def project_and_to2dim(self, pps, plane_center):
        """
        Projects the list of points pps to the plane and changes the basis from 3D to the 2D basis of the plane
        :param pps: List of points to be projected
        :return: :raise:
        """
        proj = self.projectionpoints(pps)
        [u1, u2, u3] = self.orthonormal_vectors()
        PP = np.array([[u1[0], u2[0], u3[0]],
                       [u1[1], u2[1], u3[1]],
                       [u1[2], u2[2], u3[2]]])
        xypps = list()
        for pp in proj:
            xyzpp = np.dot(pp, PP)
            xypps.append(xyzpp[0:2])
        if str(plane_center) == str('mean'):
            mean = np.zeros(2, np.float)
            for pp in xypps:
                mean += pp
            mean /= len(xypps)
            xypps = [pp - mean for pp in xypps]
        elif plane_center is not None:
            projected_plane_center = self.projectionpoints([plane_center])[0]
            xy_projected_plane_center = np.dot(projected_plane_center, PP)[0:2]
            xypps = [pp - xy_projected_plane_center for pp in xypps]
        return xypps