
123

I want to design a series of vases. Imagine the shape starting at the
bottom as a circle, and as you rise up, the circle gets smaller, then
larger (a neck). But at some point, the circle becomes an ellipse, and
then the orientation of the ellipse changes. So, the cross section
changes in radius, and X and Y scale as you go up. So, I need to
specify those three curves in order to specify the vase.
I thought of creating the curves with Bezier curves inside OpenSCAD, but
most implementations are limited to 4 control points; and working in
OpenSCAD by typing in numbers could be both laborious and nonintuitive.
I thought of creating the curves in InkScape, but 1) I'm not sure how to
move them in to OpenSCAD, and B) the whole thing becomes a bit clunky
(modify the curve in InkScape, Copy [or whatever], Paste into OpenSCAD,
F5, rinse, repeat).
Any suggestions about how to create a workflow that is less painful and
[hopefully] intuitive?
I realize that pieces of this have probably been discussed in the past
Jon

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This is the kind of shape I want to make, only with better control over
the shape It starts out symmetrical, but then the cross section changes
from circular to elliptical. Not very compelling at the moment. I want
to be able to draw a curve for the diameter, x scale, and y scale as a
function of z. And then, of course, I will want curves for x and y
translation. It never ends.
inches = 25.4;
$fn = 200;
module Crosssections(i) {
if (i < 90)
// base and neck
translate([0, 0, i])
cylinder(h = 0.1, d = (3 * cos(4*i) + 6) * inches);
else if (i <= 180)
// transition to ellipse
translate([0, 0, i])
scale([1, 90 / i, 1])
cylinder(h = 0.1, d = 9 * inches);
else if (i < 360)
// transition to other ellipse
translate([0, 0, i])
scale([360 / (2 * i), (180 + i) / 720, 1])
cylinder(h = 0.1, d = 9 * inches);
}
for (i = [1:360])
hull() {
Crosssections(i);
Crosssections(i+1);
}
On 2/15/2018 5:03 PM, jon wrote:
> I want to design a series of vases. Imagine the shape starting at the
> bottom as a circle, and as you rise up, the circle gets smaller, then
> larger (a neck). But at some point, the circle becomes an ellipse,
> and then the orientation of the ellipse changes. So, the cross
> section changes in radius, and X and Y scale as you go up. So, I
> need to specify those three curves in order to specify the vase.
>
> I thought of creating the curves with Bezier curves inside OpenSCAD,
> but most implementations are limited to 4 control points; and working
> in OpenSCAD by typing in numbers could be both laborious and
> nonintuitive.
>
> I thought of creating the curves in InkScape, but 1) I'm not sure how
> to move them in to OpenSCAD, and B) the whole thing becomes a bit
> clunky (modify the curve in InkScape, Copy [or whatever], Paste into
> OpenSCAD, F5, rinse, repeat).
>
> Any suggestions about how to create a workflow that is less painful
> and [hopefully] intuitive?
>
> I realize that pieces of this have probably been discussed in the past
>
> Jon
>

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Hi Jon,
I did this a while back by stacking a bunch of linear_extrude() segments:
The $t stuff was to play with animations to discover fun variants.
SLABS = 30;
HEIGHT = 80;
TWIST = 90*sin(2*$t*360+90);
FREQ=180 + 360*$t;
START=200+4*360*$t;
SCALE=0.3;
IDX=2;
slab(HEIGHT/SLABS, 0, TWIST/SLABS, scale(0), scale(1/SLABS)) cross();
for (i = [0:SLABS1]) {
translate([0,0,i*HEIGHT/SLABS]) {
slab(HEIGHT/SLABS, i*TWIST/SLABS, (i+1)*TWIST/SLABS,
scale(i/SLABS), scale((i+1)/SLABS)) slice();
}
}
module cross() {
minkowski() {
circle(r=3, $fn=16);
union() {
square([10,20], center=true);
square([20,10], center=true);
}
}
}
module slab(h, rot_from, rot_to, scale_from, scale_to) {
linear_extrude(height=h, twist=rot_torot_from, scale=scale_to/scale_from) {
rotate(rot_from)
scale(scale_from)
children();
}
}
function scale(t) = 1+SCALE*(sin(t*FREQ + START)+1);
module slice() {
difference() {
cross();
offset(1) cross();
}
}
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> $fn = 200;
I've never needed such a high setting (especially while developing!)
indeed some of my best pen pots relied on $fn being so small that the
triangulation was a feature of the design...
adding a twist to linear_extrude can make some great effects....
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On 20180216 10:03, Troberg wrote:
> Another way of doing it is stacking cross sections, and then hulling an
> unioning them in sequence.
This will only work if the cross sections are solid, without holes. For
the typical vase it will not be the case, unless you are ok with
creating 2 with slightly different X/Y scaling and subtract one from the
other.
Carsten Arnholm
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I agree. My effort is towards allowing me to specify the cross sections
in a manner that is efficient and intuitive, rather than laborious and
obscure.
On 2/16/2018 4:03 AM, Troberg wrote:

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You may consider using Bezier subdivision as expressed in [1]. That was in principle to generate points in a cubic Bezier curve defined by 4 control points but may be used in a more general setting. If you feed subdivb3() with more than 4 control points, it will generate points of all cubic Bezier arcs defined by
p[3*j]... p[3*(j+1)] for some integer j
To get smooth transition between arcs you will need some conditions on the control points:
p[3*j] is in the segment with extremes p[3*j1] p[3*j+1] for all j>0
An easy way to satisfy this condition is to choose:
p[3*j] = ( p[3*j1] + p[3*j+1] ) / 2
In subdivb3, n is the depth of recursion and should be a low integer.
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> This will only work if the cross sections are solid, without holes. For
> the typical vase it will not be the case, unless you are ok with
> creating 2 with slightly different X/Y scaling and subtract one from the
> other.
How I've done similar tasks:
* Have all the cross sections and make a solid shape by hulling and
unioning.
* Then, take each cross section (except the first, if you want a bottom), do
a negative offset on each, hull and union.
* Make a difference between the first object and the second object.

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On 20180216 13:47, Troberg wrote:
> How I've done similar tasks:
>
> * Have all the cross sections and make a solid shape by hulling and
> unioning.
>
> * Then, take each cross section (except the first, if you want a
> bottom), do
> a negative offset on each, hull and union.
>
> * Make a difference between the first object and the second object.
Yes, I agree this makes sense in many situations.
Carsten Arnholm
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I am happy to create a solid vase and then use my 3D printer to only
print the exterior.
On 2/16/2018 5:59 AM, [hidden email] wrote:
> On 20180216 10:03, Troberg wrote:
>> Another way of doing it is stacking cross sections, and then hulling an
>> unioning them in sequence.
>
> This will only work if the cross sections are solid, without holes.
> For the typical vase it will not be the case, unless you are ok with
> creating 2 with slightly different X/Y scaling and subtract one from
> the other.
>
> Carsten Arnholm
>
> _______________________________________________
> OpenSCAD mailing list
> [hidden email]
> http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org>
>

Sent from my desktop computer.
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(which is a land line).
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Jon,
I think your project is just another example, why a more general interface
for linear_extrude() would make sense. Of course sweep/skin functionality
will also do as it provides the most general interface for extrusions.
To show you some example code I implemented a fast solution on top of my
Naca_sweep library. The general shape results from some fancy vase()
function of z. It uses a translation, a component oriented scaling and some
rotation. You can of course alter it to your needs provided you don't
introduce selfintersection.
vase() is used to define the inner and outer walls. To gain a constant wall
thickness for distorted circles I implemented some sloppy outsetXY()
function which works for wellbehaved polygons, but will fail on zaggy
stuff.
The trajectory climbs up the inner wall (starting with index 1 up to N) and
then down the outer wall (ending with index N) and can be fed into a single
sweep() call.
use <Naca_sweep.scad> // https://www.thingiverse.com/thing:900137$fn=100;
sweep(concat(inner(), outer()));
cube(); // test for manifoldness
function inner(N=100) =
[for(i=[0:N]) vase(i)] ;
function outer(N=100) =
[for(i=[N:1:1]) outsetXY(vase(i), 2)];
function vase(i) = //
Rz_(i*i/30, // rotate polygon
(Tz_(pow(i, 2)/100, // translate polygon
S_(cos(i)+3, sin(4*i)+3,1, // scale polygon
vec3D(circle()))))); // polygon
function circle(r=10, d = undef, N=$fn?$fn:360/$fa) =
let(r_ = d==undef?r:d/2) [for(i=[0:N1]) r_*[cos(360/N*i), sin(360/N*i)]];
function outsetXY(P, d=10) = [for(i=[0:len(P)1])
let(p=P[i]P[(i+1)%len(P)])
let(p_ = p/norm([p.x, p.y]))
P[i]+d*[p_[1], p_[0], 0] ];

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I have to correct my code to better match my explanation. Sorry for that.
renamed outsetXY() into insetXY() as it does an inset, and inner() and
outer() are reversed.
< http://forum.openscad.org/file/t887/vase.png>
use <Naca_sweep.scad>
$fn=100;
sweep(concat(outer(), inner()));
cube(); // test for manifoldness
function outer(N=100) =
[for(i=[0:N]) vase(i)] ;
function inner(N=100) =
[for(i=[N:1:1]) insetXY(vase(i), 3)];
function vase(i) = //
Rz_(i*i/30, // rotate polygon
(Tz_(pow(i, 2)/100, // translate polygon
S_(cos(i)+3, sin(4*i)+3,1, // scale polygon
vec3D(circle()))))); // polygon
function circle(r=10, d = undef, N=$fn?$fn:360/$fa) =
let(r_ = d==undef?r:d/2) [for(i=[0:N1]) r_*[cos(360/N*i), sin(360/N*i)]];
function insetXY(P, d=10) = [for(i=[0:len(P)1])
let(p=P[i]P[(i+1)%len(P)])
let(p_ = p/norm([p.x, p.y]))
P[i]+d*[p_[1], p_[0], 0] ];

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The terseness of your code always astonishes me. That said, what is
missing is a way to control the shape easily or intuitively. I do not
want to limit my shapes to those that can be calculated with a few
sin/cos variants. This is why I was heading towards using a series of
smoothed curves to specify scaling, translation, and rotation. You have
shown how I could use those scaling, translation, and rotation values if
I could calculate them as a function of Z. What remains is a way to
control these things "easily". Intuitively? Quickly?
Note that there is no need to create the walls (create a hollow
container) since I can use a slicer to accomplish that.
Jon
On 2/16/2018 9:14 AM, Parkinbot wrote:
> use <Naca_sweep.scad> // https://www.thingiverse.com/thing:900137>
> $fn=100;
> sweep(concat(inner(), outer()));
> cube(); // test for manifoldness
>
> function inner(N=100) =
> [for(i=[0:N]) vase(i)] ;
>
> function outer(N=100) =
> [for(i=[N:1:1]) outsetXY(vase(i), 2)];
>
> function vase(i) = //
> Rz_(i*i/30, // rotate polygon
> (Tz_(pow(i, 2)/100, // translate polygon
> S_(cos(i)+3, sin(4*i)+3,1, // scale polygon
> vec3D(circle()))))); // polygon
>
> function circle(r=10, d = undef, N=$fn?$fn:360/$fa) =
> let(r_ = d==undef?r:d/2) [for(i=[0:N1]) r_*[cos(360/N*i), sin(360/N*i)]];
>
> function outsetXY(P, d=10) = [for(i=[0:len(P)1])
> let(p=P[i]P[(i+1)%len(P)])
> let(p_ = p/norm([p.x, p.y]))
> P[i]+d*[p_[1], p_[0], 0] ];
>

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On 15/02/18 22:03, jon wrote:
I
thought of creating the curves with Bezier curves inside OpenSCAD,
but most implementations are limited to 4 control points; and
working in OpenSCAD by typing in numbers could be both laborious
and nonintuitive.
I've been designing
a load of teapots and using splines to go from a few control
points that I create to something smooth. For the bodies, I
often just change diameter, but for the handles, I place
circles in space and change both size and angle. Changing how
elliptical would be very easy.
See code here for an
example.
https://www.thingiverse.com/thing:2590534
Add "HData =
HControl;
" after the assignment of hdata to see the control
points  I tend to comment such a line in and out when moving
control points to aid placement.
Sorry it's not
intuitive and graphical, but I've been happy with the results.
Links to required
libraries are at the top of the file.
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123
