Shape modification and deformation play an important role in the filed of geometry modeling, computer graphics, conceptual design and so on. A novel physically based shape modification approach is presented in this article, with beam model in finite element method （FEM）. By means of interactively creating a beam with circle cross section based on pre-defined local coordi- nate system, the primitive geometry model is embedded in the beam globally or locally. After imposing external loads, such as concentrated force or couple, on selected nodes, their displacement can be computed. Moreover, deflection, axial deformation and twist angle of beam model can also be interpolated using shape function matrix. As a result, object is modified as a part of beam. The proposed approach is linear, simple and fast, by which stretch, bending, taping and twist deformation can be accom- plished. Finally, some experimental results are given to demonstrate that the presented method is potentially useful in geometry modeling and shape design.
By introducing Information fusion techniques into a control field, a new theory of information fusion control （IFC） is proposed. Based on the theory of information fusion estimation, optimal control of nonlinear discrete control system is investi- gated. All information on control strategy, including ideal control strategy, expected object trajectory and dynamics of system, are regarded as measuring information of control strategy. Therefore, the problem of optimal control is transferred into the one of information fusion estimation. Firstly, the nonlinear information fusion estimation theorems are described. Secondly, an algorithm of nonlinear IFC theory is detailedly deduced. Finally, the simulation results of manipulator shift control are given, which show the feasibility and effectiveness of the presented algorithm.
This article uses arc-length parameters for path planning to carry out robotic fibre placement （RFP） over open-contoured structures This allows representing the initial path and offset points using an identical mathematical equation and computation by more simple arithmetic. With the help of classical differential geometry, the calculation of fiber-placing paths may be reduced to solution of initial-value problems of first-order ordinary differential equations in the parametric domain （parametrically defined mould surface） or in 3D space （an implicitly defined mould surface）, thereby significantly improving on the existing methods. Compared with the conventional methods, the proposed method, besides its computational simplicity, has a better error control mechanism in computing the initial path and offset points. Numerical experiments are also carried out to demonstrate the feasibility of the new method in composite forming processes and also its potential application in computer numerical control （CNC） machining, surface trim, and other industrial practices.
This article presents a new method for G2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surfaee with prescribed tangent direction and curvature vector, respectively, at every point. First, a G2 continuous curve is constructed in three-dimensional space. Then the curve is projected normally onto the given surface. The desired interpolation curve is just the projection curve, which can be obtained by numerieally solving the initialvalue problems for a system of first-order ordinary differential equations in the parametric domain for parametric case or in three-dimensional space for implicit ease. Several shape parameters are introduced into the resulting curve, which can be used in subsequent interactive modification so that the shape of the resulting curve meets our demand. The presented method is independent of the geometry and parameterization of the base surface. Numerical experiments demonstrate that it is effective and potentially useful in numerical control （NC） machining, path planning for robotic fibre placement, patterns design on surface and other industrial and research fields.
Wang Xiaoping,An Luling,Zhou Laishui,Zhang Liyan Jiangsu Key Laboratory of Precision and Macro-manufacturing Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China
