binu * pts[i][1]
    return (x, y)

class BezierDrawer(QtGui.QWidget):
  
    def __init__(self):
        super(BezierDrawer, self).__init__()

        self.setGeometry(300, 300, 1000,1000)
        self.setWindowTitle('Bezier Curves')

    def paintEvent(self, e):
      
        qp = QtGui.QPainter()
        qp.begin(self)
        qp.setRenderHints(QtGui.QPainter.Antialiasing, True)
        self.doDrawing(qp)        
        qp.end()
        
    def doDrawing(self, qp):

        blackPen = QtGui.QPen(QtCore.Qt.black, 1, QtCore.Qt.DashLine)
        redPen = QtGui.QPen(QtCore.Qt.red, 1, QtCore.Qt.DashLine)
        bluePen = QtGui.QPen(QtCore.Qt.blue, 1, QtCore.Qt.DashLine)
        greenPen = QtGui.QPen(QtCore.Qt.green, 1, QtCore.Qt.DashLine)
        redBrush = QtGui.QBrush(QtCore.Qt.red)

        steps = 400
        min_t = 0.0
        max_t = 1.0

        dt = (max_t - min_t)/steps
        # controlPts = [randPt(0,1000) for i in range(6)]
        # controlPts.append(controlPts[1])
        # controlPts.append(controlPts[0])
        controlPts = [(100,100), (600,100), (600,600), (100,600)]
        oldPt = controlPts[0]
        pn = 1
        qp.setPen(redPen)
        qp.setBrush(redBrush)
        qp.drawEllipse(oldPt[0]-3, oldPt[1]-3, 6,6)

        qp.drawText(oldPt[0]+5, oldPt[1]-3, '{}'.format(pn))
        for pt in controlPts[1:]:
            pn+=1
            qp.setPen(blackPen)
            qp.drawLine(oldPt[0],oldPt[1],pt[0],pt[1])
            
            qp.setPen(redPen)
            qp.drawEllipse(pt[0]-3, pt[1]-3, 6,6)

            qp.drawText(pt[0]+5, pt[1]-3, '{}'.format(pn))
            oldPt = pt
            
        qp.setPen(bluePen)
        oldPt = controlPts[0]
        for i in range(steps+1):
            t = dt*i
            pt = C(t, controlPts)
            qp.drawLine(oldPt[0],oldPt[1], pt[0],pt[1])
            oldPt = pt

def main(args):
    app = QtGui.QApplication(sys.argv)
    ex = BezierDrawer()
    ex.show()
    app.exec_()
    
if __name__=='__main__':
    main(sys.argv[1:])