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hello,
My first attempts.
Curves are defined with Cartesian parameters: x=f(t), z=g(t).
The profile is a simple polygon.
Basic texture, lighting with area_light.
Low resolution (800x600).
--
kurtz le pirate
compagnie de la banquise
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Attachments:
Download 'param_limaconofpascal .png' (75 KB)
Download 'param_hypotrochoidet.png' (173 KB)
Download 'param_lemniscateofbernoulli.png' (86 KB)
Preview of image 'param_limaconofpascal .png'
Preview of image 'param_hypotrochoidet.png'
Preview of image 'param_lemniscateofbernoulli.png'
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kurtz le pirate <kur### [at] free fr> wrote:
> Curves are defined with Cartesian parameters: x=f(t), z=g(t).
> The profile is a simple polygon.
Nice job with the profiles.
What's the arc-length of that lemniscate? :D
- BE
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From: kurtz le pirate
Subject: Re: profile following a parametric curve
Date: 1 May 2025 09:53:55
Message: <68137cf3@news.povray.org>
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On 01/05/2025 14:39, Bald Eagle wrote:
> kurtz le pirate <kur### [at] freefr> wrote:
>
>> Curves are defined with Cartesian parameters: x=f(t), z=g(t).
>> The profile is a simple polygon.
>
> Nice job with the profiles.
>
> What's the arc-length of that lemniscate? :D
Simple. Here, half-width a = 24 = c√2.
2*π
Then, length = --------- * c
M(1,1/√2)
With M(a,b) the arithmetic–geometric mean function.
;)
--
kurtz le pirate
compagnie de la banquise
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On 5/1/25 06:22, kurtz le pirate wrote:
> My first attempts.
>
> Curves are defined with Cartesian parameters: x=f(t), z=g(t).
> The profile is a simple polygon.
Cool!
Bill P.
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kurtz le pirate <kur### [at] freefr> wrote:
> Simple. Here, half-width a = 24 = c√2.
>
> 2*π
> Then, length = --------- * c
> M(1,1/√2)
>
>
Maybe not so simple?
https://en.wikipedia.org/wiki/Elliptic_function#History
(I only know that because I was trying to hunt down a good overview of
calculating the arc-length of a catenary, and move along the curve at regular
intervals.)
- BW
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On 01/05/2025 17:37, Bald Eagle wrote:
> kurtz le pirate <kur### [at] freefr> wrote:
>
>> Simple. Here, half-width a = 24 = c√2.
>>
>> 2*π
>> Then, length = --------- * c
>> M(1,1/√2)
>>
>>
>> With M(a,b) the arithmetic–geometric mean function.
>
> Maybe not so simple?
> https://en.wikipedia.org/wiki/Elliptic_function#History
That's right.
But my answer is more of a joke and a simple copy/paste from Wiki
<https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli#Arc_length_and_elliptic_functions>
--
kurtz le pirate
compagnie de la banquise
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kurtz le pirate <kur### [at] freefr> wrote:
> That's right.
>
> But my answer is more of a joke and a simple copy/paste from Wiki
>
<https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli#Arc_length_and_elliptic_functions>
Nice. (I suspected)
"It therefore obviously follows that . . ." ;)
- BW
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