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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 __voronoi_finite_polygons_2d(vor, radius=None):
 """ Reconstruct infinite voronoi regions in a 2D diagram to finite regions. Parameters vor : Voronoi Input diagram radius : float, optional Distance to 'points at infinity'. Returns ------- regions : list of tuples Indices of vertices in each revised Voronoi regions. vertices : list of tuples Coordinates for revised Voronoi vertices. Same as coordinates of input vertices, with 'points at infinity' appended to the end. """


        if vor.points.shape[1] != 2:
            raise ValueError("Requires 2D input")

        new_regions = []
        new_vertices = vor.vertices.tolist()

        center = vor.points.mean(axis=0)
        if radius is None:
            radius = vor.points.ptp().max()

        # Construct a map containing all ridges for a given point
        all_ridges = {}
        for (p1, p2), (v1, v2) in zip(vor.ridge_points, vor.ridge_vertices):
            all_ridges.setdefault(p1, []).append((p2, v1, v2))
            all_ridges.setdefault(p2, []).append((p1, v1, v2))

        # Reconstruct infinite regions
        for p1, region in enumerate(vor.point_region):
            vertices = vor.regions[region]

            if all(v >= 0 for v in vertices):
                # finite region
                new_regions.append(vertices)
                continue

            # reconstruct a non-finite region
            if p1 not in all_ridges:
                continue

            ridges = all_ridges[p1]
            new_region = [v for v in vertices if v >= 0]

            for p2, v1, v2 in ridges:
                if v2 < 0:
                    v1, v2 = v2, v1
                if v1 >= 0:
                    # finite ridge: already in the region
                    continue

                # Compute the missing endpoint of an infinite ridge

                t = vor.points[p2] - vor.points[p1] # tangent
                t /= np.linalg.norm(t)
                n = np.array([-t[1], t[0]])  # normal

                midpoint = vor.points[[p1, p2]].mean(axis=0)
                direction = np.sign(np.dot(midpoint - center, n)) * n
                far_point = vor.vertices[v2] + direction * radius

                new_region.append(len(new_vertices))
                new_vertices.append(far_point.tolist())

            # sort region counterclockwise
            vs = np.asarray([new_vertices[v] for v in new_region])
            c = vs.mean(axis=0)
            angles = np.arctan2(vs[:,1] - c[1], vs[:,0] - c[0])
            new_region = np.array(new_region)[np.argsort(angles)]

            # finish
            new_regions.append(new_region.tolist())

        return new_regions, np.asarray(new_vertices)