Who first used B-spline?
Geral Farin [1, page 119] mentions that B-splines were investigated as early as the nineteenth century by Nikolai Lobachevsky at Kazan University in Russia.
[1] Farin, G. E., & Farin, G. (2002). Curves and surfaces for CAGD: a practical guide. Morgan Kaufmann.
Never heard of Lobachevsky using B-Splines.
Here is a brief history of the modern invention of the spline from Bezier and de Casteljau. http://www.alatown.com/spline-history-architecture/
Dear Rushan Ziatdinov ,
I think that by asking this question you want to turn attention to an important issue.
Not all that we read is the truth. Is there a struggle between nations to claim many of the discoveries to their own culture?
Exactly the same as in the famous statement:
The winner writes the history.
So, sometimes history is biased and doesn't reflect reality.
According to
https://en.wikipedia.org/wiki/Isaac_Jacob_Schoenberg
Issac Jacob is the inventor of B-splines.
I believe that he did essential advances and contributions to the topic.
But he is not the first!!
To follow the right history one needs to do great efforts to reach exact facts.
Best regards
"And who deserves the credit? And who deserves the blame? Nicolai Ivanovich Lobachevsky is his name! "
Tom Lehrer - Lobachevsky, 1953
https://www.youtube.com/watch?v=gXlfXirQF3A
https://genius.com/Tom-lehrer-lobachevsky-lyrics
Dear Rushan,
The B-Spline was first discovered by D. Boor and this is commonly known D-Boor algorithm.You can see the citation/ references for the same.
Spline functions are important in approximation theory, but in CAGD, Parametric Spline curves are mush important. B-spline curves and NURBS are most common which the term “B-spline" was coined by Isaac Jacob Schoenberg in 1946, and is short for basis spline. A spline function of order n is a piecewise polynomial function of degree n-1 in a variable x. The places where the pieces meet are known as knots. The key property of spline functions is that they and their derivatives may be continuous, depending on the multiplicities of the knots.
B-splines of order n are basis functions for spline functions of the same order defined over the same knots, meaning that all possible spline functions can be built from a linear combination of B-splines, and there is only one unique combination for each spline function.
Ashish
To add some fuel to the discussion:
Generally, Prof. Isaac Jacob Schoenberg (1903–1990) is regarded as the father of splines, particularly on account of his pioneering two-part paper [ I.J. Schoenberg, Quart. Appl. Math., 4 (1946) 45–99; idid., 112–141]. There being a father of splines, there also has to be a grandfather or great.., grandfather. Indeed, Schoenberg himself states that “B-splines were probably known to Hermite and certainly to Peano" and, further, “B-splines were already known to Laplace” (1820).
Prof. Arnold Sommerfeld was the first one [Butzer et al., Arch. Hist. Exact Sci. 39 (1988) 137–156 ] to draw the first four spline curves in his 1904 paper concerned with an especially descriptive derivation of the Gauss-Laplace law of probability.
Probably some of you will be interested in the following special issue.
"Modern Geometric Modeling: Theory and Applications II" (IF=2.258) (Deadline: February 28, 2022) URL: https://www.mdpi.com/journal/mathematics/special_issues/Modern_Geometric_Modeling_Theory_Applications_II
Video: https://www.youtube.com/watch?v=aomv_9-FGkU The scope of the Special Issue includes but is not limited to original research works within the subject of geometric modeling and its applications in engineering, arts, physics, biology, medicine, computer graphics, architecture, etc., as well as theoretical mathematics and geometry which can be applied to problems of geometric modeling. For this Special Issue, we plan to accept the following types of manuscripts:
- Overviews;
- Research manuscripts;
- Short manuscripts which discuss open problems in geometric modeling.
Thanks for the interesting discussion.
Prof. Rushan Ziatdinov
Keimyung University, South Korea
https://www.ziatdinov-lab.com/
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