Constructing Explicit B-Spline

2014/09/12 by R. O. Linger, Linger, R. O., H. R. N. van Erp +3
Engineering · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1409.3824

openalex publication_date 2014/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce here a direct method to construct multivariate explicit B-spline bases. B-splines are piecewise polynomials, which are defined on adjacent tetrahedra and which are C^r continuous throughout. The C^r continuity is enforced by making sure that all directional derivatives of order r, and lower, on the boundaries of adjacent tetrahedra give the same values for both tetrahedra. The method presented here is explicit, in that we will provide an algorithm with which one can analytically construct the B-spline base that enforces C^r continuity for a given geometry.

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