En parcourant le livre “Mathematiques et graphismes” de 1985, j’ai trouvé page 41 un programme intéressant en BASIC (pour TO7/Apple/Commodore 64/Oric etc) permettant de tracer une enveloppe de droites (de la forme ax+by+c = 0). En faisant varier a,b et c en fonction d’un paramètre (noté t dans le programme), on obtient des visuels sympathiques :
Traduction en Python (avec 18 exemples)
import turtle
from math import *
from time import sleep
t = turtle.Turtle()
t.hideturtle()
t.pensize(2)
w, h = 800, 600
wn = turtle.Screen()
wn.colormode(255)
t.pencolor(255, 255, 0)
def ex0():
def g(t):
return 2 - t * t, -2 * t, t**3
return g, -5, 5, -2, 1.5, -3, 3
def ex1():
def g(t):
return cos(3 * t), sin(3 * t), sin(t) ** 2
return g, -1, 1, -1.1, 1.1, 0, 2 * pi
def ex2():
def g(t):
return cos(3 * t), sin(3 * t), cos(t)
return g, -1.2, 0.8, -1.2, 1.2, -pi / 2, pi / 2
def ex3():
def g(t):
return cos(t), sin(t), exp(-exp(-t / 5))
return g, -2, 2, -2, 3, -5, 10
def ex4():
def g(t):
return cos(t), sin(t), -sin(t) / t
return g, -0.3, 1.2, -0.9, 0.9, -5, 5
def ex5():
def g(t):
return cos(t), sin(t), -1 - int(t / 2 / pi)
return g, -6, 6, -6, 6, 0, 10 * pi
def ex6():
def g(t):
return cos(t), sin(t), 1 / t
return g, -2, 2, -1, 0.5, -10, 10
def ex7():
def g(t):
return cos(t), sin(t), log10(t)
return g, -4, 4, -4, 4, 0.2, 20
def ex8():
def g(t):
return cos(t), sin(t), t * t * sin(t)
return g, -4, 4, -10, 3, -pi, pi
def ex9():
def g(t):
return cos(t), sin(t), t * t / (1 + t * t)
return g, -1, 1, -1, 1, -2 * pi, 2 * pi
def ex10():
def g(t):
return cos(t), sin(t), (1 - t * t) / (1 + t * t)
return g, -1.5, 1.5, -1.5, 1.5, -2 * pi, 2 * pi
def ex11():
def g(t):
return cos(t), sin(t), sqrt(abs(t))
return g, -4, 4, -4, 4, -10, 10
def ex12():
def g(t):
return cos(t), sin(t), t / (1 + t)
return g, -3, 3, -3, 3, -10, 10
def ex13():
def g(t):
return cos(t), sin(t), 2 + cos(t / 2)
return g, -4, 4, -4, 4, -2 * pi, 2 * pi
def ex14():
def g(t):
return cos(t), sin(t), -0.5 + cos(t / 2)
return g, -2, 2, -2, 2, -2 * pi, 2 * pi
def ex15():
def g(t):
return cos(t), sin(t), t * t * sin(t)
return g, -4, 4, -10, 3, -pi, pi
def ex16():
def g(t):
return cos(t), sin(t), t * t / (1 - t * t)
return g, -1.5, 2, -2, 2, -2 * pi, 2 * pi
def ex17():
def g(t):
return cos(t), sin(t), sin(t) + sin(t) ** 2 / 2 + sin(t) ** 3 / 3
return g, -2, 2, -3, 0, -pi, pi
def tracer(x, y):
global f, pts
if x < xi or x > xs or y < yi or y > ys:
return
f += 1
pts[f] = [
-w / 2 + ceil(w * (x - xi) / (xs - xi)),
-h / 2 + ceil(h * (y - yi) / (ys - yi)),
]
if f == 1 and pts[0] == pts[1]:
f = -1
elif f == 1:
t.penup()
t.goto(pts[0])
t.pendown()
t.goto(pts[1])
t.hideturtle()
for k in range(18):
turtle.Screen().bgcolor(0, 0, 0)
t.clear()
wn.tracer(0)
g, xi, xs, yi, ys, ti, ts = eval("ex" + str(k) + "()")
pts = [[0, 0], [0, 0]]
n = 200
th = (ts - ti) / (n - 1)
for i in range(n):
try: a, b, c = g(ti + i * th)
except: continue
f = -1
if b != 0:
tracer(xi, -(c + a * xi) / b)
tracer(xs, -(c + a * xs) / b)
if a != 0:
tracer(-(c + b * yi) / a, yi)
tracer(-(c + b * ys) / a, ys)
wn.update()
sleep(2)
