我不敢肯定,这是否是一个完整的答案,但它可能包含一些有益的想法。 (有些是数学,但我认为该守则也很重要,因此,我认为SO是这一问题的一个合理地点。)

最后一个方程式可能有多种解决办法,但在实践中,>scipy.optimize.newton。 似乎趋向于最小的圆环。 而且,它具有矢量,因此你可以一劳永逸地解决几个方面的问题。

import numpy as np
from scipy.optimize import newton

import matplotlib.pyplot as plt
from matplotlib import colors as mcolors
colors = list(mcolors.TABLEAU_COLORS.values())

# amplitude, angular frequency, phase, and y-offsets
params1 = 1, 1, 0, 0
params2 = 0.5, 0.5, 1, 2

# Sinusoid
def y(x, params):
    A, w, p, y = params
    return A*np.cos(w*x + p) + y

# Derivative of Sinusoid
def dy(x, params):
    A, w, p, y = params
    return -w*A*np.sin(w*x + p)

# Angle of Sinusoid Surface Normal
def phi(x, params):
    return np.arctan2(-1, dy(x, params))

# Radius of circle required given y-coordinates
def ry(y1, y2, phi1, phi2):
    return (y2 - y1)/(np.sin(phi1) + np.sin(phi2))

# Radius of circle required given x-coordinates
def rx(x1, x2, phi1, phi2):
    return (x2 - x1)/(np.cos(phi1) + np.cos(phi2))

# At the solution, the radius of the circle given y-coordinates
# must agree with the radius of the circle given x-coordinates
def f(x2, x1):
    y1, y2 = y(x1, params1), y(x2, params2)
    phi1, phi2 = phi(x1, params1), phi(x2, params2)
    return rx(x1, x2, phi1, phi2) - ry(y1, y2, phi1, phi2)

# Coordinate of center of circle
def x0y0(x1, r):
    y1 = y(x1, params1)
    phi1 = phi(x1, params1)
    return (x1 + r*np.cos(phi1), y1 + r*np.sin(phi1))

# Plot Sinusoids
t_plot = np.linspace(0, 15, 300)
y1 = y(t_plot, params1)
y2 = y(t_plot, params2)
plt.plot(t_plot, y1,  k , t_plot, y2,  k )
ax = plt.gca()
plt.ylim(-2, 4)
plt.axis( equal )

# Coordinates on sinusoid 1
x1 = np.asarray([1, 4.5, 7, 11, 13])
y1 = y(x1, params1)

# X-coordinates on sinusoid 2
x2 = newton(f, x1, args=(x1,))
y2 = y(x2, params2)

# Circle radii and centers
phi1 = phi(x1, params1)
phi2 = phi(x2, params2)
r = rx(x1, x2, phi1, phi2)
x0, y0 = x0y0(x1, r)

for i in range(len(x1)):
    color = colors[i]

    # Mark points on curve
    plt.plot(x1[i], y1[i], color, marker= * )
    plt.plot(x2[i], y2[i], color, marker= * )

    # Plot circles 
    circle = plt.Circle((x0[i], y0[i]), r[i], color=color, fill=False)
    ax.add_patch(circle)

Two caveats:

• scipy.optimize.newton is not guaranteed to converge, and even if it does, it is not guaranteed to converge to the circle with minimum radius (unless it can be proven otherwise...). If it is not reliable for your particular parameters but you like the approach, consider posting a more specific question about how to reliably solve the relevant equations numerically. It may just be a matter of solving for one circle and using that as the guess for the next circle.
• This code doesn t consider the possibility of the circle intersecting with a second point on the lower curve before it touches the upper curve. I couldn t tell from the problem statement if this was required because the question mentioned "stepping up in radius until intersection with the upper curve". This is easy enough to check, though, due to symmetry of the convex portion of the sinusoid.