object_placement_bisection.py

#%%
from math import *
import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 10, 1001)
f = lambda z: z * sin(z)
y = np.sin(x) * x
#plt.plot(x, y)

x0, y0 = x[0], y[0]
circle_radius = req_dist = 0.5

#%%
def func(est):
    y = f(est)
    dist = sqrt((x0-est)**2 + (y0-y)**2)
    return dist - req_dist

def bisection(cf, a, b, tol, max_iter):
    sign = lambda z: copysign(1, z)
    n = 1
    while n <= max_iter:
        c = (a+b)/2
        if abs(cf(c)) < tol:
            return c
        n += 1
        if sign(cf(c)) == sign(cf(a)):
            a = c
        else:
            b = c
    return None

guess = bisection(func, x[0], x[-1], 1e-3, 1000)
fig, axes = plt.subplots()
axes.set_aspect('equal', adjustable='datalim')
circle = plt.Circle((guess, f(guess)), circle_radius, fill=None)
axes.add_patch(circle)

req_dist *= 2

for i in range(35):
    x0, y0 = guess, f(guess)
    guess = bisection(func, x0, x[-1], 1e-3, 1000)
    circle = plt.Circle((guess, f(guess)), circle_radius, fill=None)
    axes.add_patch(circle)

plt.plot(x, y)
plt.show()