ECT B Spline Curve Interpolation

The ECT B spline comes from the connected incidence matrix at each node by basing on the typical ECT group. If each incidence matrix is non-singular, suboccipital triangle, totally positive, then there is ECT B spline function which is non-negative with minimum support base and is unitary.ECT B spline shares many important characteristics similar to that of polynomial spline. By studying the number of zero of function in the ECT spline space, the interpolation uniqueness theory of ECT B spline is offered and its generalized theory is also offered. When the interpolating point and the ECT B spline node meet a certain distribution status, there is one unique solution to the ECT B spline interpolation. The Schoenberg Whitney interpolation uniqueness theory of polynomial B spline is promoted to the ECT spline space. Last but not least, the ECT B spline node inserted algorithm is introduced, after inserting the new node, the control vertex of the new ECT B spline is the linear combination of the previous control vertex. And with the aid of this finding, the variation-diminishing result of the polynomial B spline is promoted to the ECT spline space.