Repository: ManimCommunity/manim
File: manim/utils/bezier.py (Python)

Code before:

    Returns
    -------
        list[float]
            List containing possible parameters for the given point on
            the given bezier curve.
            This usually only contains one or zero elements, but if the
            point is, say, at the beginning/end of a closed loop, may return
            a list with more than 1 value, corresponding to the beginning and
            end etc. of the loop.

    Raises
    ------
    :class:`ValueError`
        When ``point`` and the control points have different shapes.
    """
    if not all(np.shape(point) == np.shape(c_p) for c_p in control_points):
        raise ValueError(
            f"Point {point} and Control Points {control_points} have different shapes."
        )
    control_points = np.array(control_points)
    n = len(control_points) - 1

    roots = []
    for dim, coord in enumerate(point):
        control_coords = c_c = control_points[:, dim]
        terms = []
        for term_power in range(n, -1, -1):
            outercoeff = choose(n, term_power)
            term = []
            negative = 1
            for subterm_num in range(term_power, -1, -1):
                innercoeff = choose(term_power, subterm_num) * negative
                subterm = (
                    innercoeff * c_c[subterm_num]
                    if term_power > 0
                    else ((innercoeff * c_c[subterm_num]) - coord)
                )
                term.append(subterm)
                negative = -1 if negative > 0 else 1
            terms.append(outercoeff * sum(np.array(term)))
        bezier_polynom = np.polynomial.Polynomial(terms[::-1])
        polynom_roots = bezier_polynom.roots()
        if len(polynom_roots) > 0:
            roots.append(polynom_roots)

    roots = np.around(roots, int(np.log10(1 / round_to)))
    roots = [[root for root in rootlist if root.imag == 0] for rootlist in roots]
    roots = reduce(np.intersect1d, roots)  # Get common roots.
    roots = np.array([r.real for r in roots]).tolist()
    return roots

Review comment (performance):
Now that the coefficients aren't hardcoded, I don't see much benefit to keeping `c_c` around, and I think you should just use `control_coords` instead.

Code after:
    round_to
        A float whose number of decimal places all values
        such as coordinates of points will be rounded.

    Returns
    -------
        np.ndarray[float]
            List containing possible parameters (the proportions along the bezier curve)
            for the given point on the given bezier curve.
            This usually only contains one or zero elements, but if the
            point is, say, at the beginning/end of a closed loop, may return
            a list with more than 1 value, corresponding to the beginning and
            end etc. of the loop.

    Raises
    ------
    :class:`ValueError`
        When ``point`` and the control points have different shapes.
    """
    # Method taken from
    # http://polymathprogrammer.com/2012/04/03/does-point-lie-on-bezier-curve/

    if not all(np.shape(point) == np.shape(c_p) for c_p in control_points):
        raise ValueError(
            f"Point {point} and Control Points {control_points} have different shapes."
        )

    control_points = np.array(control_points)
    n = len(control_points) - 1

    roots = []
    for dim, coord in enumerate(point):
        control_coords = control_points[:, dim]
        terms = []
        for term_power in range(n, -1, -1):
            outercoeff = choose(n, term_power)
            term = []
            sign = 1
            for subterm_num in range(term_power, -1, -1):
                innercoeff = choose(term_power, subterm_num) * sign
                subterm = innercoeff * control_coords[subterm_num]
                if term_power == 0:
                    subterm -= coord
                term.append(subterm)
                sign *= -1
            terms.append(outercoeff * sum(np.array(term)))
        if all(term == 0 for term in terms):
            # Then both Bezier curve and Point lie on the same plane.
            # Roots will be none, but in this specific instance, we don't need to consider that.
            continue
        bezier_polynom = np.polynomial.Polynomial(terms[::-1])