bezier2.py

Created by vnap0v

Created on July 01, 2025

2.27 KB

Bezier curves

This script defines functions which can draw Bezier curves using the kandinsky library

the function that does the actual drawing is:

draw_bezier(funct_bezier,points,Nsteps,col)
  • funct_bezier: either bezier1(), bezier2() or bezier3()
  • points is a list or tuple of (x,y)
  • Nsteps: number of points calculated, are connected with straight lines
  • col: color to draw


# bezier curves
import kandinsky

# draw a line between an 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

# draw boxes at the points given
# points is a list or tuple of (x,y)
def mark_points(points,col):
  for p in points:
    kandinsky.fill_rect(p[0]-2,p[1]-2,4,4,col)

# linear Bézier curve (just a straight line)
# defined by 2 points
# points is a list or tuple of (x,y)
# t is the position along the curve 0<=t<=1
def bezier1(points,t):
  p0,p1=points
  x=(1-t)*p0[0]+t*p1[0]
  y=(1-t)*p0[1]+t*p1[1]
  return (int(x),int(y))

# Quadratic Bézier curve, defined by 3 points
# points is a list or tuple of (x,y)
# t is the position along the curve 0<=t<=1
def bezier2(points,t):
  p0,p1,p2=points
  x=(1-t)**2*p0[0]+2*(1-t)*t*p1[0]+t**2*p2[0]
  y=(1-t)**2*p0[1]+2*(1-t)*t*p1[1]+t**2*p2[1]
  return (int(x),int(y))

# Cubic Bézier curves, defined by 4 points
# points is a list or tuple of (x,y)
# t is the position along the curve 0<=t<=1
def bezier3(points,t):
  p0,p1,p2,p3=points
  x=(1-t)**3*p0[0]+3*(1-t)**2*t*p1[0]+3*(1-t)*t**2*p2[0]+t**3*p3[0]
  y=(1-t)**3*p0[1]+3*(1-t)**2*t*p1[1]+3*(1-t)*t**2*p2[1]+t**3*p3[1]
  return (int(x),int(y))

# draw any of the bezier curves by specifying the bezier function
# funct_bezier: either bezier1(), bezier2() or bezier3()
# points is a list or tuple of (x,y)
# Nsteps: number of points calculated, are connected with straight lines
# col: color to draw
def draw_bezier(funct_bezier,points,Nsteps,col):
  for k in range(Nsteps):
    t=k/(Nsteps-1)
    x,y=funct_bezier(points,t)
    if k==0:
      kandinsky.set_pixel(x,y,col) # first point gets a single dot
    else:
      connect(xold,yold,x,y,col) # other points connected with line
    xold,yold=x,y

def demo():
  pa=(10,10)
  pb=(300,60)
  pc=(10,160)
  pd=(300,210)
  mark_points((pa,pb,pc,pd),"black")
  draw_bezier(bezier2,(pa,pb,pd),50,"red")
  kandinsky.draw_string("Quadratic Bézier curve",90,3,"red","white")
  draw_bezier(bezier3,(pa,pb,pc,pd),50,"blue")
  kandinsky.draw_string("Cubic Bézier curve",30,190,"blue","white")

demo()

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