POV-Ray : Newsgroups : povray.general : Request for Comments: Quadratic Bezier Splines Server Time
19 Jun 2024 19:49:58 EDT (-0400)
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From: Mike Horvath
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 9 Jun 2021 18:56:56
Message: <60c14738$1@news.povray.org>
On 6/7/2021 1:23 PM, clipka wrote:
> 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.

See here:

https://www.geogebra.org/m/h779nwhd


Mike


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From: clipka
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 9 Jun 2021 20:35:40
Message: <60c15e5c$1@news.povray.org>
Am 10.06.2021 um 00:56 schrieb Mike Horvath:

>> 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.
> 
> See here:
> 
> https://www.geogebra.org/m/h779nwhd

That's a neat demonstration.
Thanks for sharing.


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From: Mr
Subject: Re: Request for Comments: Quadratic Bezier Splines
Date: 10 Jun 2021 14:00:00
Message: <web.60c252f484e2d21b6adeaecb3f378f2@news.povray.org>
clipka <ano### [at] anonymousorg> wrote:
> Am 10.06.2021 um 00:56 schrieb Mike Horvath:
>
> >> 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.
> >
> > See here:
> >
> > https://www.geogebra.org/m/h779nwhd
>
> That's a neat demonstration.
> Thanks for sharing.

Thanks, awesome visual, and sorry for increasing confusion then. I will look
better at the chosen result to try and clear my mind about this. I still hope it
won't look like "mesh2"


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