Research on None Uniform Rational B-spline Surface and Agent for Numerically Controlled Layout Design

Research on the integrated NC conceptual layout design (I-NCC) concerned with a broader area of interests. The key issues of I-NCC system are associated with NURBS and agent. Firstly, formulas for the derivatives and normal vectors of non-rational B-spline and NURBS are proved based on de BOOR’s recursive formula. Compared with the existing approaches targeting at the non-rational B-spline basis functions, these equations are directly targeted at the controlling points, so the algorithms and programs for NURBS curve and surface can also be applied to the derivatives and normals, the calculating performance is increased. A simplified equation is also proved in this paper. Secondly, the NC conceptual configuration design is transformed into a 3D cuboids layout problem by the introduction of three typical modules: translation module, rotation module and base module based on the analysis of the normal unit vector of work piece surface (in NURBS format). 3D cuboids layout problem is viewed as a generalization of the quadratic assignment problem and therefore belongs to the class of NP hard problems. Apart from the complexity and variety of 3D layout optimization algorithms, this paper introduces agent oriented cooperative design system. Agent models and the corresponding design management systems are put forward to deal with the creative NC layout design. Though the key theoretical issues are now applied to the NC system design, there should be more industrial applications because of the prevalent proliferation nature of NURBS and agent. Copyright © 2014 IFSA Publishing, S. L.