Bézier curve fitting with SciPy

Question

I have a set of points which approximate a 2D curve. I would like to use Python with numpy and scipy to find a cubic Bézier path which approximately fits the points, where I

Answer 1

I had the same problem as detailed in the question. I took the code provided Roland Puntaier and was able to make it work. Here:

def get_bezier_parameters(X, Y, degree=2):
    """ Least square qbezier fit using penrose pseudoinverse.

    Parameters:

    X: array of x data.
    Y: array of y data. Y[0] is the y point for X[0].
    degree: degree of the Bézier curve. 2 for quadratic, 3 for cubic.

    Based on https://stackoverflow.com/questions/12643079/b%C3%A9zier-curve-fitting-with-scipy
    and probably on the 1998 thesis by Tim Andrew Pastva, "Bézier Curve Fitting".
    """
    if degree < 1:
        raise ValueError('degree must be 1 or greater.')

    if len(X) != len(Y):
        raise ValueError('X and Y must be of the same length.')

    if len(X) < degree + 1:
        raise ValueError(f'There must be at least {degree + 1} points to '
                         f'determine the parameters of a degree {degree} curve. '
                         f'Got only {len(X)} points.')

    def bpoly(n, t, k):
        """ Bernstein polynomial when a = 0 and b = 1. """
        return t ** k * (1 - t) ** (n - k) * comb(n, k)

    def bmatrix(T):
        """ Bernstein matrix for Bézier curves. """
        return np.matrix([[bpoly(degree, t, k) for k in range(degree + 1)] for t in T])

    def least_square_fit(points, M):
        M_ = np.linalg.pinv(M)
        return M_ * points

    T = np.linspace(0, 1, len(X))
    M = bmatrix(T)
    points = np.array(list(zip(X, Y)))
    return least_square_fit(points, M).tolist()

To fix the end points of the curve, ignore the first and last parameter returned by the function and use your own points.