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.

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 self-intersection.
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 well-behaved 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_(ii/30,    // rotate polygon
(Tz_(pow(i, 2)/100,  // translate polygon
S_(cos(i)+3, sin(4i)+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:N-1]) r_[cos(-360/Ni), 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_(ii/30,    // rotate polygon
(Tz_(pow(i, 2)/100,  // translate polygon
S_(cos(i)+3, sin(4i)+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:N-1]) r_[cos(-360/Ni), 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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As I wrote, it is up to you to define or configure the vase() function to fit
your needs. You can define it piecewise, or use any other given or
user-defined functions and shapes. However, OpenSCAD demands you to use Math
to describe it :-) I guess, this is the non-intuitive part you plan to
avoid. Can't help you there, as it is intuitive for me.

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