I would like to fit a graph that closely follow the characteristics of a scatterplot using Python.

I have searched many curve-fitting techniques, and I have tried many different polynomial and linear regression approach powered by Scikit-Learn library.

However, the best I could get is the following
The result of polynomial regression

What I expect is somewhat like the following, denoted in green.
enter image description here

I have thought about simple connecting the dots, but I think that it would not give me a concrete mathematical expression of the graph. So I need to come up with a way to draw a graph that looks like one in the green above, which can be described in a certain mathematical expression.

Can you guys suggest me the ways that I can do it? I was also thinking if combining logarithmic or exponential functions are necessary for this purpose. If anyone has a reasonable idea. I would appreciate your reply and would be glad to upvote!

Just to give you an idea of what kind of code that I used, I am attaching my piece of python code that I used to produce the results displayed with the first picture.

import numpy as np
import pandas as pd
import plotly.express as px
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt

# Load the point cloud data
data = pd.read_csv('data/selected_2.csv')
points = data.to_numpy()
points_x = points[:, 0]
points_y = points[:, 1]
points_z = points[:, 2]

poly = PolynomialFeatures(degree=40, include_bias=False)
poly_features = poly.fit_transform(points_x.reshape(-1, 1))

poly_reg_model = LinearRegression()
poly_reg_model.fit(poly_features, points_z)
z_predicted = poly_reg_model.predict(poly_features)

plt.figure(figsize=(10, 6))
plt.title("Your first polynomial regression – congrats! :)", size=16)
plt.scatter(points_x, points_z)
plt.plot(points_x, z_predicted, c="red")
plt.show()```

the data that I used is a point cloud data composed of 'X', 'Y', and 'Z' columns, with each row indicating the coordinates. The size of the data is (23, 3).

Thanks!