In adopting a suggestion from Bill Walker, an implementation of an 
inbuilt f_catenary() function, documentation and an example scene file 
will be included in release R15 of yuqk.

Bill P.

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Attachments:
Download 'f_catenary.txt' (4 KB) Download 'f_catenary_story.png' (169 KB)

Preview of image 'f_catenary_story.png'

William F Pokorny <ano### [at] anonymousorg> wrote:
> In adopting a suggestion from Bill Walker, an implementation of an
> inbuilt f_catenary() function, documentation and an example scene file
> will be included in release R15 of yuqk.
>
> Bill P.

This sounds very useful!

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William F Pokorny <ano### [at] anonymousorg> wrote:
> In adopting a suggestion from Bill Walker, an implementation of an
> inbuilt f_catenary() function, documentation and an example scene file
> will be included in release R15 of yuqk.
>
> Bill P.

Thanks Bill!   :)

I don't understand what the pointy curves are - shouldn't they all have rounded
minima?

I'm happy that some of these basic curve shapes that are often used in modeling
are being implemented into the source of your fork.


Also for your consideration, it would be useful to have f_bezier or f_bernstein
for modeling quadratic or cubic curves, and perhaps f_voronoi which would take a
list of seed values as an argument.

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On 5/21/24 11:12, Cousin Ricky wrote:
> This sounds very useful!

:-) I hope it proves so. It's something to play with in any case.

The approach / form isn't the only possible. I borrowed mostly from 
Wikipedia and my old copy of "The VNR Concise Encyclopedia of 
Mathematics (2nd edition)."

Another approach was used by PM 2RING for his catenary.inc set up 
specifically for chains with definable links. This include might have 
been in the object collection..? My copy of it came by way of a post 
from Thomas a few years ago.

Bill P.

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On 5/21/24 11:46, Bald Eagle wrote:
> I don't understand what the pointy curves are - shouldn't they all have rounded
> minima?
> 
Only the upper row, left and center are based on catenary curves.

With the rest I was using results from the other modes to create the 
shapes. IIRC, it's y' (slope) in the upper right. The bottom row being 
arc length, t and angle.

The bottom center - if inverted - is close to the main roof line of the 
Sears & Roebuck barn on the tiny farm where I lived for most of my 
youth. :-)

> ...
> 
> Also for your consideration, it would be useful to have f_bezier or f_bernstein
> for modeling quadratic or cubic curves, and perhaps f_voronoi which would take a
> list of seed values as an argument.

:-)

A somewhat more flexible form of the quilted pattern's 2D 'quilt_cubic' 
is available as an inbuilt in yuqk as f_quilt_cubic(), FWIW. With the 
first two, I'd lean toward adding them as additional splines(a). It 
might be hgpovray38 has these - it supports many additional splines.

The f_voronoi() inbuilt is on my list (with additional metrics). The 
hgpovray38 fork has already some of the voronoi with specified vertices 
functionality already too.

Bill P.

(a) - Or maybe that and plus an inbuilt f_bezier() with two or more 
internal control points..? Suppose where I've implemented inbuilt 
patterns as true inbuilt functions too, I've almost always done this in 
a way that the function is much more flexible with respect to options 
and return values.

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William F Pokorny <ano### [at] anonymousorg> wrote:

> IIRC, it's y' (slope) in the upper right. The bottom row being
> arc length, t and angle.

Ah, they are graphs.   Got it.

>  With the
> first two, I'd lean toward adding them as additional splines(a). It
> might be hgpovray38 has these - it supports many additional splines.

But then I'm trapped by the restriction of only using those with in a spline
keyword block.  Better would be to allow spline {} to take any function as a
spline definition (whether it would make sense to from a spline perspective or
not).

> The f_voronoi() inbuilt is on my list (with additional metrics). The
> hgpovray38 fork has already some of the voronoi with specified vertices
> functionality already too.

It's still a challenge (for me) to return a result of "I am in cell 'N', closest
to seed 'n' " rather than just returning the seed-ignorant value of the distance
to the nearest seed.
That seems to lie firmly in the realm of
under-the-hood-algorithm-masquerading-as-a-function.


As always much interesting stuff to think about, and fun stuff to play with.
RL is being a real bugger lately, so not much povving has been done.

- BW

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William F Pokorny <ano### [at] anonymousorg> wrote:
>
> Another approach was used by PM 2RING for his catenary.inc set up
> specifically for chains with definable links. This include might have
> been in the object collection..? My copy of it came by way of a post
> from Thomas a few years ago.

It was never in the Object Collection.  My copy came from this post:

https://news.povray.org/web.43182c9b30c60c8bbc2b06b10%40news.povray.org

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hi,

"Cousin Ricky" <rickysttATyahooDOTcom> wrote:
> William F Pokorny <ano### [at] anonymousorg> wrote:
> > Another approach was used by PM 2RING for his catenary.inc ...
> It was never in the Object Collection.  ...

the collection does have Chris B's 'rope' set of macros though, where 'catenary'
is among the given keywords.  no idea if useful / applicable, but attached here.


regards, jr.

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Attachments:
Download 'pov_oc_000154.zip' (1042 KB)

On 5/22/24 12:45, jr wrote:
> Chris B's 'rope' set of macros though, where 'catenary'
> is among the given keywords.

Yes, perhaps this is what I was remembering... With my old head one can 
never be sure. :-)

Bill P.

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On 5/22/24 06:32, Bald Eagle wrote:
> Better would be to allow spline {} to take any function as a
> spline definition (whether it would make sense to from a spline perspective or
> not).

That's an interesting idea. Where the functions support 't' or at least 
a rough equivalent I suppose.

Once in a while I look at Ingo's gradient.inc with the idea of 
supporting something like that whole collection as one inbuilt function 
with 'modes' or 'selections' to run each.

Bill P.

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