radial.py 文件源码

def _get_weights(self, X, Y):
        """
        This private method, given the original control points and the deformed
        ones, returns the matrix with the weights and the polynomial terms, that
        is :math:`W`, :math:`c^T` and :math:`Q^T`. The shape is
        (n_control_points+1+3)-by-3.

        :param numpy.ndarray X: it is an n_control_points-by-3 array with the
            coordinates of the original interpolation control points before the
            deformation.
        :param numpy.ndarray Y: it is an n_control_points-by-3 array with the
            coordinates of the interpolation control points after the
            deformation.

        :return: weights: the matrix with the weights and the polynomial terms.
        :rtype: numpy.matrix
        """
        n_points = X.shape[0]
        dim = X.shape[1]
        identity = np.ones((n_points, 1))
        dist = self._distance_matrix(X, X)
        H = np.bmat([
            [dist, identity, X], 
            [identity.T, np.zeros((1, 1)), np.zeros((1, dim))],
            [X.T, np.zeros((dim, 1)), np.zeros((dim, dim))]
        ])
        rhs = np.bmat([[Y], [np.zeros((1, dim))], [np.zeros((dim, dim))]])
        weights = np.linalg.solve(H, rhs)
        return weights