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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _stroke_simplification(self, pointlist):
 """The Douglas-Peucker line simplification takes a list of points as an argument. It tries to simplifiy this list by removing as many points as possible while still maintaining the overall shape of the stroke. It does so by taking the first and the last point, connecting them by a straight line and searchin for the point with the highest distance. If that distance is bigger than 'epsilon', the point is important and the algorithm continues recursively."""


        # Find the point with the biggest distance
        dmax = 0
        index = 0
        for i in range(1, len(pointlist)):
            d = geometry.perpendicular_distance(pointlist[i],
                                                pointlist[0],
                                                pointlist[-1])
            if d > dmax:
                index = i
                dmax = d

        # If the maximum distance is bigger than the threshold 'epsilon', then
        # simplify the pointlist recursively
        if dmax >= self.epsilon:
            # Recursive call
            rec_results1 = self._stroke_simplification(pointlist[0:index])
            rec_results2 = self._stroke_simplification(pointlist[index:])
            result_list = rec_results1[:-1] + rec_results2
        else:
            result_list = [pointlist[0], pointlist[-1]]

        return result_list