Interpolate between two points with splines

points_interpolation_spines.py

import numpy as np
from scipy.interpolate import interp1d, splprep, splev, CubicHermiteSpline
import matplotlib.pyplot as plt

pts = np.array(
    [
        [-846724, 0],
        [-423362, 10029],
        [0, 13942],
        [289000, 14733],
        [547558, 13942],
        [730000, 11948],
        [846746, 9015],
        [846746, 0],
        [423373, -8311],
        [0, -12759],
        [-486000, -14733],
        [-846724, -12759],
        [-846724, 0],
    ]
)

tck, u = splprep(pts.T, u=None, s=0, k=1, per=1)
u_new = np.linspace(u.min() + 0.45, u.max(), 1000)
x_new, y_new = splev(u_new, tck, der=0)


center = np.mean(pts, axis=0)


def derivative_at_point(p) -> float:
    radial_vector = p - center
    return -(radial_vector[0] / radial_vector[1]) / np.linalg.norm(radial_vector)


def derivative_via_neighbors(index) -> float:
    delta = pts[index + 1] - pts[index - 1]
    return delta[1] / delta[0]


fix, axs = plt.subplots()

axs.plot(x_new, y_new, "b-")

for i in range(6):
    spline = CubicHermiteSpline(
        pts[i : i + 2, 0],
        pts[i : i + 2, 1],
        [derivative_at_point(pts[i]), derivative_at_point(pts[i + 1])],
    )
    spline_x = np.linspace(*spline.x)
    spline_y = spline(spline_x)
    # axs.plot(spline_x, spline_y, "g-")

for i in range(5):
    spline = CubicHermiteSpline(
        pts[i : i + 2, 0],
        pts[i : i + 2, 1],
        [derivative_via_neighbors(i), derivative_via_neighbors(i + 1)],
    )
    spline_x = np.linspace(*spline.x)
    spline_y = spline(spline_x)
    axs.plot(spline_x, spline_y, "r--")


# axs.plot(center[0], center[1], "r+")
axs.plot(pts[:, 0], pts[:, 1], "ro")
# axs.set_aspect("equal", "box")
plt.show()