Pointlist to Bezier?

[Roland Huettmann]

It looks pretty amazing and very nice in the web browser (Chrome). And
comparing to the actual stack it really is a true representation of the
original stack.. ) A very nice user interface!

Unfortunately I can not comment any of the algorithms. Also I could not see
a change applying those to selected drawings. But interesting to follow...)



On 7 December 2015 at 22:18, [-hh] <hh at livecode.org> wrote:

> Hi Michael and all,
>
> meanwhile I looked closer at the math of the two algorithms that Alejandro
> implemented.
>
> TMO, this is the answer, no matter if you wish to approximate/smooth
> bezier-curves or any other path by curves of lower/higher order:
>
> [1] If you have not too much points, say an N-gon with N <= 32, then the
> two (very good) by Alejandro implemented algorithms are better, although
> they produce a lot of points. One can see that also in Alejandro's
> demo-stack.
>
> [2] For smoothing "nasty" lists, like hand-drawing, the methods I used
> seem to do a slightly better job. They need more time for the 'preparation'
> of smoothing but also produce a smaller amount of points (less points than
> the input).
>
>
> You can compare the three methods by yourself with the updated
> "krikelKrakel" (the input stack is downloadable there):
> http://www.hyperhh.org/html5/krikelKrakel2a-8.0.0-dp-9X.html
>
> May be --- I hope so --- Alejandro will improve the usage of 'his' two
> algorithms in the card's script or even make a better one.
>
> > Michael K. wrote:
> > I might not have been precise enough….what I meant was:
> > To a given curve (or pointlist) which bezier will fit it.
> > Kind of reverse-engeneering beziers
>
> Feel free to change the script, for example in order to use some
> approximate bezier curves of "any" order (square, cubic,...) as input
> instead of the drawn user-points ( which are collected by mouseMove).
>
> And please show us the result if you succeed with your changes.
>
> If you mean by "reverse-engineering beziers" to find out from alist of
> points the curve-type "Bezier", the order of it and the control points,
> then this is far out of my mathematical horizon (approximating closely yes,
> but not finding out the exact model).
>
> Hermann
>
> p.s. The approach of Scott R. is a really clever one for *drawing
> /visualizing* (cubic) bezier curves. For approximation by such curves I
> don't understand until now what the advantage of using 'behaviour' could be.
>
>
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