Abstract
An algorithm is presented to compute the Taylor expansion of a polynomial B-spline function from its de Boor points. It is shown to be more efficient than existing methods and has the additional advantage of being reversible.
Zusammenfassung
Es wird ein Algorithmus für die Berechnung der Taylorkoeffizienten eines Polynomsplines aus dessen de Boor-Punkten angegeben. Er ist schneller als die üblichen Methoden und dazu umkehrbar.
References
de Boor, C.: On calculating with B-splines. J. Approx. Theory6, 50–62 (1972).
de Boor, C., Fix, G.: Spline approximation by quasi-interpolants. J. Approx. Theory8, 19–45 (1973).
Boehm, W.: Inserting new knots into B-spline curves. Computer-Aided Design12, 199–201 (1980).
Boehm, W.: Generating the Bézier points of B-spline curves and surfaces. Computer-Aided Design13, 365–366 (1981).
Lee, E.: A simplified B-spline computation routine. Computing29, 365–373 (1982).
Sablonnière, P.: Spline and Bézier polygons associated with a polynomial spline curve. Computer-Aided Design10, 257–261 (1978).
Schumaker, L.: Spline functions: Basic Theory, pp. 189–199. J. Wiley 1981.