POV-Ray : Newsgroups : povray.general : Request for Comments: Quadratic Bezier Splines Server Time
27 Jul 2021 00:48:56 EDT (-0400)
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From: ingo
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 7 Jun 2021 10:54:41
Message: <XnsAD42AC07BF9DEseed7@news.povray.org>
in news:XnsAD42761851048seed7@news.povray.org ingo wrote:

> as it is clear that it is a spline, or curve, bezier2, bezier3

actually, it is a curve, not a spline ;)


-- 
https://ingoogni.nl


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From: Mike Horvath
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 7 Jun 2021 10:54:46
Message: <60be3336$1@news.povray.org>
On 6/6/2021 5:52 PM, clipka wrote:
> - Quadratic splines are also occasionally referred to as "conic splines" 
> or "conic arcs", for reasons I'm not entirely sure of.


IIRC, quadratic splines are parabolic segments or arcs, which are also 
conic sections.


Mike


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From: clipka
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 7 Jun 2021 13:16:26
Message: <60be546a$1@news.povray.org>
Am 07.06.2021 um 16:54 schrieb ingo:
> in news:XnsAD42761851048seed7@news.povray.org ingo wrote:
> 
>> as it is clear that it is a spline, or curve, bezier2, bezier3
> 
> actually, it is a curve, not a spline ;)

That very much depends on the context you're using the word in. It has 
different definitions in computer graphics, mathematics and traditional 
shipbuilding.

The mathematical definition is certainly the one with can lay the least 
claim to the term. Because what they call splines actually started out 
as nothing more than a mathematical framework invented to _describe_ 
_proper_ splines. The "function of a variable" is something the 
mathematicians bolted on to a pre-existing concept.

In all other fields that don't define "spline" as a physical tool, a 
"spline" _is_ the very thing that a mathematician might call a "spline 
curve". Or whatever they tend to call it.


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From: clipka
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 7 Jun 2021 13:23:10
Message: <60be55fe$1@news.povray.org>
Am 07.06.2021 um 16:54 schrieb Mike Horvath:
> On 6/6/2021 5:52 PM, clipka wrote:
>> - Quadratic splines are also occasionally referred to as "conic 
>> splines" or "conic arcs", for reasons I'm not entirely sure of.
> 
> 
> IIRC, quadratic splines are parabolic segments or arcs, which are also 
> conic sections.

I'm aware of this connection in general, but I'm not really sure whether 
the spline curve segments are necessarily parabolic, or whether that 
only applies to the individual components in a value/result plot; and 
what's more, there's the snag that they can't represent any other conic 
sections. They can't even represent sections of ellipses.


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From: Mr
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 8 Jun 2021 04:45:00
Message: <web.60bf2d2584e2d21b16086ed03f378f2@news.povray.org>
clipka <ano### [at] anonymousorg> wrote:
> Hi folks,
>
> the `prism` primitive currently supports, among others, cubic Bezier
> spline outlines.
>
> For certain technical reasons, I may need to add support for _quadratic_
> Bezier splines at the render engine level as well, but it would be a
> waste to not expose them to the scene description language (and, while
> I'm at it, possibly also extend `lathe` accordingly).
>
> An open question is, what keyword should be used for this type of spline?
>
>
> For the records:
>
> - Quadratic Bezier splines are a flavor of quadratic splines, aka 2nd
> order polynomial splines.
>
> - Quadratic splines are also occasionally referred to as "conic splines"
> or "conic arcs", for reasons I'm not entirely sure of.
>
> - `bezier_spline` is the current moniker for cubic Bezier splines.
>
> - `quadratic_spline` is already in use for some quirky flavor of
> quadratic spline that, in my mind, doesn't even deserve to live, but has
> a long-standing tradition of existing under this moniker and therefore
> isn't going anywhere in POV-Ray v3.x.
>
>
> Here are some ideas:
>
> - `quadratic_bezier_spline`, being the most accurate term.
>
> - `conic_bezier_spline`, being a bit shorter.
>
> - `conic_spline`, being yet shorter.
>
> - `bezier2_spline`, the "2" referring to the polynomial order.
>
>
> Personally, I'm somewhat unhappy with the very first for being rather
> verbose, and the third for being prone to confusion with both
> `cubic_spline` and `conic_sweep`, the latter being also used in `prism`.
> I'm also not quite happy with the second one, because it's still
> somewhat lengthy, and I think it isn't the most accurate of terms.
>
>
> Thoughts, anyone?


Well, Probably the least technical thought ever, but I find names like
something2  something3 rather drafty looking. Even mesh2 doesn't look like the
"goto" syntax it should be; it just makes it look secondary to me. Also because
without any space or underscore makes it look like a backend programer's stuff
not eyepleasing user API level... In many software the  word b_spline
("B-Spline") seems quite conventional to talk about bezier spline if less
verbosity is needed, maybe that could provide inspiration for more options?
Also, sorry if below point even increases the challenge, but to be future proof,
couldn't this be planned with respect to the eventuality of NURBS getting into
POV master one day, avoiding collisions, but also solving the confusion existing
in most other software between these (different? hierarchized?) kinds of
geometry?


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From: ingo
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 8 Jun 2021 10:59:16
Message: <XnsAD43ACCDBACADseed7@news.povray.org>
in news:web.60bf2d2584e2d21b16086ed03f378f2@news.povray.org Mr wrote:

> In many software the  word b_spline
> ("B-Spline") seems quite conventional to talk about bezier spline if
> less verbosity is needed,

there are b-splines, the quadratic b-spline, the cubic b-spline and the 
cubic b-spline with tension and bias. The latter is mostly called beta-
spline. b-spline for a bezier curve would be realy confusing,

ingo

-- 
https://ingoogni.nl


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From: Cousin Ricky
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 8 Jun 2021 15:32:32
Message: <60bfc5d0$1@news.povray.org>
On 2021-06-08 4:41 AM (-4), Mr wrote:
> clipka <ano### [at] anonymousorg> wrote:
>>
>> For certain technical reasons, I may need to add support for _quadratic_
>> Bezier splines at the render engine level as well, but it would be a
>> waste to not expose them to the scene description language (and, while
>> I'm at it, possibly also extend `lathe` accordingly).
>>
>> An open question is, what keyword should be used for this type of spline?
>>
>> [...]
>>
>> Here are some ideas:
>>
>> - `quadratic_bezier_spline`, being the most accurate term.
>>
>> - `conic_bezier_spline`, being a bit shorter.
>>
>> - `conic_spline`, being yet shorter.
>>
>> - `bezier2_spline`, the "2" referring to the polynomial order.
> 
> Well, Probably the least technical thought ever, but I find names like
> something2  something3 rather drafty looking. Even mesh2 doesn't look like the
> "goto" syntax it should be; it just makes it look secondary to me. Also because
> without any space or underscore makes it look like a backend programer's stuff
> not eyepleasing user API level... In many software the  word b_spline
> ("B-Spline") seems quite conventional to talk about bezier spline if less
> verbosity is needed, maybe that could provide inspiration for more options?

B-splines, though mathematically related to Bezier splines, are a
completely different animal, and the b_spline keyword is already used
elsewhere in POV-Ray for... B-splines.  To repurpose it for quadratic
Bezier prisms would be confusing on more than one level.

Maybe the keyword "mesh2" is hackish, but for a 2nd degree polynomial,
appending a "2" to "bezier" would be totally appropriate.


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From: Bald Eagle
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 8 Jun 2021 16:25:00
Message: <web.60bfd1cb84e2d21b1f9dae3025979125@news.povray.org>
Cousin Ricky <ric### [at] yahoocom> wrote:

> B-splines, though mathematically related to Bezier splines, are a
> completely different animal, and the b_spline keyword is already used
> elsewhere in POV-Ray for... B-splines.  To repurpose it for quadratic
> Bezier prisms would be confusing on more than one level.
>
> Maybe the keyword "mesh2" is hackish, but for a 2nd degree polynomial,
> appending a "2" to "bezier" would be totally appropriate.

Let's do the Google thing and "not be evil", by avoiding all confusion,
conflation, and commingling of Bezier splines, B-splines, NURBS knots, and
plagiarized Shakespearean literature.

I propose:


knot2_b_spline


.. . .



What was the question?


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From: Tor Olav Kristensen
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 8 Jun 2021 18:40:00
Message: <web.60bff13884e2d21beefc13a89db30a9@news.povray.org>
"Bald Eagle" <cre### [at] netscapenet> wrote:
> Cousin Ricky <ric### [at] yahoocom> wrote:
>
> > B-splines, though mathematically related to Bezier splines, are a
> > completely different animal, and the b_spline keyword is already used
> > elsewhere in POV-Ray for... B-splines.  To repurpose it for quadratic
> > Bezier prisms would be confusing on more than one level.
> >
> > Maybe the keyword "mesh2" is hackish, but for a 2nd degree polynomial,
> > appending a "2" to "bezier" would be totally appropriate.
>
> Let's do the Google thing and "not be evil", by avoiding all confusion,
> conflation, and commingling of Bezier splines, B-splines, NURBS knots, and
> plagiarized Shakespearean literature.
>
> I propose:
>
>
> knot2_b_spline
>...

But, but, but... That confuses me.

When I see the name b-spline I always think of the type of splines used in
NURBS, never Bezier splines. And most (or all ?) splines have knots ?

--
Tor Olav
http://subcube.com
https://github.com/t-o-k


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From: clipka
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 8 Jun 2021 20:16:43
Message: <60c0086b$1@news.povray.org>
Am 08.06.2021 um 10:41 schrieb Mr:

> not eyepleasing user API level... In many software the  word b_spline
> ("B-Spline") seems quite conventional to talk about bezier spline if less
> verbosity is needed, maybe that could provide inspiration for more options?

B-Splines are a different beast entirely. There, the "B" stands for 
"basis", not "Bezier".

> Also, sorry if below point even increases the challenge, but to be future proof,
> couldn't this be planned with respect to the eventuality of NURBS getting into
> POV master one day, avoiding collisions, but also solving the confusion existing
> in most other software between these (different? hierarchized?) kinds of
> geometry?

I don't see a conflict between any of the proposed monikers and "NURBS". 
Oh, and those are _still_ another matter, being an extension to the 
concept of B-Splines.


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