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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