Rogier, in your example the number of contours changes.  This is what
Kenneth's paper calls the "branching" problem and algorithms like mine (and
I assume Sanjeev's) don't even address this problem at all.  We are
looking just at the problem of how to align one contour with another one.

On Mon, Jan 23, 2023 at 5:50 AM Rogier Wolff R.E.Wolff@bitwizard.nl wrote:

yes, in my case i can only use this when the number of points in both the
sections are same.

although a generic arrangement can be developed by following
[sec1]*len(sec2) and [sec2]*len(sec1) to make them equal and this works,
but i dont think this is correct

regards

On Mon, 23 Jan 2023 at 16:43, Adrian Mariano avm4@cornell.edu wrote:

Hi,

Right now i am developing linear_extrude with an ARBRITARY profile (with
help of python)

possible application might look like this:

[image: image.png]
hoping that this can become baseline sometime in the future.
working locally already here :)

On Sun, Jan 22, 2023 at 3:15 PM Kenneth R Sloan kennethrsloan@gmail.com
wrote:

If I have to import my python library openscsd1.py and use, how will that
work.

Also would not like to overwrite the native openscad modules.

On Mon, 23 Jan, 2023, 7:07 pm Guenther Sohler, guenther.sohler@gmail.com
wrote:

It sounds like you are writing a function that duplicates the skin()
function found originally in list-comprehension-demos and expanded in
BOSL2, though if you truly mean arbitrary shapes it will be interesting.
So you can connect 4 rings to a single hexagon, say?

For your example, it can be done without python:

include<BOSL2-fork/std.scad>

function prof(h) =
let(
ang = 180*(h-5)/10,
c=5sin(ang),
s=5sin(ang)
)
[[-c,-s,h],[10+c,-s,h],[10+c,10+s,h],[-c,10+s,h]];

profiles = [for(i=[0:1/2:20]) prof(i)];

skin(profiles,slices=0);

On Mon, Jan 23, 2023 at 8:37 AM Guenther Sohler guenther.sohler@gmail.com
wrote:

Sanjeev, I make no assumption that the number of points in both sections
are the same.  It didn't look like you were making this assumption:  in
your example with the star the number of points is different.

But I assume that there is only one contour at each layer, so you cannot
have a ring, because that has two contours.  You would have to handle that
by modeling the hole separately from the outside of the object.

On Mon, Jan 23, 2023 at 6:34 AM Sanjeev Prabhakar sprabhakar2006@gmail.com
wrote:

For producing a polyhedron, the number of points in different levels needs
to be same is what I assume. If there is any other way, I am not sure.

In the example shared, points were made same with ray intersection method.

From the center of the sections, lines were drawn in circular orientation
to find intersections.
Since these are 360 lines, the points in each section were 360. But in this
case vertex to vertex mapping is not possible.

The other method I use is nearest point mapping method depending on the
shape of the 2 sections and most of the time this works if the sections are
convex.

Now with the new minimum distance orientation solution, this new method of
[sec1]×len(sec2) and [sec2]×len(sec1) can be used. This cannot be directly
used though, all the similar points needs to be grouped together to work.

On Tue, 24 Jan, 2023, 2:49 am Adrian Mariano, avm4@cornell.edu wrote:

My approach is to duplicate points, so if you want to match a pentagon to a
hexagon, you duplicate one of the pentagon's points so that you have a
pentagon with 6 points.  Then the points can be aligned.  Then you resample
the edges of the points, and linearly interpolate to generate the desired
number of slices.  This generates a polyhedron with some degenerate faces,
which can then be discarded automatically.

So when I'm doing a distance optimization, that optimization is done on the
5 points of the pentagon and 6 points of the hexagon, not on the resampled
curves.  This ensures that the corners align with each other, which (I
think) produces the best outcome.

I don't think I understand what you mean about [sec1]×len(sec2) and
[sec2]×len(sec1).  If I don't want to use the minimum distance method, but
instead want to use the arc length based approach, then I resample (or
originally generate) the curves so that they have the same number of
points, uniformly spaced in length along the curve.  Then it's a question
of deciding where to start.  I do this by considering every possible
starting position (rotations of the point lists of one of the curves) and
computing the total distance between all pairs.  Choosing the one with
minimum total distance gives a good starting position.

My other approach, which I think resembles your rays approach is as
follows:  given one curve and a point to map, find a tangent plane at that
point on the curve such that the tangent plane also intersects the other
curve in a single point.  That defines the mapping.  I never understood how
your rays method works when the curves are in 3 space, not parallel to each
other.

On Mon, Jan 23, 2023 at 5:50 PM Sanjeev Prabhakar sprabhakar2006@gmail.com
wrote:

following is the code in python which matches a pentagon with an octagon
with minimum distance method without any slices:

sec1=circle(5,s=6)
sec2=circle(7,s=9)

sec3=c2t3(concatenate(array([sec1]*len(sec2)).transpose(1,0,2)))
sec4=translate([0,0,10],concatenate(array([sec2]*len(sec1)).transpose(1,0,2)))

sol=align_sec(sec3,sec4)

with open('/Users/sanjeevprabhakar/iCloud Drive
(Archive)/Documents/Download/openscad/trial.scad','w+') as f:
f.write(f'''
{swp(sol)}
''')

function c2t3 converts a 2d to 3d by adding 0 in place of 'z' axis.
function translate is used to translate a 2d section up by 10 units in this
case and hence making it 3d
function align_sec is for aligning the points
you can notice the grouping of points with python numpy functions

following result is produced:
[image: Screenshot 2023-01-24 at 5.28.03 AM.png]

Align function is written yesterday and is not checked for any possible
bugs yet, but it works as of now in various similar cases

On Tue, 24 Jan 2023 at 04:48, Adrian Mariano avm4@cornell.edu wrote:

This is my result for pentagon to octagon.  It has two obviously curved
faces.  (All faces are somewhat curved.)

[image: image.png]

On Mon, Jan 23, 2023 at 7:00 PM Sanjeev Prabhakar sprabhakar2006@gmail.com
wrote: