euler_spiral.py

Created by vnap0v

Created on June 29, 2025

1.34 KB

This script draws an “Euler’s Spiral” also known as “Cornu Spiral”.

Two Fresnel integrals have to be calculated, this code uses a Maclaurin series approximation.

Also the Numworks math module does not seem to have a factorial function, so this had to be coded as well.

It also uses a function coded here in Python to draw a line between any two x,y points.

It is possible to draw this spiral using the Numworks calculator’s graphing app as well.

import kandinsky

# factorial not natively available in Numworks
def factorial(n):
  fact=1
  for k in range(2,n+1):
    fact*=k
  return fact

# Fresnel integrals using Maclaurin series 
def S(x,Nsteps):
  sum=0
  sign=1
  for n in range(Nsteps):
    sum+=sign*x**(4*n+3)/(factorial(2*n+1)*(4*n+3))
    sign=-sign
  return sum

def C(x,Nsteps):
  sum=0
  sign=1
  for n in range(Nsteps):
    sum+=sign*x**(4*n+1)/(factorial(2*n)*(4*n+1))
    sign=-sign
  return sum

# draw a line between any two points
def connect(x1,y1,x2,y2,co="black"):
  xspan=x2-x1;yspan=y2-y1
  steps=max(abs(xspan),abs(yspan))
  if steps==0:
    kandinsky.set_pixel(x1,y1,co)
    return
  dx=xspan/steps;dy=yspan/steps
  x=x1;y=y1
  for k in range(steps):
    kandinsky.set_pixel(int(x+.5),int(y+.5),co)
    x+=dx;y+=dy

kandinsky.fill_rect(0,0,320,230,"black")

# parameters
Npoints=800 # number of x,y points calculated
Nmaclaurin=50 # number of terms for series
# drawing loop
first_iter=True
for k in range(-Npoints//2,Npoints//2):
  p=10*k/(Npoints-1) # variable used for Maclaurin series
  x=int(160+C(p,Nmaclaurin)*110+.5)
  y=int(115-110*S(p,Nmaclaurin)+.5)
  if first_iter: # first run initialise x_old,y°old
    x_old,y_old=x,y
    first_iter=False
  connect(x_old,y_old,x,y,"white")
  x_old,y_old=x,y
kandinsky.draw_string("Euler's Spiral",20,20,"white","black")