Abstract: Construction of surfaces interpolating 3D curve network is an important research problem in geometric modeling.Given a 3D curve network,a new method is proposed to interpolate the curve network by using the product of two B-spline functions,the fundamental knowledge of differential geometry and the thin-plate-spline energy optimization.The curve segments are specified into three categories:curvature lines of the B-spline surface,feature lines across which the B-spline surface is G0 continuous,and smooth lines at which the B-spline surface is G1 continuous.We derive constraint conditions of the control points of the B-spline surface at the curvature lines and smooth lines.Then the B-spline surface patches are constructed by minimizing the thin-plate-spline energy together with the curvature line and smooth constraints.That is fair surfaces using above method which is widely used in the construction of B-spline surfaces.We perform experiments on several models.The results demonstrate the correctness and effectiveness of our method.