general extrusion (imperfect)
I've written an incomplete and imperfect generalized extrusion (arbitrary
curve) routine.
Being rather thick-skulled, I tried writing without checking and learning
from the sweep code in github. So I'm not sure how mine compares to state
of the art. Github is responding extremely slowly for me now and I'm too
exhausted... So I just toss out some result now, maybe I'm making a fool of
myself... anyway...
Anyway the calling convention is:
extrude(path, orient) shape();
Where both path and orient are a vector of vectors in the format
[[x0,y0,z0], [x1,y1,z1], [x2,y2,z2], ...]
The each element of path is a point in the arbitrary curve. Each element of
orient is a vector indicating the direction that shape()'s "north" should be
pointing. This module will extrude the 2D shape() along this path keeping
shape()'s "north" (as close as possible) to orient's direction.
Shape() should be a polygon on the X-Y plane. "North" is defined by the
positive Y-axis. Any 2D primitives, or combination/transformation of 2D
primitives can be used as shape().
The module is incomplete because I still haven't made the joints between
segments, BTW number of segments shall be (len(path)-1).
The module is imperfect because there's a singularity (?) at the N- and
S-pole. I.e. if the path vector swing pass the +Z or -Z axial directions,
the orientation of the shape() is liable to become discontinuous.
I only have energy to make a couple test cases now: Moebius I-Beam (4- or
24-segments versions) The 4-segment version is ugly be it illustrates
clearly the unsatisfactory joints but also shows each segment is twisted to
connect the changing orient vectors.
When I get home I will take a look at github for the "unofficial official
version" and its test cases. I also welcome anyone to post some (torture?)
test cases for me to try, see below for format. For the time being, I don't
want to share the source of this work-in-progress.
http://forum.openscad.org/file/n14740/Moebius-Ibeam-4.png
http://forum.openscad.org/file/n14740/Moebius-Ibeam-24.png
--
View this message in context: http://forum.openscad.org/general-extrusion-imperfect-tp14740.html
Sent from the OpenSCAD mailing list archive at Nabble.com.
If you don't want to calculate all your extruding path (and parameter)
information you will love multivariate splines. As I just finished my
library, which I (painfully) ported from Matlab to OpenSCAD, I can show you
some first results:
http://forum.openscad.org/file/n14752/spline_demo.png
By the way, you said: "But I've found porting from Matlab to OpenSCAD to be
quite un-painful." Have you ever tried to port some matrix related stuff?
Even expressing a simple algorithm with a functional language it just a big
mass, NO FUN AT ALL. Not to mention that the result can't be read anymore.
- Rudolf
--
View this message in context: http://forum.openscad.org/general-extrusion-imperfect-tp14740p14752.html
Sent from the OpenSCAD mailing list archive at Nabble.com.
Hello,
It's funny because I work also for fun on bezier curve in Openscad.
It put my code in my vcad library (on github).
http://forum.openscad.org/file/n14758/bezier.png
With same A:
Vicnet
--
View this message in context: http://forum.openscad.org/general-extrusion-imperfect-tp14740p14758.html
Sent from the OpenSCAD mailing list archive at Nabble.com.
Oh, that is lovely. Looks almost the same!
I suppose Bezier stuff is even more sophisticated than splines. I never dove
into it, but I guess the framework to do n-dim interpolation with it should
be quite similar and the only difference will be how the core equation
system is set up.
Without having looked into your code yet (reading functional code is
definitely not, how I want to spend my afternoon), I’d like to ask you for
some general information about your approach:
-
I’m using (natural) cubic splines. Do use cubic Beziers (i.e. two control
points)? -
My approach is n-dim over one-dim – i.e. I calculate a line integral as
common auxiliary x-dimension and apply an ordinary cubic spline sequence
spline2D(x, y_i, N) to any given dimension (y_i) in A. I guess you follow
the same way? -
How do you automatically choose your control points? I guess there is
some freedom … -
Beyond the different basic approaches, also the common line integral
plays an important role, as I’ve found out comparing results calculated on
the basis of the Euclidian norm and Eugene Lee's centripetal scheme. How do
you calculate yours?
I’m planning to publish my library as part of some thingiverse project, as I
have done before with other libraries. But first let me play around with it
a bit and do some more testing to see how it reacts to pathological
datasets. I’m a fan of fail-safe code. Also, I might extend my code to
additionally cover circular curves and special boundary conditions. But if
you are interested, I’d send you my current implementation via PM.
Hmm, we might combine our libraries and offer the functions through a
"common interface", like:
--
View this message in context: http://forum.openscad.org/general-extrusion-imperfect-tp14740p14763.html
Sent from the OpenSCAD mailing list archive at Nabble.com.
Parkinbot said 'By the way, you said: "But I've found porting from Matlab
to OpenSCAD to be quite un-painful." Have you ever tried to port some
matrix related stuff? Even expressing a simple algorithm with a functional
language it just a big mass, NO FUN AT ALL. Not to mention that the result
can't be read anymore.'
OpenSCAD isn't a functional language. The minimum requirement for that is
to support functions as first class values, that can be passed as arguments
to functions, and returned as results (hence the name "functional"). This
is the basis of the rich set of control structures found in functional
languages, but missing in OpenSCAD (except that we now have list
comprehensions). True functional languages also have either lazy
evaluation, or at minimum support infinite lists.
If your starting point is Matlab, these features (first class functions and
infinite lists) might not mean much to you. Matlab has only limited support
for function values, not enough to support the functional style of
programming. And Matlab's generators are not as powerful as infinite lists.
But I can assure you that if you are porting a large, idiomatic functional
program to OpenSCAD (or to Matlab), then it is going to be very painful,
and the translated code will probably be much larger.
OpenSCAD is a declarative language, but it isn't powerful enough to qualify
as functional. OpenSCAD is very weak compared to anything that people
normally call a programming language, which is why we often claim that it
isn't a programming language.
I don't know your specific issues with porting Matlab code, but it is quite
possible that your problems are specific to OpenSCAD, and do not generalize
to functional programming languages.
And yeah, we could do better in the future. My OpenSCAD2 proposal is a baby
step into the world of functional programming. But there is a tricky
balancing act involved: making OpenSCAD more powerful without making it too
complex and ruining the properties that make it popular for non-programmers.
PS, I know nothing of splines and beziers; it's something I'd like to learn
now that I see what you and others are doing with it in OpenSCAD.
On 25 November 2015 at 10:30, Parkinbot rudolf@parkinbot.com wrote:
If you don't want to calculate all your extruding path (and parameter)
information you will love multivariate splines. As I just finished my
library, which I (painfully) ported from Matlab to OpenSCAD, I can show you
some first results:
http://forum.openscad.org/file/n14752/spline_demo.png
By the way, you said: "But I've found porting from Matlab to OpenSCAD to be
quite un-painful." Have you ever tried to port some matrix related stuff?
Even expressing a simple algorithm with a functional language it just a big
mass, NO FUN AT ALL. Not to mention that the result can't be read anymore.
- Rudolf
--
View this message in context:
http://forum.openscad.org/general-extrusion-imperfect-tp14740p14752.html
Sent from the OpenSCAD mailing list archive at Nabble.com.
OpenSCAD mailing list
Discuss@lists.openscad.org
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
Parkinbot wrote
- I’m using (natural) cubic splines. Do use cubic Beziers (i.e. two
control points)?
Yes, 2 controls points, automatically generated (with points before and
after one point).
Parkinbot wrote
- My approach is n-dim over one-dim – i.e. I calculate a line integral as
common auxiliary x-dimension and apply an ordinary cubic spline sequence
spline2D(x, y_i, N) to any given dimension (y_i) in A. I guess you follow
the same way?
I not sure to understand integral...
I use this: https://en.wikipedia.org/wiki/B%C3%A9zier_curve and quadratic
bezier curve function to calculate intermediate positions between 2 points
and the 2 associated control points.
Parkinbot wrote
- How do you automatically choose your control points? I guess there is
some freedom …
For each point, take vector from point before to after and apply a weight to
get control point before and after.
Parkinbot wrote
- Beyond the different basic approaches, also the common line integral
plays an important role, as I’ve found out comparing results calculated on
the basis of the Euclidian norm and Eugene Lee's centripetal scheme. How
do you calculate yours?
Oops, I don't understand at all
For norm I use euclidien norm, so the same function in OpenSCAD.
Parkinbot wrote
I’m planning to publish my library as part of some thingiverse project, as
I have done before with other libraries. But first let me play around with
it a bit and do some more testing to see how it reacts to pathological
datasets. I’m a fan of fail-safe code. Also, I might extend my code to
additionally cover circular curves and special boundary conditions. But if
you are interested, I’d send you my current implementation via PM.
Hmm, we might combine our libraries and offer the functions through a
"common interface", like:
Why not !
a+
Vicnet
--
View this message in context: http://forum.openscad.org/general-extrusion-imperfect-tp14740p14765.html
Sent from the OpenSCAD mailing list archive at Nabble.com.
doug.moen wrote
OpenSCAD isn't a functional language. The minimum requirement for that is
to support functions as first class values, that can be passed as
arguments to functions, and returned as results (hence the name
"functional"). This is the basis of the rich set of control structures
found in functional languages, but missing in OpenSCAD (except that we now
have list comprehensions). True functional languages also have either lazy
evaluation, or at minimum support infinite lists.
Ok, I don't want to get into a paradigm and purism discussion. My concern is
very practical and aims at the expressive power I can use to write useful
and readable code for designing stuff, I want to design. So let's call it a
small subset of a functional language. In your roadmap I can see that you
want to brush it up to go further into this direction.
Are you sure, novice programmers will be happy or even able to follow you
there? We talk about playing around with vectors, matrices and Euclidian
spaces and functions. And about algorithms dealing with those entities. No
one wants to juggle around with infinite lists or write a parser or a
compiler.
As the subset for now is still very small, I think OpenSCAD’s functions
could be also brushed up to go more into the procedural direction, like
QBASIC or basic C, which also can live without functional arguments and
pointers. Thus allowing for things like statement sequences, local variables
and random write access to vectors and matrices, as I already proposed in
http://forum.openscad.org/feature-request-plug-ins-tp14663p14721.html
doug.moen wrote
Matlab has only limited support for function values, not enough to support
the functional style of programming. And Matlab's generators are not as
powerful as infinite lists.
My starting point by far is not restricted to Matlab, which is by the way
the most expressive language I have ever programmed with. So forget about
this.
doug.moen wrote
But I can assure you that if you are porting a large, idiomatic functional
program to OpenSCAD (or to Matlab), then it is going to be very painful,
and the translated code will probably be much larger.
I also doubt that, beside the fact that functional programs are unreadable,
trying to be elegant at the first place. But this is also not the point.
doug.moen wrote
OpenSCAD is very weak compared to anything that people normally call a
programming language, which is why we often claim that it isn't a
programming language.
So why not opening it up with a plugin-API, instead of dreaming about an
expressive power far beyond Matlab and which 99% of the users will curse at.
doug.moen wrote
I don't know your specific issues with porting Matlab code, but it is
quite possible that your problems are specific to OpenSCAD, and do not
generalize to functional programming languages.
I’ve given a code example, doing some very usual matrix related steps. Have
a try …
doug.moen wrote
PS, I know nothing of splines and beziers; it's something I'd like to
learn now that I see what you and others are doing with it in OpenSCAD.
I’m sure this concept can also be useful for you, e.g. to read newer
DXF-formats into OpenSCAD or refine meshing.
- Rudolf
--
View this message in context: http://forum.openscad.org/general-extrusion-imperfect-tp14740p14767.html
Sent from the OpenSCAD mailing list archive at Nabble.com.
vicnet wrote
I not sure to understand integral...
A line integral is a measure for the length of a line (in our case the
polygon defined by the base points). You can use the natural Euclidian norm,
called 2-norm, (you say later, you do this), but there are also other
choices with calculation schemes.
vicnet wrote
Parkinbot wrote
- How do you automatically choose your control points? I guess there is
some freedom …
For each point, take vector from point before to after and apply a weight
to get control point before and after.
I understand. How do calc the weight? Or is it always the same weight, say
1.1, which may be parametrized?
vicnet wrote
Parkinbot wrote
Hmm, we might combine our libraries and offer the functions through a
"common interface", like:
Why not !
I'll put a note here with a link to the thing, as soon as I've published it!
@Neon22
You said you'd prefer B-splines over beziers. They are a good choice to
flatten a polygon, but don't contain the polygon points. Will you implement
them? Then we might reserve you some space in the lib
Rudolf
--
View this message in context: http://forum.openscad.org/general-extrusion-imperfect-tp14740p14777.html
Sent from the OpenSCAD mailing list archive at Nabble.com.
Parkinbot wrote
I understand. How do calc the weight? Or is it always the same weight, say
1.1, which may be parametrized?
It is a parameter.
a+
Vicnet
https://github.com/vicnet/vcad
--
View this message in context: http://forum.openscad.org/general-extrusion-imperfect-tp14740p14786.html
Sent from the OpenSCAD mailing list archive at Nabble.com.
Rudolf,
No sorry but it's beyond me. I can make stuff, I know a couple of things,
but I'm not a mathematician.
Kochanek splines would get my vote as they are well behaved and the curves
go through the knots.
I've used them a lot several years ago(87).
So if implemented using basis function (array) then could have a number of
spline types by changing just the basis array.
-
https://en.wikipedia.org/wiki/Kochanek%E2%80%93Bartels_spline
Basis array pseudcode: - http://cubic.org/docs/hermite.htm
Cheers...
--
View this message in context: http://forum.openscad.org/general-extrusion-imperfect-tp14740p14787.html
Sent from the OpenSCAD mailing list archive at Nabble.com.