Algorithms For Recursive Into ECT B Splines Curves

The ECT spline curves of multiple nodes are generated by the ECT group defined in the association matrix. If the correlation matrix is lower triangular matrix and the positive, then there exists ECT B spline non negative and with minimal support. The basis function can be defined by the generalized difference quotient. Also, under certain conditions, ECT B spline recursive algorithm can be reduced to the de Boor recursive algorithm in the general polynomial spline and the Lyche recursive algorithm in the chebyshev spline. The spline coefficients are available through a recursive algorithm to calculate. This paper is a recursive algorithm and node insertion algorithm of ECT B spline curve, and the main research contents and the results are as follows:1.To draw the ECT spline space from the concept and nature of different types of ECT group.The spline function of r ECT and l ECT are defined.To construct a sub space of Sn. And the r ECT B spline function is defined, whose important properties are proved.2.On the basis of the definition of green function, to define r ECT B spline function by generalized difference quotient method, and that some properties of the r ET and l ET groups and the weight coefficient range through the calculation of generalized difference quotient, and further through the recursive method to calculate ECT B spline curve. At the same time, a simple two node for ECT B spline insertion and node inserted are discussed.3.In polynomial spline spaces, algebraic hyperbolic spline space and algebraic trigonometric spline space that several specific ECT space, the recursive calculation of the corresponding weight coefficient and the corresponding calculation model and display of the ECT group is given. Show the whole process of solving recursive algorithm and node insertion algorithm of several low-level ECT B spline curve,, and draw their diagrams.