Reparameterize a curve by its arc-length.

reparameterization.py

"""Numerically reparameterize a curve by its arc-length.

"""

from typing import Optional

import numpy as np
import scipy
import scipy.interpolate


def reparameterize(X: np.ndarray, num_steps: Optional[int] = None) \
        -> np.ndarray:
    """Reparameterize a closed curve by its arc-length.

    Parameters
    ----------
    X: np.ndarray
      An array of shape (num_points, 2) containing the points of the curve.

    num_steps: int or None
      Number of steps for the reparameterized curve. If set to None, the
      resulting curve contains the same number of points as the original
      curve.

    Returns
    -------
    Y: np.ndarray
      An array containing the points of the reparameterized curve.

    """
    def interpolator(x, y):
        return scipy.interpolate.PchipInterpolator(x, y, extrapolate=True)

    n = X.shape[0]
    t = np.linspace(0, 1, n)

    x1, x2 = interpolator(t, X[:, 0]), interpolator(t, X[:, 1])
    dx1, dx2 = x1.derivative(), x2.derivative()

    s = np.cumsum(np.sqrt(dx1(t)**2 + dx2(t)**2))
    tau = interpolator(s, t)
    ss = np.linspace(s[0], s[-1], num_steps or n)

    return np.c_[x1(tau(ss)), x2(tau(ss))]