An Algorithm for Direct Multiplication of B-Splines

• Published in: IEEE transactions on automation science and engineering Vol. 6; no. 3; pp. 433 - 442
• Main Authors: Xianming Chen, Riesenfeld, R.F., Cohen, E.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2009; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Blossoming; Computation; Equations; Interpolation; Kernel; Mathematical analysis; Mathematical models; Multiplication; Multiplication & division; Numerical analysis; NURBS multiplication; Polynomials; Sampling methods; Sliding; sliding windows algorithm; Spline; Surface reconstruction; Surface topography; Tensile stress; Tensors
• ISSN: 1545-5955; 1558-3783
• DOI: 10.1109/TASE.2009.2021327

B-spline multiplication, that is, finding the coefficients of the product B-spline of two given B-splines is useful as an end result, in addition to being an important prerequisite component to many other symbolic computation operations on B-splines. Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of polynomial pieces using various bases. The original direct approach is complicated. B-spline blossoming provides another direct approach that can be straightforwardly translated from mathematical equation to implementation; however, the algorithm does not scale well with degree or dimension of the subject tensor product B-splines. To addresses the difficulties mentioned heretofore, we present the sliding windows algorithm (SWA), a new blossoming based algorithm for the multiplication of two B-spline curves, two B-spline surfaces, or any two general multivariate B-splines.