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References

The standard references for spline theory are de Boor [1] and Schumaker [2]. The recursion this package evaluates is Cox's and de Boor's [6], [7]. Piegl and Tiller [3] treat the geometric-modelling side, which this package deliberately does not; Höllig [4] and Cottrell, Hughes and Bazilevs [5] treat the finite-element and isogeometric settings it is written for. Basis recombination as a device for imposing boundary conditions is discussed by Boyd [8].

Every identifier below was checked against Crossref. Two entries carry no DOI because none is registered for the edition cited: de Boor's revised edition of 2001 — the only Crossref record for that title is the 1978 first edition's eBook, whose landing page no longer resolves — and Boyd's Dover second edition, for which only the 1989 Springer first edition is registered.

[1]
C. de Boor. A Practical Guide to Splines. Revised Edition, Vol. 27 of Applied Mathematical Sciences (Springer, New York, 2001). ↩1 ↩2
[2]
L. L. Schumaker. Spline Functions: Basic Theory. Third Edition, Cambridge Mathematical Library (Cambridge University Press, Cambridge, 2007). ↩1 ↩2
[3]
L. Piegl and W. Tiller. The NURBS Book. Second Edition, Monographs in Visual Communication (Springer, Berlin, 1997). ↩1 ↩2
[4]
K. Höllig. Finite Element Methods with B-Splines. Vol. 26 of Frontiers in Applied Mathematics (SIAM, Philadelphia, 2003). ↩1 ↩2 ↩3
[5]
J. A. Cottrell, T. J. Hughes and Y. Bazilevs. Isogeometric Analysis: Toward Integration of CAD and FEA (Wiley, Chichester, 2009). ↩1 ↩2
[6]
M. G. Cox. The numerical evaluation of B-splines. IMA Journal of Applied Mathematics 10, 134–149 (1972). ↩1 ↩2
[7]
C. de Boor. On calculating with B-splines. Journal of Approximation Theory 6, 50–62 (1972). ↩1 ↩2
[8]
J. P. Boyd. Chebyshev and Fourier Spectral Methods. Second Edition (Dover, Mineola, New York, 2001). ↩1 ↩2
[9]
D. Toshniwal, H. Speleers, R. R. Hiemstra and T. J. Hughes. Multi-degree smooth polar splines: A framework for geometric modeling and isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 316, 1005–1061 (2017). ↩1
[10]
E. Zoni and Y. Güçlü. Solving hyperbolic-elliptic problems on singular mapped disk-like domains with the method of characteristics and spline finite elements. Journal of Computational Physics 398, 108889 (2019). ↩1