Sweeping polygon over irregular shape?

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Sweeping polygon over irregular shape?

kdtop

I know that we can sweep a polygon around a circle like this, making a 3D object.  :

rotate_extrude($fn=100) polygon(points = MyPts);

Recently, however, I wanted to construct a cover for a lathe that had curved sides, but when viewed face-on had an irregular shape.  It's shaped like a triangle with curved corners.  It would have been very nice to create a polygon for the side contour and then been able to sweep it around my custom shape.

Can OpenSCAD do this?  If not, would it be a complex feature to add?

Thanks in advance,
Kevin T

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Re: Sweeping polygon over irregular shape?

MichaelAtOz
Administrator
kdtop wrote

> ...
> Recently, however, I wanted to construct a cover for a lathe that had
> curved sides, but when viewed face-on had an irregular shape.  It's shaped
> like a triangle with curved corners.  It would have been very nice to
> create a polygon for the side contour and then been able to sweep it
> around
> my custom shape.
>
> Can OpenSCAD do this?  If not, would it be a complex feature to add?
>
> Thanks in advance,
> Kevin T
>
> _______________________________________________
> OpenSCAD mailing list

> Discuss@.openscad

> http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org

I'm not visualising it well, a picture is worth a thousand lines of code...

I suspect sweep() would be suited, *can someone point to the latest sweep()*
I'm out of date on the topic.



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Re: Sweeping polygon over irregular shape?

Parkinbot
In reply to this post by kdtop
please use the forum search for questions like this. sweep and minkowski are
your search items.



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Re: Sweeping polygon over irregular shape?

kdtop
Thanks for the replies.

Here is a link to the object I ultimately created -- though I would like a better way of having done it:  https://www.thingiverse.com/thing:3246547

Screen Shot 2018-12-01 at 9.17.02 AM.png

Here is a picture that shows the shape with the side pieces spaced out.

Screen Shot 2018-12-01 at 8.48.25 AM.png

To make my 3D shape, I simply put many many more of these side pieces together so that there were no gaps.  The problem is that each side piece is a 3D object with a flat back and a given width.  So the side walls ended up with jags.  And it is ultimately an inefficient way of doing this.  (a CGAL render takes 1-2 HOURS!)   The sides really should be a 2D object that is then swept around a path defining the outer curves.

I don't think minkowski() would have any application in this situation.  And a hull() would make a solid object, not concave like I want.  

Apparently someone has made a sweep() function, which I didn't realize.  I searched the forums as recommended and found this discussion about sweep(): http://forum.openscad.org/Two-annoyances-tt12935.html#a13514

It appears that the sweep() is part of a library rather than an intrinsic function of OpenSCAD.  Is this correct ?  If so, then which is the best or recommended library to use?

I found these links.
Questions:
1) In this (https://github.com/openscad/list-comprehension-demos/blob/master/sweep-test.scad) code example, I see the following at the top:

use <sweep.scad>
use <scad-utils/transformations.scad>
use <scad-utils/shapes.scad>


 Is the \scad-utils\ folder a standard thing with anOpenSCAD install? I.e. can I use this directly?  I.e. is there a way in OpenSCAD to set up a search path for library folders?  So far I have been putting a copy of any library used into the folder containing my current project.  Thus I have many copies scattered  across my various projects.  I am on mac OSX.  I went to the application folder, right-clicked on OpenSCAD, chose "show package content" and from there found a folder .\Content\Resources\libraries\MCAD.  This contains many files that would seem to be helpful libraries.  How is one supposed to use these?  Copy them to a working folder?  Figure out the long complex path and link to that directly?

2) I have been using this (http://www.openscad.org/documentation.html) link as my source of documentation to learn OpenSCAD.  If some of these other features, such as sweep() are official, should they be included there?  If not official, should they be made official?  And even is sweep() is not included with the distribution, is there documentation of the libraries that ARE included with the application?

Thanks in advance,

Kevin

On Sat, Dec 1, 2018 at 6:35 AM Parkinbot <[hidden email]> wrote:
please use the forum search for questions like this. sweep and minkowski are
your search items.



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Re: Sweeping polygon over irregular shape?

Ronaldo
Kevin,

Sweep is not a built-in OpenScad operator neither it is included as a standard library. AFIK, there is two main sweep libraries around there: one was written by Oskar Linde and is part of the list comprehension demos you have found, the other was created by Parkinbot. Linde's sweep is a module that receives a planar 2D section and a sequence of affine transformations. The transformations are applied to each section to position them in the 3D space and the set of such sections is wraped in a OpenScad polyhedron. No boolean operation is used so the process is relatively fast. An utility function - paths_transforms - can be used to compute the sequence (list, array) of transformations from a sweep path. The affine transforms generated by that function are restricted to rigid body transforms. To help several tasks, Linde has written a bunch of general use libraries under the name scad-utils that can be found at:


A copy of that set of libraries should be in an appropriate location in order to be found by <use> or <include>.

Parkinbot's sweep on the other hand expects as input a sequence of 3D planar polygons already positioned in the space and, as Linde's sweep does, wrap it in a polyhedron. No utility function is included in Parkinbot's sweep library to generate the 3D planar polygon. However, Parkinbot's approach is more general than Linde's one as it allows that each 3D planar polygon has it own shape provided that all polygons have the same number of vertices.

The contribution you have found in my Github repository is deeply based on Linde's approach and restricted to: commenting the code, cleaning some functions and adopting a different way to compute the path transforms that avoids some wild twist the original strategy may produce. That new computation is based on a Linde's proposal published in this forum that have never been included in the list comprehension demo repository. My codes also requires functions of scad-utils.

None of those sweeps can be used blindly. The OpenScad render geometric engine - CGAL - will complaint if the resulting polyhedron has self-intersections. It is the user responsibility to avoid them.

Ronaldo Persiano

Em sáb, 1 de dez de 2018 às 14:34, Kevin Toppenberg <[hidden email]> escreveu:
Thanks for the replies.

Here is a link to the object I ultimately created -- though I would like a better way of having done it:  https://www.thingiverse.com/thing:3246547

Screen Shot 2018-12-01 at 9.17.02 AM.png

Here is a picture that shows the shape with the side pieces spaced out.

Screen Shot 2018-12-01 at 8.48.25 AM.png

To make my 3D shape, I simply put many many more of these side pieces together so that there were no gaps.  The problem is that each side piece is a 3D object with a flat back and a given width.  So the side walls ended up with jags.  And it is ultimately an inefficient way of doing this.  (a CGAL render takes 1-2 HOURS!)   The sides really should be a 2D object that is then swept around a path defining the outer curves.

I don't think minkowski() would have any application in this situation.  And a hull() would make a solid object, not concave like I want.  

Apparently someone has made a sweep() function, which I didn't realize.  I searched the forums as recommended and found this discussion about sweep(): http://forum.openscad.org/Two-annoyances-tt12935.html#a13514

It appears that the sweep() is part of a library rather than an intrinsic function of OpenSCAD.  Is this correct ?  If so, then which is the best or recommended library to use?

I found these links.
Questions:
1) In this (https://github.com/openscad/list-comprehension-demos/blob/master/sweep-test.scad) code example, I see the following at the top:

use <sweep.scad>
use <scad-utils/transformations.scad>
use <scad-utils/shapes.scad>


 Is the \scad-utils\ folder a standard thing with anOpenSCAD install? I.e. can I use this directly?  I.e. is there a way in OpenSCAD to set up a search path for library folders?  So far I have been putting a copy of any library used into the folder containing my current project.  Thus I have many copies scattered  across my various projects.  I am on mac OSX.  I went to the application folder, right-clicked on OpenSCAD, chose "show package content" and from there found a folder .\Content\Resources\libraries\MCAD.  This contains many files that would seem to be helpful libraries.  How is one supposed to use these?  Copy them to a working folder?  Figure out the long complex path and link to that directly?

2) I have been using this (http://www.openscad.org/documentation.html) link as my source of documentation to learn OpenSCAD.  If some of these other features, such as sweep() are official, should they be included there?  If not official, should they be made official?  And even is sweep() is not included with the distribution, is there documentation of the libraries that ARE included with the application?

Thanks in advance,

Kevin

On Sat, Dec 1, 2018 at 6:35 AM Parkinbot <[hidden email]> wrote:
please use the forum search for questions like this. sweep and minkowski are
your search items.



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Re: Sweeping polygon over irregular shape?

Parkinbot
In reply to this post by kdtop
this is not the fastest code, but it does what you se3m want


difference()
{
  triag(10, 9);  
  triag(9, 10);  
}

module triag(r = 10, h)
hull()
{
  forN(50, 3) sphere(r);
  forN(50, 3) cylinder(r=r, h=h);
}

module forN(r, n)
  for(i=[0:n-1]) rotate([0,0,360/n*i]) translate([r, 0, 0]) children();




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Re: Sweeping polygon over irregular shape?

kdtop
In reply to this post by Ronaldo
Ronaldo,

Thank you for this helpful information.  I will work on this and see if I can get it going.

Thanks again
Kevin

On Sat, Dec 1, 2018 at 12:21 PM Ronaldo Persiano <[hidden email]> wrote:
Kevin,

Sweep is not a built-in OpenScad operator neither it is included as a standard library. AFIK, there is two main sweep libraries around there: one was written by Oskar Linde and is part of the list comprehension demos you have found, the other was created by Parkinbot. Linde's sweep is a module that receives a planar 2D section and a sequence of affine transformations. The transformations are applied to each section to position them in the 3D space and the set of such sections is wraped in a OpenScad polyhedron. No boolean operation is used so the process is relatively fast. An utility function - paths_transforms - can be used to compute the sequence (list, array) of transformations from a sweep path. The affine transforms generated by that function are restricted to rigid body transforms. To help several tasks, Linde has written a bunch of general use libraries under the name scad-utils that can be found at:


A copy of that set of libraries should be in an appropriate location in order to be found by <use> or <include>.

Parkinbot's sweep on the other hand expects as input a sequence of 3D planar polygons already positioned in the space and, as Linde's sweep does, wrap it in a polyhedron. No utility function is included in Parkinbot's sweep library to generate the 3D planar polygon. However, Parkinbot's approach is more general than Linde's one as it allows that each 3D planar polygon has it own shape provided that all polygons have the same number of vertices.

The contribution you have found in my Github repository is deeply based on Linde's approach and restricted to: commenting the code, cleaning some functions and adopting a different way to compute the path transforms that avoids some wild twist the original strategy may produce. That new computation is based on a Linde's proposal published in this forum that have never been included in the list comprehension demo repository. My codes also requires functions of scad-utils.

None of those sweeps can be used blindly. The OpenScad render geometric engine - CGAL - will complaint if the resulting polyhedron has self-intersections. It is the user responsibility to avoid them.

Ronaldo Persiano

Em sáb, 1 de dez de 2018 às 14:34, Kevin Toppenberg <[hidden email]> escreveu:
Thanks for the replies.

Here is a link to the object I ultimately created -- though I would like a better way of having done it:  https://www.thingiverse.com/thing:3246547

Screen Shot 2018-12-01 at 9.17.02 AM.png

Here is a picture that shows the shape with the side pieces spaced out.

Screen Shot 2018-12-01 at 8.48.25 AM.png

To make my 3D shape, I simply put many many more of these side pieces together so that there were no gaps.  The problem is that each side piece is a 3D object with a flat back and a given width.  So the side walls ended up with jags.  And it is ultimately an inefficient way of doing this.  (a CGAL render takes 1-2 HOURS!)   The sides really should be a 2D object that is then swept around a path defining the outer curves.

I don't think minkowski() would have any application in this situation.  And a hull() would make a solid object, not concave like I want.  

Apparently someone has made a sweep() function, which I didn't realize.  I searched the forums as recommended and found this discussion about sweep(): http://forum.openscad.org/Two-annoyances-tt12935.html#a13514

It appears that the sweep() is part of a library rather than an intrinsic function of OpenSCAD.  Is this correct ?  If so, then which is the best or recommended library to use?

I found these links.
Questions:
1) In this (https://github.com/openscad/list-comprehension-demos/blob/master/sweep-test.scad) code example, I see the following at the top:

use <sweep.scad>
use <scad-utils/transformations.scad>
use <scad-utils/shapes.scad>


 Is the \scad-utils\ folder a standard thing with anOpenSCAD install? I.e. can I use this directly?  I.e. is there a way in OpenSCAD to set up a search path for library folders?  So far I have been putting a copy of any library used into the folder containing my current project.  Thus I have many copies scattered  across my various projects.  I am on mac OSX.  I went to the application folder, right-clicked on OpenSCAD, chose "show package content" and from there found a folder .\Content\Resources\libraries\MCAD.  This contains many files that would seem to be helpful libraries.  How is one supposed to use these?  Copy them to a working folder?  Figure out the long complex path and link to that directly?

2) I have been using this (http://www.openscad.org/documentation.html) link as my source of documentation to learn OpenSCAD.  If some of these other features, such as sweep() are official, should they be included there?  If not official, should they be made official?  And even is sweep() is not included with the distribution, is there documentation of the libraries that ARE included with the application?

Thanks in advance,

Kevin

On Sat, Dec 1, 2018 at 6:35 AM Parkinbot <[hidden email]> wrote:
please use the forum search for questions like this. sweep and minkowski are
your search items.



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Re: Sweeping polygon over irregular shape?

Parkinbot
In reply to this post by Parkinbot
And if want different radii, you can use minkowski over a hull of cylinders
or alternatively hull over three tori for the lower part.

<http://forum.openscad.org/file/t887/pool.png>

$fn = 50;

difference()
{
  triag(r=30, rm=10, R=50, h=19);  
  triag(r=29, rm=8, R=50, h=30);  
}

module triag(r = 10, R = 50, rm = 3, h)
{
  hull()
  {
  minkowski()
  {
    hull()
    forN(R, 3) cylinder(r=r, 1);
    sphere(rm);
  }
  forN(50, 3) cylinder(r=r+rm, h=h);
}
}

module forN(r, n)
  for(i=[0:n-1]) rotate([0,0,360/n*i]) translate([r, 0, 0]) children();




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Re: Sweeping polygon over irregular shape?

kdtop
Parkinbot,

You solved my problem without the need for sweep().  I hadn't thought about subtracting 2 hull()'s.  While I still want to learn how to use the sweep library (for other situations), I like your solution.   I had in my mind that hull() was a computationally expensive function.  But your code finished a CGAL (F6) render in about 10 seconds.  So clearly it is better than my prior method.  

In my model, one of the sides bulged out, but I could solve that by putting some more posts in there before calling the hull().

Thanks again,

Kevin

On Sat, Dec 1, 2018 at 3:04 PM Parkinbot <[hidden email]> wrote:
And if want different radii, you can use minkowski over a hull of cylinders
or alternatively hull over three tori for the lower part.

<http://forum.openscad.org/file/t887/pool.png>

$fn = 50;

difference()
{
  triag(r=30, rm=10, R=50, h=19); 
  triag(r=29, rm=8, R=50, h=30); 
}

module triag(r = 10, R = 50, rm = 3, h)
{
  hull()
  {
  minkowski()
  {
    hull()
    forN(R, 3) cylinder(r=r, 1);
    sphere(rm);
  }
  forN(50, 3) cylinder(r=r+rm, h=h);
}
}

module forN(r, n)
  for(i=[0:n-1]) rotate([0,0,360/n*i]) translate([r, 0, 0]) children();




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Re: Sweeping polygon over irregular shape?

berkenb
Your problem appears to be solved, but for what it's worth, I wrote a 'loft'
function a while ago that sweeps the interpolation between two
two-dimensional profiles along a three-dimensional path. It is very similar
to the other 'sweep' libraries mentioned (except mine is poorly documented
and the code probably unreadable, sorry ;-)). The transformations along the
path are computed using quaternions and the usual restrictions apply
(profiles have to be singly-connected and have the same number of points in
them, no self-intersections).
Maybe it is useful to somebody...
Marko

function flatten(vec) = [for (v=vec) for(e=v) e];
function Q_im(q) = [q[1], q[2], q[3]];
function Q_conj(q) = [q[0], -q[1], -q[2], -q[3]];
function Q_mult(q,p) =
[(q[0]*p[0]-q[1]*p[1]-q[2]*p[2]-q[3]*p[3]),(q[1]*p[0]+q[0]*p[1]+q[2]*p[3]-q[3]*p[2]),(q[2]*p[0]+q[0]*p[2]-q[1]*p[3]+q[3]*p[1]),(q[3]*p[0]+q[0]*p[3]+q[1]*p[2]-q[2]*p[1])];                      
function rotQ(q, a, n) = Q_mult(flatten([cos(a/2),n*sin(a/2)]),q);
function poly_rotQ(list, q) = [for (v=list)
Q_im(Q_mult(q,Q_mult([0,v.x,v.y,v.z],Q_conj(q))))];
function poly_rot2d(list, a) = [for (x=list) [cos(a)*x[0]+sin(a)*x[1],
-sin(a)*x[0]+cos(a)*x[1]]];
function poly_translate(list, d) = [for (v=list) v+d];
function interp_lists(l1, w1, l2, w2) = [for (i=[0:len(l1)-1])
w1*l1[i]+w2*l2[i]];


function poly_loft_faces (N_z, N_x, closed=false) = flatten([
     (closed ? ([for (i=[0:N_x-1]) [(N_z-1)*N_x+i, (N_z-1)*N_x+(i+1)%N_x,
i],
       for (i=[0:N_x-1]) [(i+1)%N_x, i, (N_z-1)*N_x+(i+1)%N_x]])
      : concat([[for (i=[0:N_x-1]) N_x-1-i]], [[for (i=[0:N_x-1])
(N_z-1)*N_x+i]])), // caps
       for (i=[0:N_z-2],j=[0:N_x-1]) [[(i+1)*N_x+j, i*N_x+j,
i*N_x+((j+1)%N_x)],[i*N_x+((j+1)%N_x), (i+1)*N_x+((j+1)%N_x),
(i+1)*N_x+j]]]);


// extrude a cross section linearly interpolated between cross sections cr1
and cr2 along path 'path',
// with optional tangential twist linearly increasing along path
module loft (path, cr1, cr2, twist=0) {
  p = flatten([path, [2*path[len(path)-1]-path[len(path)-2]]]);
  pts = flatten([
    for (i=1, d=p[1]-p[0], u=cross([0,0,1], d), un=norm(u), dn=norm(d),
a=asin(un/dn),
         q=un>0?rotQ([1,0,0,0],a,u/un) : [1,0,0,0], n=d/dn, cr=cr1;
         i<len(p);
         d=p[i]-path[i-1], u=cross(n, d), un=norm(u), dn=norm(d),
a=asin(un/dn),
         n=d/dn,q=un>0?rotQ(q,a,u/un):q,
cr=interp_lists(cr1,1-(i-1)/(len(p)-1),cr2,(i-1)/(len(p)-1)), i=i+1)
      poly_translate(poly_rotQ(twist!=0?[for(v=poly_rot2d([for (v=cr)
[v.x,v.y,0]],i*twist/(len(p)-1))) [v.x,v.y,0]]:[for (v=cr) [v.x,v.y,0]], q),
p[i-1])
  ]);
  fcs = poly_loft_faces(len(path), len(cr1));
  polyhedron(pts, fcs, convexity=8);
}

pH = [[-1, 1], [-0.8,1], [-0.8, 0.1], [0.8, 0.1], [0.8, 1], [1, 1],
      [1, -1], [0.8, -1], [0.8, -0.1], [-0.8, -0.1], [-0.8, -1], [-1, -1]];
pH2 = [for (v=pH) 2*v];
phelix = [for (i=[0:6:3*360]) 5*[cos(i), sin(i), i/360]];

loft(phelix, pH, pH2, -170);



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Re: Sweeping polygon over irregular shape?

kdtop
Marko,

A few years ago I was studying up on 3D engines and learned about quats, but haven't thought about them since.  I seem to recall they are a method of achieving a transformation and avoids gimble-lock that can occur with standard XYZ transformation matrices.  Is there built in functionality for quats or did you write a library for yourself?

Thanks for the code.  I will keep this as a reference.

Kevin





On Mon, Dec 3, 2018 at 3:16 PM berkenb <[hidden email]> wrote:
Your problem appears to be solved, but for what it's worth, I wrote a 'loft'
function a while ago that sweeps the interpolation between two
two-dimensional profiles along a three-dimensional path. It is very similar
to the other 'sweep' libraries mentioned (except mine is poorly documented
and the code probably unreadable, sorry ;-)). The transformations along the
path are computed using quaternions and the usual restrictions apply
(profiles have to be singly-connected and have the same number of points in
them, no self-intersections).
Maybe it is useful to somebody...
Marko

function flatten(vec) = [for (v=vec) for(e=v) e];
function Q_im(q) = [q[1], q[2], q[3]];
function Q_conj(q) = [q[0], -q[1], -q[2], -q[3]];
function Q_mult(q,p) =
[(q[0]*p[0]-q[1]*p[1]-q[2]*p[2]-q[3]*p[3]),(q[1]*p[0]+q[0]*p[1]+q[2]*p[3]-q[3]*p[2]),(q[2]*p[0]+q[0]*p[2]-q[1]*p[3]+q[3]*p[1]),(q[3]*p[0]+q[0]*p[3]+q[1]*p[2]-q[2]*p[1])];                     
function rotQ(q, a, n) = Q_mult(flatten([cos(a/2),n*sin(a/2)]),q);
function poly_rotQ(list, q) = [for (v=list)
Q_im(Q_mult(q,Q_mult([0,v.x,v.y,v.z],Q_conj(q))))];
function poly_rot2d(list, a) = [for (x=list) [cos(a)*x[0]+sin(a)*x[1],
-sin(a)*x[0]+cos(a)*x[1]]];
function poly_translate(list, d) = [for (v=list) v+d];
function interp_lists(l1, w1, l2, w2) = [for (i=[0:len(l1)-1])
w1*l1[i]+w2*l2[i]];


function poly_loft_faces (N_z, N_x, closed=false) = flatten([
     (closed ? ([for (i=[0:N_x-1]) [(N_z-1)*N_x+i, (N_z-1)*N_x+(i+1)%N_x,
i],
       for (i=[0:N_x-1]) [(i+1)%N_x, i, (N_z-1)*N_x+(i+1)%N_x]])
      : concat([[for (i=[0:N_x-1]) N_x-1-i]], [[for (i=[0:N_x-1])
(N_z-1)*N_x+i]])), // caps
       for (i=[0:N_z-2],j=[0:N_x-1]) [[(i+1)*N_x+j, i*N_x+j,
i*N_x+((j+1)%N_x)],[i*N_x+((j+1)%N_x), (i+1)*N_x+((j+1)%N_x),
(i+1)*N_x+j]]]);


// extrude a cross section linearly interpolated between cross sections cr1
and cr2 along path 'path',
// with optional tangential twist linearly increasing along path
module loft (path, cr1, cr2, twist=0) {
  p = flatten([path, [2*path[len(path)-1]-path[len(path)-2]]]);
  pts = flatten([
    for (i=1, d=p[1]-p[0], u=cross([0,0,1], d), un=norm(u), dn=norm(d),
a=asin(un/dn),
         q=un>0?rotQ([1,0,0,0],a,u/un) : [1,0,0,0], n=d/dn, cr=cr1;
         i<len(p);
         d=p[i]-path[i-1], u=cross(n, d), un=norm(u), dn=norm(d),
a=asin(un/dn),
         n=d/dn,q=un>0?rotQ(q,a,u/un):q,
cr=interp_lists(cr1,1-(i-1)/(len(p)-1),cr2,(i-1)/(len(p)-1)), i=i+1)
      poly_translate(poly_rotQ(twist!=0?[for(v=poly_rot2d([for (v=cr)
[v.x,v.y,0]],i*twist/(len(p)-1))) [v.x,v.y,0]]:[for (v=cr) [v.x,v.y,0]], q),
p[i-1])
  ]);
  fcs = poly_loft_faces(len(path), len(cr1));
  polyhedron(pts, fcs, convexity=8);
}

pH = [[-1, 1], [-0.8,1], [-0.8, 0.1], [0.8, 0.1], [0.8, 1], [1, 1],
      [1, -1], [0.8, -1], [0.8, -0.1], [-0.8, -0.1], [-0.8, -1], [-1, -1]];
pH2 = [for (v=pH) 2*v];
phelix = [for (i=[0:6:3*360]) 5*[cos(i), sin(i), i/360]];

loft(phelix, pH, pH2, -170);



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Re: Sweeping polygon over irregular shape?

berkenb
Kevin,

As far as I know, there are no quaternion functions built into the language;
however, they are quite simple to write, in the code I posted there are just
four of them, the three starting with "Q_" and "rotQ". The main reason I use
them is that I seem to be able to better remember them than rotation
matrices.

Marko



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Re: Sweeping polygon over irregular shape?

kdtop
Marko,

So I understand how one can translate the vertices of a polygon in 3D space.   But I am confused about how to make it into a 3D object.  Take for example a square that is going to be swept through space to make a square tube.  How does one figure out how to arrange the points in the resulting faces?

open_scad-1.png

In the example, as the square is swept from P_init to P_final, there should a face using points 1, 1b, 3, 3b.  And another using 1b, 1c, 3b, 3c.  That should be OK to figure out.  But doesn't the ordering of the vertices have to be in a counter-clockwise rotation so that the normal faces outward, and thus has the proper orientation?  Using all those points to build a polygon seem daunting.

Kevin T






On Mon, Dec 3, 2018 at 3:43 PM berkenb <[hidden email]> wrote:
Kevin,

As far as I know, there are no quaternion functions built into the language;
however, they are quite simple to write, in the code I posted there are just
four of them, the three starting with "Q_" and "rotQ". The main reason I use
them is that I seem to be able to better remember them than rotation
matrices.

Marko



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Re: Sweeping polygon over irregular shape?

berkenb
Kevin,

To answer your second question first: you are correct, the ordering of the
polygon points has to conform to the OpenSCAD convention. I should have
mentioned that my function assumes that the points describing the cross
sections (second and third argument to the 'loft()' call)  have to be
correctly ordered for the resulting auto-generated triangles to be oriented
correctly. This is less tricky than it sounds, though - if the order is
wrong (can be seen by rendering in 'Thrown together' mode, for example) the
order simply has to be reversed. This is a manual step, the loft function
will gladly produce an invalid polyhedron.
Also, figuring out the triangulation of the swept walls is actually fairly
straightforward (assuming adjacent polygons are pretty similar), pretty much
exactly what you described in your illustration.

As for your first question: the routine first adds a z-coordinate of 0 to
each 2D polygon point (essentially turning it into a flat polygon in the
x-y-plane);
it then figures out the appropriate rotation of this 3D polygon to orient
its normal axis along a tangent to the path (well, really the direction
between two adjacent, discrete path points) and applies it (step wise along
the path, so that the twist along the path does not develop discontinuities)
- that's the part that uses quaternions, but could equally well be done with
R3 rotation matrices;
finally, each rotated polygon is translated to its appropriate position
along the path.

The rest then is really the answer to your first question, i.e. figuring out
a triangulation for the resulting point cloud.

Hope this helps,
Marko



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Re: Sweeping polygon over irregular shape?

kdtop
It does help. 
Thanks Marko

Kevin

On Mon, Dec 3, 2018 at 6:02 PM berkenb <[hidden email]> wrote:
Kevin,

To answer your second question first: you are correct, the ordering of the
polygon points has to conform to the OpenSCAD convention. I should have
mentioned that my function assumes that the points describing the cross
sections (second and third argument to the 'loft()' call)  have to be
correctly ordered for the resulting auto-generated triangles to be oriented
correctly. This is less tricky than it sounds, though - if the order is
wrong (can be seen by rendering in 'Thrown together' mode, for example) the
order simply has to be reversed. This is a manual step, the loft function
will gladly produce an invalid polyhedron.
Also, figuring out the triangulation of the swept walls is actually fairly
straightforward (assuming adjacent polygons are pretty similar), pretty much
exactly what you described in your illustration.

As for your first question: the routine first adds a z-coordinate of 0 to
each 2D polygon point (essentially turning it into a flat polygon in the
x-y-plane);
it then figures out the appropriate rotation of this 3D polygon to orient
its normal axis along a tangent to the path (well, really the direction
between two adjacent, discrete path points) and applies it (step wise along
the path, so that the twist along the path does not develop discontinuities)
- that's the part that uses quaternions, but could equally well be done with
R3 rotation matrices;
finally, each rotated polygon is translated to its appropriate position
along the path.

The rest then is really the answer to your first question, i.e. figuring out
a triangulation for the resulting point cloud.

Hope this helps,
Marko



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Re: Sweeping polygon over irregular shape?

runsun
In reply to this post by berkenb
wow Marko, this is one of the coolest code I saw in a while !! Thx for
sharing.

btw the name "loft" seems a bit misleading. To my knowledge, "loft" means
(1)sweeping + (2)change of shape (like from square to circle): See :

https://www.cati.com/blog/2012/11/tips-and-tricks-for-using-the-solidworks-loft-feature/
berkenb wrote

> Your problem appears to be solved, but for what it's worth, I wrote a
> 'loft'
> function a while ago that sweeps the interpolation between two
> two-dimensional profiles along a three-dimensional path. It is very
> similar
> to the other 'sweep' libraries mentioned (except mine is poorly documented
> and the code probably unreadable, sorry ;-)). The transformations along
> the
> path are computed using quaternions and the usual restrictions apply
> (profiles have to be singly-connected and have the same number of points
> in
> them, no self-intersections).
> Maybe it is useful to somebody...
> Marko
>
> function flatten(vec) = [for (v=vec) for(e=v) e];
> function Q_im(q) = [q[1], q[2], q[3]];
> function Q_conj(q) = [q[0], -q[1], -q[2], -q[3]];
> function Q_mult(q,p) =
> [(q[0]*p[0]-q[1]*p[1]-q[2]*p[2]-q[3]*p[3]),(q[1]*p[0]+q[0]*p[1]+q[2]*p[3]-q[3]*p[2]),(q[2]*p[0]+q[0]*p[2]-q[1]*p[3]+q[3]*p[1]),(q[3]*p[0]+q[0]*p[3]+q[1]*p[2]-q[2]*p[1])];                      
> function rotQ(q, a, n) = Q_mult(flatten([cos(a/2),n*sin(a/2)]),q);
> function poly_rotQ(list, q) = [for (v=list)
> Q_im(Q_mult(q,Q_mult([0,v.x,v.y,v.z],Q_conj(q))))];
> function poly_rot2d(list, a) = [for (x=list) [cos(a)*x[0]+sin(a)*x[1],
> -sin(a)*x[0]+cos(a)*x[1]]];
> function poly_translate(list, d) = [for (v=list) v+d];
> function interp_lists(l1, w1, l2, w2) = [for (i=[0:len(l1)-1])
> w1*l1[i]+w2*l2[i]];
>
>
> function poly_loft_faces (N_z, N_x, closed=false) = flatten([
>      (closed ? ([for (i=[0:N_x-1]) [(N_z-1)*N_x+i, (N_z-1)*N_x+(i+1)%N_x,
> i],
>        for (i=[0:N_x-1]) [(i+1)%N_x, i, (N_z-1)*N_x+(i+1)%N_x]])
>       : concat([[for (i=[0:N_x-1]) N_x-1-i]], [[for (i=[0:N_x-1])
> (N_z-1)*N_x+i]])), // caps
>        for (i=[0:N_z-2],j=[0:N_x-1]) [[(i+1)*N_x+j, i*N_x+j,
> i*N_x+((j+1)%N_x)],[i*N_x+((j+1)%N_x), (i+1)*N_x+((j+1)%N_x),
> (i+1)*N_x+j]]]);
>
>
> // extrude a cross section linearly interpolated between cross sections
> cr1
> and cr2 along path 'path',
> // with optional tangential twist linearly increasing along path
> module loft (path, cr1, cr2, twist=0) {
>   p = flatten([path, [2*path[len(path)-1]-path[len(path)-2]]]);
>   pts = flatten([
>     for (i=1, d=p[1]-p[0], u=cross([0,0,1], d), un=norm(u), dn=norm(d),
> a=asin(un/dn),
>          q=un>0?rotQ([1,0,0,0],a,u/un) : [1,0,0,0], n=d/dn, cr=cr1;
>          i&lt;len(p);
>          d=p[i]-path[i-1], u=cross(n, d), un=norm(u), dn=norm(d),
> a=asin(un/dn),
>          n=d/dn,q=un&gt;0?rotQ(q,a,u/un):q,
> cr=interp_lists(cr1,1-(i-1)/(len(p)-1),cr2,(i-1)/(len(p)-1)), i=i+1)
>       poly_translate(poly_rotQ(twist!=0?[for(v=poly_rot2d([for (v=cr)
> [v.x,v.y,0]],i*twist/(len(p)-1))) [v.x,v.y,0]]:[for (v=cr) [v.x,v.y,0]],
> q),
> p[i-1])
>   ]);
>   fcs = poly_loft_faces(len(path), len(cr1));
>   polyhedron(pts, fcs, convexity=8);
> }
>
> pH = [[-1, 1], [-0.8,1], [-0.8, 0.1], [0.8, 0.1], [0.8, 1], [1, 1],
>       [1, -1], [0.8, -1], [0.8, -0.1], [-0.8, -0.1], [-0.8, -1], [-1,
> -1]];
> pH2 = [for (v=pH) 2*v];
> phelix = [for (i=[0:6:3*360]) 5*[cos(i), sin(i), i/360]];
>
> loft(phelix, pH, pH2, -170);
>
>
>
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Re: Sweeping polygon over irregular shape?

berkenb
Hi runsun,

Thanks. The code posted does actually linearly interpolate between two
shapes as it sweeps along the path; the 'loft' call requires a path and two
cross sections. My example is a little weak, as it uses the first profile
scaled by a factor of 2 as the second profile, i.e. the effect isn't
terribly obvious...
Try this example (with the same loft function):

pts = 24;
l = 2;
psquare =  [for (i=[0:pts/4-1]) [-l/2, l/2-i/pts*4*l],
   for (i=[pts/4:pts/2-1]) [-l/2+(i-pts/4)/pts*4*l, -l/2],
   for (i=[pts/2:3*pts/4-1]) [l/2, -l/2+(i-pts/2)/pts*4*l],
   for (i=[3*pts/4:pts-1]) [l/2-(i-3*pts/4)/pts*4*l, l/2]
 ];
pcircle = [for (i=[0:pts-1]) [sin(-i*360/pts), cos(-i*360/pts)]];
phelix = [for (i=[0:6:3*360]) 5*[cos(i), sin(i), i/360]];

loft(phelix, pcircle, psquare);

There are probably still a few bugs in the implementation, I haven't used it
too much yet.

Marko



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Re: Sweeping polygon over irregular shape?

kdtop
Marko,

I am getting a syntax error on OpenSCAD version 2015.03-2

I can't figure out what the problem is.  I tried reformatting the code so I could understand it better.  But even before reformatting, it still has the same error.  

Capture.PNG

Any suggestions?

Thanks
Kevin



On Tue, Dec 4, 2018 at 2:11 PM berkenb <[hidden email]> wrote:
Hi runsun,

Thanks. The code posted does actually linearly interpolate between two
shapes as it sweeps along the path; the 'loft' call requires a path and two
cross sections. My example is a little weak, as it uses the first profile
scaled by a factor of 2 as the second profile, i.e. the effect isn't
terribly obvious...
Try this example (with the same loft function):

pts = 24;
l = 2;
psquare =  [for (i=[0:pts/4-1]) [-l/2, l/2-i/pts*4*l],
   for (i=[pts/4:pts/2-1]) [-l/2+(i-pts/4)/pts*4*l, -l/2],
   for (i=[pts/2:3*pts/4-1]) [l/2, -l/2+(i-pts/2)/pts*4*l],
   for (i=[3*pts/4:pts-1]) [l/2-(i-3*pts/4)/pts*4*l, l/2]
 ];
pcircle = [for (i=[0:pts-1]) [sin(-i*360/pts), cos(-i*360/pts)]];
phelix = [for (i=[0:6:3*360]) 5*[cos(i), sin(i), i/360]];

loft(phelix, pcircle, psquare);

There are probably still a few bugs in the implementation, I haven't used it
too much yet.

Marko



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Re: Sweeping polygon over irregular shape?

tp3
On 04.12.18 21:10, Kevin Toppenberg wrote:
> I am getting a syntax error on OpenSCAD version 2015.03-2
>
This syntax with multiple generators is not available in
the 2015.03 release, you will need the dev version for that.

See http://www.openscad.org/downloads.html#snapshots

ciao,
   Torsten.

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Re: Sweeping polygon over irregular shape?

runsun
In reply to this post by berkenb
Thx Marko. It's phenomenal!! So simple and fast.



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12