POV-Ray : Newsgroups : povray.advanced-users : Math terminology: "degree" or "order"? : Re: Math terminology: "degree" or "order"? Server Time
23 Jun 2021 15:16:42 EDT (-0400)
  Re: Math terminology: "degree" or "order"?  
From: Cousin Ricky
Date: 26 Sep 2020 16:50:56
Message: <5f6fa9b0@news.povray.org>
On 2020-09-26 3:50 PM (-4), Bald Eagle wrote:
> Cousin Ricky <ric### [at] yahoocom> wrote:
>> I just noticed that sometimes Bézier curves (or B-splines or
>> polynomials) are referred to as 2nd or 3rd order, and sometimes as 2nd
>> or 3rd degree.  Are these terms interchangeable?
> 
> 
> I've seen people claim they are the same, but I also found this:
> 
> "In B-spline terminology, order means degree + 1."
> https://math.stackexchange.com/questions/1730596/n-order-b-splines-interpolation
> 
> So maybe order is the number of control points, and degree is the highest power
> of the polynomial?

Thanks, this gave me a springboard for further searching.  It seems that 
the term "order" not only has multiple meanings, it can also be 
ambiguous within the same meaning!  See conflicting definitions of 
"order" just between these Wikipedia articles:
   https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Higher-order_curves
   https://en.wikipedia.org/wiki/Degree_of_a_polynomial
   https://en.wikipedia.org/wiki/Order_of_a_polynomial

My takeaway is that I should purge the word "order" from my code and 
documentation, and stick to "degree."  Also, the release of quadratic 
Bézier splines in SphereSweep will be delayed a day or two because of this.


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