Bézier curves can be expressed by using De Casteljau's corner cutting algorithm. This can also be formulated using factorization matrices. Each matrix reduce the coefficient vector with 1, and each line in each matrix represent a linear interpolation describing the corner cutting. This matrix formulation may also be used for B-splines. One just have to introduce a linear transformation from the local domains of the basis function, to the interval [0;1]. This leads to a further expansion where the linear transformation is "deformed" by a perturbation function. The result is a non-polynomial spline. We will se that the typical properties of B-splines are preserved or even improved in the nonpolynomial case. Further, we describes the construction of the B-spline, and provide some practical examples.
Construction and properties of non-polynomial spline-curves
10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 ; 2014 ; Narvik, Norway
AIP Conference Proceedings ; 1637 , 1 ; 545-554
2014-12-10
10 pages
Conference paper
Electronic Resource
English
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