Working on a 3D letter design, as mentioned before in another thread.

As simple as designing a serif letter can get, it became complicated instead.
That is, because I figured out to use a 3D shape as a pen tool to draw the letter as a calligraphy.

Here are two renders of the current version of the letter:




Since then, posted a thread on blenderartists http://www.blenderartists.org/forum/showthread.php?290826-3D-calligraphy-dificulties
if they could give some advices on some modelling problems that came up.

As for creating a clean model with a nice topology, this method seems to work:

Drawing iso-lines -horizontal cutlines- of the 3D pen shape,
using each cut line to draw separate letters on the same strokes,
and putting them together in blender to have a 3D model.

Here is a render of that 3D pen shape:


Here are some dimensions on it to make it clearer:
https://www.dropbox.com/s/lav4kz4txrqrd3t/keresztm7.pdf

Here is how the strokes should be constructed:




I could construct some cut lines in inkscape described in that previous topic, and asked if anyone had an idea on using each as a pen shape.

Now that it hadn't been answered, here is what I came up with recently:

Using one of the cut-lines, tried to draw a stroke.

This first one is drawn with the motion extension.
As a path curve would be broke down to small straight segments, the overall stroke would look exactly like this.
A straight segment, then a small part of the edge of the pen shape, then another straight segment, and so on.

I would need a circle arc for the axis of the stroke,
so even steps in the rotation, even segment length seemed reasonable.

Now that the overall shape was done, I was thinking of you could always chose a smaller segment length,
the part of the pen shape would be less and less.
Resulting in a curved line, and in an exact point, where a pen shape would be tangent to the edge of the overall stroke.

This wild guess is depicted here:


These are two svg-s, so that you can open it in inkscape for a closer look.

-On a side note, how awesome is that 3D rod effect?
Well, if gradient meshes will be available... will it be implemented?-


So back to the point: now for that discover in the stroke structure, on the tangents,
the cut lines should have all their nodes preferably with exact tangents.

Not that it would be too hard to construct from the cutlines I already have, but
impossible to make them clean:
by rephrasing the path to nodes with the right tangents, they appeared to be in a bit too random position to eachother.


SO.

I would need to construct clean cutlines of the pen shape, which was put together from toruses.
Modelling, manual constructing couldn't help, maybe mathematics -and scripting?- could help.

AS it appears that the cut lines are not ordinary curves, but they are so famous, that they have their own name-names.
Namely, Cassini ovals.
http://mathworld.wolfram.com/CassiniOvals.html

The Cassini ovals are a family of quartic curves, also called Cassini ellipses, described by a point such that the product of its distances from two fixed points a distance 2a apart is a constant b^2

Haven't find a parametric way to describe them yet, but it has some sweet formula described on that site.

So basically now it is a connect two torus's data to a function for a quartic plane curve job.
Then, construct the points with the exact tangents.
After that, placing every pen shape on the stroke's axises, and connecting them for a hull.
This would be enough to start a good 3D model.

Any tips?


-Hope there will be such tool in inkscape as in gimp, that you can put a shape along a path and use it as a pen. Suggestion on the coding?

Not so sure if it would be really needed as the curved stroke is the only part that I should use this kind of cut-line method,
where the small errors from the recent iso-lines wouldn't show up that much.
I understand the limitations of that these are not cad programs,
but come on, how is that, you can draw more accurate things when zoomed in by hand, then the thing the program calculates?

These things are so parametric, might make a mock-up for that suggestion out of it :http://www.inkscapeforum.com/viewtopic.php?f=32&t=14016&hilit=+node+editor#p54843

Parameters are:
height data of a cross section's starting point
distance data to span
height of the curve
arches rotation ratio between the small and the large circle
radius of the toruses
arch lenght data on a tangent circle around the toruses on a sideview

thus creating
height data of deisred iso-line cuts
functions for te right Cassini-ovals
booleaning the two torus's Cassini-ovals
derivant function on the Cassini-oval's function,
which, described by another parameter, would produce points of the Cassini-ovals with right tangents.

Another extension for aligning the this way created Cassini-ovals on a path,
rephrasing the path into nodes with set tangent data, and finally connecting each defined point to create iso-lines on a top-view.

With a "shader modifier", all 3D specular light would be produced in gradient meshes that could be set, and actual shades drawn by paths.


That would make all this 3D caslligraphy a productive inkscape thing.

But for now I'm searching for how to create and work with latex files, to create a good presentation on the mathematical background on the "ever be scripts".

Did a similar parametric node-based editor panel schema for a possible 3D meethod in blenderartists forum.
http://www.blenderartists.org/forum/showthread.php?290826-3D-calligraphy-dificulties/page4

Starting a new topic on the programming.