POV-Ray : Newsgroups : povray.advanced-users : Math terminology: "degree" or "order"? : Re: Math terminology: "degree" or "order"? Server Time
23 Jun 2021 13:31:22 EDT (-0400)
  Re: Math terminology: "degree" or "order"?  
From: William F Pokorny
Date: 27 Sep 2020 09:49:02
Message: <5f70984e$1@news.povray.org>
On 9/26/20 4:50 PM, Cousin Ricky wrote:
> 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?
...
> 
> 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 non-zero 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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