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 non-intuitive.

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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How do you feel about creating the curves of the cross section along the
Z-axis and performing a rotate_extrude?

You get the fine detail control of Inkscape and very little code in
OpenSCAD.

https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/2D_to_3D_Extrusion#Rotate_Extrude

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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 = 90sin(2$t360+90);
FREQ=180 + 360$t;
START=200+4360$t;
SCALE=0.3;
IDX=2;

slab(HEIGHT/SLABS, 0, TWIST/SLABS, scale(0), scale(1/SLABS)) cross();
for (i = [0:SLABS-1]) {
translate([0,0,iHEIGHT/SLABS]) {
slab(HEIGHT/SLABS, iTWIST/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_to-rot_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();
}
}

Another way of doing it is stacking cross sections, and then hulling an
unioning them in sequence.

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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[3j]... p[3(j+1)] for some integer j

To get smooth transition between arcs you will need some conditions on the
control points:

p[3j] is in the segment with extremes
p[3j-1] p[3*j+1] for all j>0

An easy way to satisfy this condition is to choose:

p[3j] = ( p[3j-1] + p[3*j+1] )  / 2

In subdivb3, n is the depth of recursion and should be a low integer.

[1] http://forum.openscad.org/OpenSCAD-programming-question-
recursion-functions-and-modules-tp23197p23217.html

Em 15 de fev de 2018 8:04 PM, "jon" jon@jonbondy.com escreveu:

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 non-intuitive.