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polynomials) are referred to as 2nd or 3rd order, and sometimes as 2nd
or 3rd degree. Are these terms interchangeable?
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Cousin Ricky <ric### [at] yahoocom> wrote:
> I just noticed that sometimes Bézier curves (or Bsplines 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 Bspline terminology, order means degree + 1."
https://math.stackexchange.com/questions/1730596/norderbsplinesinterpolation
So maybe order is the number of control points, and degree is the highest power
of the polynomial?
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From: Cousin Ricky
Subject: Re: Math terminology: "degree" or "order"?
Date: 26 Sep 2020 16:50:56
Message: <5f6fa9b0@news.povray.org>



 
 


On 20200926 3:50 PM (4), Bald Eagle wrote:
> Cousin Ricky <ric### [at] yahoocom> wrote:
>> I just noticed that sometimes Bézier curves (or Bsplines 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 Bspline terminology, order means degree + 1."
> https://math.stackexchange.com/questions/1730596/norderbsplinesinterpolation
>
> 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#Higherorder_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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From: William F Pokorny
Subject: Re: Math terminology: "degree" or "order"?
Date: 27 Sep 2020 09:49:02
Message: <5f70984e$1@news.povray.org>



 
 


On 9/26/20 4:50 PM, Cousin Ricky wrote:
> On 20200926 3:50 PM (4), Bald Eagle wrote:
>> Cousin Ricky <ric### [at] yahoocom> wrote:
>>> I just noticed that sometimes Bézier curves (or Bsplines or
>>> polynomials) are referred to as 2nd or 3rd order, and sometimes as 2nd
>>> or 3rd degree. Are these terms interchangeable?
...
>
> 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.
Expect reasonable.
The day to day use is foggy  me as guilty as any I expect. In doing the
solver work a couple years back, I came to the following understanding:
The degree of a polynomial equation is that of the largest term by
exponent with a nonzero coefficient.
While programming for polynomials the order is the maximum degree a
given algorithm can handle. This might be greater than the degree of any
given equation being evaluated, manipulated, solved for roots, or
whatever  using that algorithm. The coefficient storage required in
these domains then is usually the (order + 1) * coefficient_size.
When matrix math comes into play, folks tend to think in terms of matrix
order which is degree + 1 or 'polynomial' order + 1.
Your kilometers may vary.
Bill P.
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