Hello
In ChitChat I made a link to all about Bezier-Curves OK here again:
http://pomax.github.io/bezierinfo/
Where you can learn nearly all about Bezier; with a lot of interactive pictures (Pages.js and Bezier.js) , very very nice for beginners as wel as experts (to become

I was intrigued by the Casteljau-algorithm to compute points of a Bezier curve, implemented it in a PythonFu Plugin:

And here a picture for some explanations:


OK, try as follows:
1. download the *.zip en unzip it either in existing plugin directory, Gimp looks at, or an new one and inform Gimp where to look to.
2. start Gimp and open say a new window (empty or not)
3. the plugin should occur under a Tab in the main window under PKHG ;-) with name: Casteljau alemein ..
4. first try if it works and aftwards play with the parameters

In the upper image you see the handles of a Path and what the Plugin does with not changed parameters (maybe the number of points around 200 say).

The Brush is not yet active, though you can push it, help to activate it for the plugin is appreciated

If the handle- vectors are set (anti-)symmetric and a vertical then the painted points are symmetrical too, if not, the number of point on one end may be much more or so ... try

Comments are welcome ;-)

Peter

Well that was fast.



All the points seem to work well. I set it to go from the left to the right dropping slightly at the end. Fun to play with for sure.

Thank you.

First of all, welcome to the forum

I can hardly believe the good timing of your arrival and the subject you're talking about!
Perhaps you can advise me on the following:

Some time ago I implemented a G'MIC filter based on parametric quadratic transform, after reading a blog about it here: parameterized quadratic conformal transformation

This itself is based on a form of Bezier by the same author: e-bezier

The question I have is this: can the calculation be inverted so that rather than distributing source pixels to a new (x,y), we form a map of (x,y) locations from which to "pull" pixels from the source image?

As a start I created a simple 1-dimensional warp using inverse of the "e-bezier" function, but have no idea whether it can be done entirely (I'm sadly in no way a mathematician). I've tried contacting the blog author but so far received no reply.

Apologies for slightly hijacking your thread! It might be better to message directly instead of posting here...

You hit the nail on the head with most BPT ideas... they look fine but their suitability to a graphic program is not demonstrated. For instance how do you manipulate E_splines in real life? The Bezier curves have anchors and handles that make it easy, so what is the equivalent for E-splines? How do you string several of them to create an arbitrary line? Are they preserved by an affine transform (rotation, scaling...).

BPT could be good with algebra (or with Mathematica) but some of his posts are surprising, and in any case many of this stuff is just playing with formulas and seeing what happens. If this had any real value it would be published in more formal settings. But of course, peer review could uncover problems. For instance, can you spot the problem in that one (it's totally obvious)?

My main question is why don't you use a Gimp path... Gimp paths are Bezier splines (or a string of such). From a path object it is easy to get the coordinates of the 4 points, which is a much better interface than entering 8 coordinates. Plenty of examples here. See in particular path-dump and path-csv.

Also, when you publish something on the Internet, English is the de facto language (for the UI, but also for code comments and function/variable names).

I was about to edit to say I've added the test bezier-based warp to filters in G'MIC under testing > garagecoder > Inverse Bezier Warp - it won't be available until David does an update so maybe tomorrow.

Yes it's clear a lot of it is just random trains of thought which could have many issues, but this one just appeals somehow... I like the idea of a fast controllable warp in G'MIC. Perhaps there are better ways but it's beyond my current ability

The method described does work to some degree but a properly interpolated warp would be so much nicer. Incidentally I did implement it (minus oversampling or any controls) under testing > garagecoder > PQCT example

Again this should really not be in this thread, I'll take further replies to PM - sorry!

Clear, it is nothing more than using the Calsteljau function
More important is the link to the very nice description of Bezier, from easy to high level math!
And a lot of this is builtin in Gimp

One part maybe interesting though, to use the Casteljau def ... with more than 4 points for higher order Bezier Curves ...; will try myself soon.

One thing in Gimp is, as it looks like, one can step in equal steps over a PATH ... (have built that too using only Gimp tools), this is NOT the case in this 'primitive' path filling method of the plugin I added in this thread.

What you may help me with is: how to activate the in the UI chosen brush for the plugin.
Read something that it is maybe (yet) impossible??? Context-problem???

EDIT:
Casteljau with longer input_list gave e.g. these points:

See my stroke-visible-paths script at the same place.

You can set the brush using pdb.gimp_context_set_brush(brush) but you normally don't need this. When you write a script that uses a single brush, you should assume that the current brush is what the user wants, so you don't need to ask for a brush. This gives more choices to the user than what you can do in your dialog. Furthermore for clean results you want to stroke the path in "line" mode but this is unfortunately not available through an API, so it's best left to the user (it's just a two-click operation).

Hallo,
The plugin is now made with English names and using Clipboard as BRUSH
To add checks etc .. to be done ...

First quick test:


EDIT:
A new revised version for really too higher order Bezier Curves.


not yet 100% waterproof

The list of points may now be of greater than 4 (3rd order Bezier) it is a String-Parameter
which you may make longer or shorter to see the differences ... of the orders ...
The string is "evaled" and may be not suitable, therefore a try except is used.
A function for checking if an object is a list of 2d-points is used against errors from the input

Who knows a better solution; next version of Gimp will have probably numpy and then a lot of things may be done much nicer (and faster?!)...

Have to stop now (sports-evening) , will look tomorrow morning here ...
Good night and ciao
Peter

When ever you have a new version ready to submit just delete the old attachment via
User Control Panel button (top right) then select (on the left column) "Manage Attachments"
A list of your attachments will pop up and you can delete any you wish.

It is best to delete the old file and then attach the new one in the first post. Otherwise you get a huge list of attachments and someone is bound to download and install an incorrect version.

I hope all of that was clear enough for you to understand. If not just PM (Private Message) me about further instructions.

Thanks!

OK, will be done tomorrow ...

Hm, thinking about it, I should not delete the first version.
Reason: the first is suitable to play with 3rd order Bezier (with start- end- point and two vectors)
the last one is to examine to different orders of Bezier Curves ;-) and has a different UI

which is not optimal, could need help to make it clearer

Perhaps a reset could be added.