# Copyright (c) 2017 Computer Vision Center (CVC) at the Universitat Autonoma de
# Barcelona (UAB).
#
# This work is licensed under the terms of the MIT license.
# For a copy, see <https://opensource.org/licenses/MIT>.
#
# Modified by ERDOS team.

import numpy as np
from scipy.misc import comb


def bernstein_poly(i, n, t):
    """
     The Bernstein polynomial of n, i as a function of t
    """

    return comb(n, i) * (t**(n - i)) * (1 - t)**i


def bezier_curve(points, nTimes=1000):
    """
       Given a set of control points, return the
       bezier curve defined by the control points.

       points should be a list of lists, or list of tuples
       such as [ [1,1],
                 [2,3],
                 [4,5], ..[Xn, Yn] ]
        nTimes is the number of time steps, defaults to 1000

        See http://processingjs.nihongoresources.com/bezierinfo/
    """

    nPoints = len(points)
    xPoints = np.array([p[0] for p in points])
    yPoints = np.array([p[1] for p in points])

    t = np.linspace(0.0, 1.0, nTimes)

    polynomial_array = np.array(
        [bernstein_poly(i, nPoints - 1, t) for i in range(0, nPoints)])

    xvals = np.dot(xPoints, polynomial_array)
    yvals = np.dot(yPoints, polynomial_array)

    return xvals, yvals
